School of Physics & Astronomy

Find a PhD Project Here

Opportunities for fully funded PhD or EngDoc research projects are available in all fields of research within the School. You may search for current projects on this page. APPLY HERE for a PhD Place.

 PhD in Photonics
 PhD in Condensed Matter
 PhD in Astrophysics

Search current PhD opportunities in the School of Physics & Astronomy:-




Condensed Matter

Coexistence or Competition: Resolving the phase diagram of unconventional superconductors through atomic scale imaging of emergent phases
Wahl, Prof Peter - gpw2@st-andrews.ac.uk

In many unconventional superconductors, magnetism and superconductivity occur in close proximity to each other - which is surprising given that they are usually considered mutually exclusive properties of a material. This is also true for the iron pnictide superconductors, where in several materials magnetism and superconductivity appear to coexist from macroscopic measurements. In this project, you will take an atomic scale view at the magnetic order and the superconducting properties using low temperature spin-polarized scanning tunneling microscopy[1]. Combining images of the magnetic order with a characterization of superconductivity from tunneling spectroscopy will allow to establish whether magnetism and superconductivity coexist microscopically, or whether they are really competing. These results provide important benchmarks for theory, and may help to establish an understanding of superconductivity in these materials.

You will be using bespoke low temperature scanning tunneling microscopes, which are installed in a new ultra-low-vibration facility at the University of St Andrews.

[1] Enayat et al., Science 345, 653 (2014).
Quantum Critical Points in Ferroelectrics
Scott, Prof Jim - jfs4@st-andrews.ac.uk

When crystals undergo phase transitions at or near zero degrees Kelvin their dynamics differ from those at higher temperatures. Entropy is still involved but arises from quantum mechanical uncertainty, rather than classical effects; this mixes together spatial and temporal fluctuations. Most systems studied thus far involve ferromagnetism or superconductivity, but some work [1,2] has been done by Scott on ferroelectrics. In a pseudo-cubic structure such as SrTiO3 or KTaO3 the main effect is that the isothermal electric susceptibility (dielectric constant) varies as 1/T-squared, rather than the classic Curie-Weiss 1/T, and the effective dimensionality is d+1 = 4. But in highly uniaxial materials, the effective dimensionality is d+1 = 5, which results in the dielectric constant varying exactly as 1/T-cubed [3].

We have recently demonstrated that in the uniaxial materials BaFe12O19, SrFe12O19, and PbFe(12-x)Ga(x)O3. The Ba-isomorph is the most profitable magnetic material in Nature, with £2 billion in sales every year (a few grams for every person on Earth!), primarily as the magnetic stripe material for credit cards. Therefore, although this project is unapplied, it is related to device materials of great commercial interest.

[1] S. E. Rowley et al., Nature Physics (2014)
[2] S. E. Rowley et al., arXiv condmat (2014)
[3] D. Khmelnitskii, JETP Lett. (2014)

The thesis work will not involve growing crystals (they are already in hand) nor building a lab; most of the kit is already operational in Dr. F. Morrison's lab in the School of Chemistry. However, a relatively sophisticated level of data analysis and modelling will be encouraged. Therefore although the project is experimental, students with a high level of interest in theory might find it attractive.

It is probable that summer salary would be available for a PhD student wishing to begin in June or July.
Room-temperature Multiferroics
Scott, Prof Jim - jfs4@st-andrews.ac.uk

Multiferroics are usually defined as crystals that are simultaneously ferromagnetic and ferroelectric. Most are also magnetoelectric, meaning that their magnetization M can be switched by applied electric field and their polarization P switched via applied magnetic field H.

This PhD thesis project will emphasize the materials GaFeO3 and its isomorphs, as well as PbFe(1/2)Nb(1/2)O3 and related Ta, Ti, and Nb compounds.

The thesis work will not involve growing crystals (they are already in hand) nor building a lab; most of the kit is already operational in Dr. F. Morrison's lab in the School of Chemistry. However, a rewlatively sophisticated level of data analysis and modelling will be encouraged. Therefore although the project is experimental, students with a high level of interest in theory might find it attractive.

It is probable that summer salary would be available for a PhD student wishing to begin in June or July.
Superconductivity in Non-Centrosymmetric Materials and Structures
Wahl, Prof Peter - gpw2@st-andrews.ac.uk

The aim of this project is to investigate experimentally the influence of broken inversion symmetry on superconductivity in a variety of non-centrosymmetric (NCS) materials.
Most crystalline metals have a structure that maps onto itself exactly under inversion of spatial coordinates. Such materials are termed “centrosymmetric” and when they become superconducting, the spatial part of the Cooper pair wavefunction must have a definite parity, i.e. inversion simply multiplies it by ±1. This imposes restrictions also on the spin configuration within the Cooper pair. By contrast, in non-centrosymmetric superconductors where the crystal structure breaks inversion symmetry, such restrictions do not apply. Amongst the properties predicted for non-centrosymmetric superconductors are mixed spin-singlet/spin-triplet pairing, enhanced critical fields and spatially modulated superconducting states. Whilst unusual superconducting properties have been detected in a number of NCS materials, there is relatively little firm experimental evidence linking these to the lack of inversion symmetry; for example only in very few cases has a substantial triplet component of the order parameter been firmly established.
The project will be focused on NCS superconductors where the electronic correlations are weak, since these offer the chance to isolate the role of the broken inversion symmetry. The experiments will focus on using low temperature scanning tunneling microscopy and spectroscopy to establish the structure of the superconducting order parameter and study the influence of defects of different dimensionalities on the superconducting properties.
2D Quantum Materials
King, Prof Phil - pdk6@st-andrews.ac.uk

As part of a generously-funded research project from the Leverhulme Trust, we are seeking ambitious and motivated PhD students to join a major research initiative aimed at investigating the electronic structure and collective states of two-dimensional quantum materials. The remarkable properties of graphene, a single atom-thick layer of carbon, has spurred enormous interest in 2D materials. In this project, you will seek to develop 2D material systems which incorporate the effects of pronounced electronic interactions, focusing on transition-metal dichalcogenide (TMD) compounds. Bulk TMDs are known to support a wide variety of striking physical properties such as superconductivity and charge density-wave states, but how these are modified when the material is restricted to just a single layer in thickness are only starting to be explored. Combining strongly-interacting 2D materials in different configurations and environments promises a huge array of exciting possibilities to stabilise rich phase diagrams and unique properties. The work undertaken will build on the group’s existing activity in the study of bulk and monolayer TMDs [e.g. 1-5], and ultimately aims to develop new routes towards the “on-demand” control of the quantum many-body system underpinning the physical properties of 2D quantum materials. Projects are available developing the growth of single monolayers and heterostructures of TMD compounds using a recently-installed state-of-the art molecular-beam epitaxy system in St Andrews and utilizing a linked system for angle-resolved photoemission spectroscopy, as well as further ARPES and spin-resolved ARPES work at international synchrotrons, to probe the resulting electronic structure and many-body interactions of the materials synthesized. There are also possibilities to spend extended research visits with our collaborators in Tokyo and in Italy. As part of this project, you will undertake experiments at national and international facilities. Thus, a willingness to travel is an essential prerequisite. For further information, or to discuss specific research possibilities, please contact philip.king@st-andrews.ac.uk.

[1] Riley et al., Nature Physics 10 (2014) 835
[2] Riley et al., Nature Nano. 10 (2015) 1043
[3] Bawden et al., Nature Commun. 7 (2015) 11711
[4] Bahramy, Clark et al., Nature Materials, 17 (2018) 21
[5] Feng et al., Nano Lett. 18 (2018) 4493
Ambient pressure photoemission spectroscopy of organic semiconductor devices
Turnbull, Prof Graham - gat@st-andrews.ac.uk

Ambient pressure photoemission spectroscopy is a new technique to measure the energy levels of materials. Combined with scanning Kelvin probe spectroscopy APS can provide information about the electronic properties of thin film materials relevant to LEDs, solar cells, sensors and lasers. The aim of this project will be to combine measurements of the energy levels of organic semiconductors to understand their operation in optoelectronic devices.

The HOMO and LUMO levels of organic semiconductors are crucial to charge injection, exciton formation, energy transfer and charge transfer in OLEDs, solar cells, lasers and chemical sensors. Currently the standard measurement to determine energy levels is cyclic voltammetry but this is typically used to measure individual molecules in solution, and there would be a lot of advantage if we could measure directly the materials int he solid-state including thin films as used in devices.

Applications of these measurements would be to better understand the operation of solar cells, OLEDs and thin film chemical sensors.
Artificial quantum materials
King, Prof Phil - pdk6@st-andrews.ac.uk
Wahl, Prof Peter - gpw2@st-andrews.ac.uk

The epitaxial compatibility of many oxides which, in bulk form, host an extraordinarily wide array of physical properties opens almost limitless possibilities for creating new artificial materials structured at the atomic scale [1]. Recent advances in atomically-precise deposition techniques have opened new potential to manipulate the properties of these ubiquitous but still poorly-understood materials [2], creating new "designer" compounds with tailored properties not found in bulk. You will exploit a brand new £1.8M growth facility to build up transition-metal oxide materials one atomic layer at a time, exploiting tuning parameters such as epitaxial strain and the layering of disparate compounds to selectively tune their functional properties. To provide direct feedback on how this influences the underlying quantum states in these complex materials, you will employ advanced spectroscopic probes such as angle-resolved photoemission [3] or scanning tunneling microscopy and spectroscopy [4], utilizing our state-of-the-art capabilities in St Andrews. Together, this promises new insight into the rational design of quantum materials and their potential for future quantum technologies.

[1] J. Mannhart and D. Schlom, Science 327, 1607 (2010).
[2] P.D.C. King et al., Nature Nano. 9, 443 (2014).
[3] V. Sunko et al., Nature 549, 492 (2017).
[4] M. Enayat et al., Science 345, 653 (2014).
Artificial Quantum Materials - Thermodynamics And Transport
Rost, Dr Andreas - ar35@st-andrews.ac.uk

Artificial designer heterostructures of correlated electron systems open up a wide range of exciting possibilities for the creation of new materials. The atomic-layer-by-atomic-layer deposition now achievable in thin films gives a unique potential to manipulate the properties of this still poorly explored new class of materials, ultimately allowing the creation of new phases with properties difficult to attain in bulk compounds [1]. St Andrews has recently opened a new dedicated MBE growth facility with the aim of exploiting the possibilities of such tailored materials.

This new class of materials, however, poses a key challenge to experimentalists interested in such basic thermodynamic properties as specific heat and magnetisation. The extremely low ‘thermal mass’ of such materials compared to bulk systems ultimately requires the development of a new bespoke set of experimental tools for measurement. To bring the paradigm of such fundamental thermodynamic measurements to nanoscale thin films is the key aim of a new research program established at the University of St Andrews of which you will be a key member. During your PhD you will contribute to the development of these new tools with the aim to applying them to the study of designer quantum materials spanning phenomena such as superconductivity, novel (topological) Dirac- and Weyl- systems and (quantum) spin liquids.

[1] J. Mannhart and D. Schlom, Science 327, 1607 (2010).
Atomic-scale imaging of complex magnetic orders in quantum materials
Wahl, Prof Peter - gpw2@st-andrews.ac.uk

Many quantum materials exhibit complex magnetic orders, which often are sensitive to external stimuli, such as magnetic field or doping, making them in principle interesting for many technological applications. Characterization of the spatial structure of the magnetic order has mostly been done through Neutron scattering, which however average over a macroscopic sample volume. Spin-polarized scanning tunneling microscope provides real space images of magnetic order at the atomic scale, thereby providing new insights into the spatial structure of the complex magnetic orders. In this project, you will use low temperature scanning tunneling microscopy in a vector magnetic field to characterize the magnetic structure of quantum materials. The studies will aim to establish the surface impact on the magnetic order, knowledge which is critical for technological exploitation and interfacing to other materials, but also to provide a microscopic picture of the magnetic order which will help to identify the dominant contributions to the magnetic interactions in the material. We are in particular interested in metamagnetic phases, where the external magnetic fields can drive phase transitions in the material.

You will be using bespoke low temperature scanning tunneling microscopes, which are installed in a new ultra-low-vibration facility at the University of St Andrews.

[1] Enayat et al., Science 345, 653 (2014).
[2] Singh et al., Phys. Rev. B 91, 161111 (2015).
[3] Trainer, et al., Rev. Sci. Instr. 88, 093705 (2017).
Controlling emergent quantum phases through strain-tuning of electronic structure
Hicks , Dr Clifford - cwh10@st-andrews.ac.uk
King, Prof Phil - pdk6@st-andrews.ac.uk
Mackenzie, Prof Andy - apm9@st-andrews.ac.uk

The strong interactions at the heart of correlated electron materials yield striking collective states such as superconductivity or magnetism, and often mediate giant responses to small external perturbations. This offers unique opportunities to tune these subtle quantum many-body systems, to shed new light on their underlying physics and ultimately to engineer desired functional properties. In this project, you will exploit externally-applied and continuously-tunable mechanical strain in an attempt to harness control over emergent phases in correlated solids, for example tuning unconventional superconductivity in Sr2RuO4 and controlling quantum criticality in Sr3Ru2O7. You will perform low-temperature transport measurements as a function of uni- and bi-axial strain using custom apparatus within the world-leading facilities of the Max-Planck Institute for the Chemical Physics of Solids in Dresden, Germany. You will also design similar apparatus that can be integrated within our state-of-the-art system for angle-resolved photoemission (ARPES) in St Andrews, as well as in ARPES systems at synchrotron light sources. This will allow you to track the corresponding electronic structure changes that control the materials’ transport and thermodynamic properties with unprecedented detail. This project is offered as part of a Max Planck – CM-DTC initiative (http://cm-dtc.supa.ac.uk/research/max%20planck.php). You will spend part of your time performing research in MPI Dresden (with Dr. Hicks & Prof. Mackenzie), part in St Andrews (with Prof. King), and will also undertake experiments at national and international facilities. Thus, a willingness to travel is an essential prerequisite.
Dynamical Coulomb blockade in arbitrary environments with backaction
Braunecker, Dr Bernd - bhb@st-andrews.ac.uk

The electron transport through nanostructures is always exposed to the electromagnetic fluctuations of the environment. This is a notable and measurable effect in quantum-coherent conductors, in which the motion of a single electron excites nearby electromagnetic modes which in turn act back on the electrons and cause a nonlinear reduction of the conductance. For weakly transmitting conductors this physics is known as environmental Coulomb blockade and well explained by the “P(E) theory” [1]. But this theory does not extend to highly transmitting conductors in which the transmission time becomes comparable with the environment's reaction time. This regime, the dynamical Coulomb blockade regime, requires to model the environment as a quantum object. For specific conditions important advances have been made over the last few years [2]. But recent experimental work has shown that there is still much unknown in the regime of strong backaction of an arbitrary environment [3]. In this PhD project we will access this physics head-on and derive a modelling of the full counting statistics, which gives access to all current correlators, of a mesoscopic electron system coupled to an arbitrary dynamical quantum enviroment. We will focus on an analytical, non-perturbative many-body modelling of the phenomenon, involving bosonisation similar to [4] and further mappings on scattering type boundary value problems that can be solved with recently developed techniques [5].

[1] G.-L. Ingold and Y. Nazarov, in Single Charge Tunneling ed. by H. Grabert and M. H. Devoret, Ch. 2 (Plenum, 1992).
[2] K. A. Matveev, D. Yue and L. I. Glazman, Phys. Rev. Lett. 71, 3351 (1993); L. W. K. Molenkamp, Flensberg and M. Kemerink, Phys. Rev. Lett. 75, 4282 (1995). Y. V. Nazarov, Phys. Rev. Lett. 82, 1245 (1999); M. Kindermann and Y. V. Nazarov, Phys. Rev. Lett. 91, 136802 (2003); I. Safi and H. Saleur, Phys. Rev. Lett. 93, 126602 (2004); D. S. Golubev, A. V., Galaktionov and A. D. Zaikin, Phys. Rev. B 72, 205417 (2005).
[3] F. D. Parmentier, A. Anthore, S. Jezouin, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly
and F. Pierre, Nat. Phys. 7, 935 (2011).
[4] J.-R. Souquet, I. Safi, and P. Simon, Phys. Rev. B 88, 205419 (2013).
[5] B. A. Muzykantskii and Y. Adamov, Phys. Rev. B 68, 155304 (2003); B. Muzykantskii, N. d'Ambrumenil, and B. Braunecker, Phys. Rev. Lett. 91, 266602 (2003); J. Zhang, Y. Sherkunov, N. d'Ambrumenil, and B. Muzykantskii, Phys. Rev. B 80, 245308 (2009); B. Braunecker, Phys. Rev. B. 73, 075122 (2006).
Electron transport through molecules: A new kind of open quantum system theory (with Dr Erik Gauger, Heriot Watt)
Lovett, Dr Brendon - bwl4@st-andrews.ac.uk

Controlling how electrons flow through molecular structures is key to designing future miniaturised electronic components [1]. Understanding and manipulating such charge transport is a very challenging problem at this nanoscopic scale, especially in the common situation of strong interactions between the charges carriers and the vibrational mode structure of the environment [2]. In this project, you will develop such an understanding using advanced techniques for simulating open quantum systems.

We have recently developed a groundbreaking new theoretical method [3] which relies on a combination of Feynman path integrals and matrix product states, and which opens up the possibility of a multitude of new calculations. The tool that you will develop will be a significant adaptation of this new method, and will describe any quantum problem in which a small system is coupled to both bosonic and fermionic environments.

We hope to reveal new insights into how electron currents in molecules behave, and this will allow us to design new molecular devices that exploit quantum coherence.

[1] S. V. Aradhya and L. Venkataraman, Nat. Nanotechnol. 8 399 (2013).
[2] J. Sowa, J. A. Mol, G. A. D. Briggs, and E. M. Gauger, The Journal of Chemical Physics 149 in press (2018); arXiv:1807.08502
[3] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett. , Nature Communications 9 3322 (2018)
Emergent Order in Hybrid Photon-Atom Systems
Braunecker, Dr Bernd - bhb@st-andrews.ac.uk

Novel self-ordered phases can emerge in a conductor with interacting electrons and embedded magnetic moments [1,2]. This is quite surprising because the energy and time scales of the considered magnetic moments (e.g., nuclear spins) differ by orders of magnitude from those of electrons. Yet, within this decoupling of scales, the ordering mechanism is general and not bound to specific materials. Quite remarkably such self-ordered phases have made recently a strong link with the currently much discussed physics of topological superconductors and Majorana bound states [3].

In this PhD project, we shall explore systems in which the time and energy scales are turned upside down, notably, in which the effective interaction that triggers the order travels at a turtle's pace. This is an extreme limit in which this slow dynamics will play a further important role. For a definite example we will focus on cavity photons that are coupled through an interacting atomic gas, which is of the type of systems that are under investigation, for instance, in the group of Prof Jon Simon at the University of Chicago (http://simonlab.uchicago.edu).

[1] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. Lett. 102, 116403 (2009) [arXiv:0808.1685].
[2] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. B 80, 165119 (2009) [arXiv:0908.0904].
[3] B. Braunecker and P. Simon, Phys. Rev. Lett. 111, 147202 (2013) [arXiv:1307.2431].
Engineering non-equilibrium material states with cold atoms in optical cavities
Keeling, Dr Jonathan - jmjk@st-andrews.ac.uk

A triumph of 20th century condensed matter physics is the understanding of the phases of matter, arising from interacting many body problems in thermal equilibrium. However, not all matter is in equilibrium, and the understanding of matter out of equilibrium is far less developed. To develop our understanding of this, it is necessary both to develop new theoretical techniques, and to identify clean experimental systems where these approaches can be tested against known problems.

Ultracold atoms have provided an excellent testbed for simulating canonical models in equilibrium, and can be adapted to probe non-equilibrium physics. In particular, ultracold atoms placed in optical cavities can be used to prepare and control non-equilibrium states of matter. Specifically, these experiments involve driving by scattering a pump laser into the optical cavity, leading to cavity mediated interactions between atoms, accompanied with collective dissipation processes. While experiments on atoms single mode cavities have been studied extensively, experiments on multimode cavities are only just beginning. These have the potential to transform the kinds of behaviour one can study.

Our theoretical group collaborates closely with the experimental group of Benjamin Lev (Stanford) who have built a multimode optical cavity[1,2], and are now in the position to use this to explore novel states of matter. Several ideas in this direction have been proposed[3,4,5], including liquid crystaline phases of matter[3], spin glass states [4] and Hopfiled associative memories[5]. However, understanding of the non-equilibrium nature of these phases is yet unclear.

This PhD will explore a number of these topics; we will work in close collaboration with the Lev group in Stanford, so the precise projects will be determined in order to match ongoing and future experiments. We will make use of a variety of analytical and numerical techniques, potentially including matrix product state calculations.



[1] "Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED", V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballantine, A. J. Kollár, J. Keeling, and B. L. Lev, Phys. Rev. X 8 011002 (2018)
[2] "Sinor self-ordering of a quantum gas in a cavity." R. M. Kroeze, Y. Guo, V. D. Vaidya, J. Keeling, B. L. Lev arXiv:1807.04915
[3] "Emergent Crystallinity and Frustration with Bose-Einstein Condensates in Multimode Cavities", S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Nat. Phys. 5, 845 (2009).
[4] "Frustration and Glassiness in Spin Models with Cavity-Mediated Interactions." S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Phys. Rev. Lett. 107, 277201 (2011).
[5] "Exploring Models of Associative Memory via Cavity Quantum Electrodynamics", S. Gopalakrishnan, B. L. Lev, and P. M. Goldbart, Philos. Mag. 92, 353 (2012).
Exciton Diffusion in Organic Semiconductors
Samuel, Prof Ifor - idws@st-andrews.ac.uk

The discovery of semiconducting properties in organic materials has opened major new directions in semiconductor physics. Organic semiconductors combine the simple fabrication and tuning of properties that is typical of plastics with novel optoelectronic properties useful for devices such as light-emitting diodes and solar cells. The low-dimensional nature of these materials means that excitons (electron-hole pairs) are strongly bound even at room temperature and play a very important role in their physics. Whilst charge transport has been widely studied, exciton transport has been largely overlooked. We have now developed techniques based on time-resolved spectroscopy that allow the measurement of exciton diffusion. We now wish to apply them to understand the physics of exciton diffusion and the factors controlling it. A breakthrough in this field could in turn lead to a breakthrough in the efficiency of organic solar cells.
Experimental and Theoretical Investigation of Spatially Modulated Magnetic Phases Near to Quantum Criticality
Huxley, Prof Andrew - ah311@st-andrews.ac.uk

The possibility of magnetic spin-crystals formed by the superposition of helical spin modulations with different wave-vectors has been a subject of much recent experimental and theoretical work. Signatures of phases with this property have been found in an array of materials including MnSi and Sr3Ru2O7. On the theoretical side, there are several ways in which such states might form. These include the formation of spiral modulation due to a Dzyalosinskii-Moriya spin-orbit interaction in itinerant magnets, residual, small-wavevector nesting due to the electron dispersion in a lattice [1,2] and from competing interactions that can give rise to a series of transitions forming a Devil's Staircase [3]. Perhaps the most intriguing suggestion - and one that has most captured the imagination of condensed matter theorists of late - is that an itinerant system on the brink of a quantum phase transition might possess an intrinsic instability to the formation of modulated magnetic phases [4]. In any particular material, one or more of these effects may operate with the possibility of a complicated interplay between them.

This project aims to investigate the phenomenon of spatially modulated magnetism from both an experimental and theoretical perspective. We will use techniques of quantum many-body physics and field theory to investigate the possibility of spatially modulated magnetism in real systems. These investigations will be carried out in concert with neutron scattering experiments to provide inspiration for and validate this theory. The experimental part will include growing the crystals for these experiments as well as performing the measurements. We anticipate that a student will spend approximately 2/3 of their time on theory and 1/3 on experimental work, working both in Edinburgh and St Andrews as well as at international facilities.

[1] A. M. Berridge, A. G. Green, S. A. Grigera and B. D. Simons "A Magnetic Analogue of the of the FFLO state: Inhomogeneous Instabilities Near to Tricritical Points" Physical Review Letters 102, 149903 (2009).
[2] G. J. Conduit, A. G. Green, and B. D. Simons, "Inhomogeneous phase formation on the border of itinerant ferromagnetism" Physical Review Letters 103, 207201 (2009) [spotlighted in Physics 2, 93 (2009)]
[3] P. Bak & J. von Boehm, "Ising model with solitons, phasons, and 'the devil's staircase'", Phys Rev B 21 5297 (1980)
[4] J. Rech C.Pépin, V.Chubukov, "Quantum critical behaviour in intinerant electron systems: Eliashberg theory and instability of a ferromagentic quantum critical point" Phys Rev B 74 195126 (2006)
Fidelity plateaux from correlated noise: beyond the two-state case
Hooley, Dr Chris - cah19@st-andrews.ac.uk

When disorder is studied in the solid state, it is usually considered to be independent of time, and to affect only one parameter of the Hamiltonian (e.g. the on-site energy or the nearest-neighbour hopping amplitude). In the cold-atom context, neither of these assumptions is likely to hold. Disorder will generally be time-dependent, arising for example from the failure of the laser controller to achieve some desired ramp profile. It will also generally appear in a correlated way in multiple parameters of the Hamiltonian.

CM-CDT student Scott Taylor and I have recently shown [1] that this leads to a striking effect, viz. the occurrence of arbitrarily long plateaux in the state-preparation fidelity. However, our work so far has dealt only with the simplest case of a driven two-level system.

The aim of this project is to study the effects of correlated time-dependent disorder in a broader range of Hamiltonians, especially those with a Hilbert space of dimension greater than two. In particular, it aims to connect the abovementioned observation with the phenomenon of many-body localisation [2] and the new phases of matter possible in driven non-equilibrium quantum systems [3].
[1] S.R. Taylor and C.A. Hooley, arXiv:1711.05131 (2017).
[2] R. Nandkishore and D.A. Huse, Annu. Rev. Cond. Matt. Phys. 6, 15 (2015).
[3] F. Harper and R. Roy, Phys. Rev. Lett. 118, 115301 (2017).

Category: Theoretical Hard Condensed Matter
Finite-temperature behaviour of quantum Kasteleyn systems
Hooley, Dr Chris - cah19@st-andrews.ac.uk

Recent work on the so-called ‘spin ice’ materials [1] has produced a resurgence of interest in Kasteleyn transitions [2]. In a typical demagnetisation transition, the magnetism of a sample is reduced by the formation of local domains of flipped spins. In a Kasteleyn transition, however, these are effectively forbidden, and the transition is driven instead by the appearance of lines of flipped spins that extend all the way from one side of the sample to the other.
The standard theory of these transitions is purely classical, with the transition being driven by increasing temperature. But it is interesting to ask whether there is a quantum version of such a transition, driven by (for example) a transverse magnetic field [3]. If so, it should give rise to interesting finite-temperature phenomena: the Kasteleyn analogues of the quantum criticality observed in the conventional case [4].

The initial goal of this project is to determine whether a quantum Kasteleyn transition exists in a particular toy model [3], and then to develop a theory of the finite-temperature behaviour of the model in the vicinity of the quantum Kasteleyn point.

[1] C. Castelnovo, R. Moessner, and S.L. Sondhi, Nature 451, 42 (2008).
[2] L.D.C. Jaubert, J.T. Chalker, P.C.W. Holdsworth, and R. Moessner, Phys. Rev. Lett. 100, 067207 (2008).
[3] S.A. Grigera and C.A. Hooley, arXiv:1607.04657.
[4] S. Chakravarty, B.I. Halperin, and D.R. Nelson, Phys. Rev. B 39, 2344 (1989).

Category: Theoretical Hard Condensed Matter
Giant Rydberg polaritons
Ohadi, Dr Hamid - ho35@st-andrews.ac.uk

Exploiting the laws of quantum mechanics for the benefit of humanity in the so-called "second quantum revolution" is one of the greatest challenges of the 21st century. For this we need to efficiently produce particles, control their states, detect them and make them interact strongly at the single-particle level. Photons, the quantum particles of light, are one of the most promising candidates. We can easily detect and control their states and we can efficiently produce them individually. However, making them interact strongly to build a large quantum network is a notoriously difficult task because photons do not interact at low energies. To make them interact indirectly, one can hybridise them with other massive particles that strongly interact and form quasiparticles called 'polaritons'.

In this project, we aim to hybridise photons with Rydberg excitons [1]. Rydberg excitons are highly excited (principal quantum number n~20) electron-hole pairs that can span macroscopic dimensions. Because of their macroscopic dimensions they strongly repel. The semiconductor device that we have chosen for hybridisation is a 2-dimensional semiconductor microcavity formed by two highly reflective mirrors encapsulating a cuprous oxide microcrystals and thin film. Photons confined in the microcavity strongly couple to Rydberg excitons in cuprous oxide to form Rydberg polaritons. This will allow us to explore quantum optics at the single-particle limit and form 2-dimensional networks of strongly correlated photons for future quantum simulators.


[1] Kazimierczuk et al, Nature 514, 343 (2014).
High speed spintronics using room-temperature polariton condensates
Ohadi, Dr Hamid - ho35@st-andrews.ac.uk
Samuel, Prof Ifor - idws@st-andrews.ac.uk
Turnbull, Prof Graham - gat@st-andrews.ac.uk

Our aim is to build ultra-highspeed (50 GHz) room-temperature opto-electronic chips based on our recent demonstration of spontaneously magnetised polariton condensates [1,2]. Exciton-polaritons (polaritons) are superpositions of photons in a Fabry-Pérot microcavity and confined excitons in 2-dimensional quantum wells. They are very light (100,000 times lighter than electrons) and very fast (>100 GHz) thanks to their photonic component, but they can also strongly interact with each other due to their excitonic part. Polaritons can form macroscopic quantum states like atomic Bose-Einstein condensates, and using organic materials they can condense at room temperature. In certain conditions, polariton condensates can spontaneously acquire macroscopic spins of up or down. In this project we aim to exploit them to make ultra-highspeed optoelectronic switches and true random number generators on a chip that can be integrated into the next generation of CPUs and telecommunications. You will fabricate electrically contacted organic-based microcavities in close collaboration with Prof. Turnbull and Prof. Samuel’s group, and study the condensation and specifically their spin properties. You are also expected to travel to the sunny island of Crete in Greece for some parts of the fabrication process.

[1] Physical Review X 5, 031002 (2015)
[2] Nature Materials 15, 1074 (2016)

Industry link: Hitachi (http://www.hit.phy.cam.ac.uk/)
Holographic traps and guides for superfluidity studies and atom interferometry
Cassettari, Dr Donatella - dc43@st-andrews.ac.uk

Holographic traps are a new kind of optical traps for neutral atoms which are promising for a wide range of applications, e.g. quantum information processing and quantum simulation. They are produced by diffracting a laser beam off a computer-controlled optical device, known as a Spatial Light Modulator (SLM). This apparatus offers unparalleled flexibility in the choice of trapping geometry, and different experiments can be done simply by reconfiguring the SLM.
In this PhD project you will work on:

- Double well traps for confined atom interferometry, which is promising for the development of sensitive devices (see [1] for a review).

- Ring-shaped atom guides (see [2] and [3]), which can be used to observe superfluid motion of a Bose-Einstein condensate, e.g. persistent current states. BECs in these geometries and the study of their critical velocities (where superflow stops) have very important technological applications in sensing devices, such as superconducting quantum interference devices (SQUIDs). Moreover, theoretical proposals have been put forward in which coherent superposition of different BEC flows can be used as qubits.

[1] http://rmp.aps.org/abstract/RMP/v81/i3/p1051_1
[2] http://prl.aps.org/abstract/PRL/v106/i13/e130401
[3] http://lanl.arxiv.org/abs/1008.2140
Holographic traps for the efficient production of Bose-Einstein condensates
Cassettari, Dr Donatella - dc43@st-andrews.ac.uk

Evaporative cooling is an essential stage in the creation of Bose-Einstein condensates (BECs) in atomic gases. Recently we suggested [1] that holographic optical traps can be used to increase the evaporation efficiency, leading to larger BECs. In this PhD project you will implement this scheme, which will result in a simplified apparatus for the productions and subsequent manipulation of BECs.

[1] http://pra.aps.org/abstract/PRA/v84/i5/e053410

Integrated Magnetic Resonance Doctoral Training Centre
Smith, Prof Graham - gms@st-andrews.ac.uk

The new EPSRC Doctoral Training Centre in Integrated Magnetic Resonance is a collaboration between 6 of the UK's leading Universities in Advanced Magnetic Resonance Instrumentation and Techniques and includes St. Andrews, Dundee, Aberdeen, Warwick, Nottingham and Southampton.

The aim is to provide a coherent training program for doctoral students whilst working on new research topics in instrumentation and methodology, associated with Magnetic Resonance Imaging, Electron Magnetic Resonance, Nuclear Magnetic Resonance and Dynamic Nuclear Polarisation (which collectively represent £multi-Billion annual markets). Training is delivered from all centres, through residential workshops and over the Access Grid, primarily in the first two years of study.

Funded 4 year PhDs include fees and maintenance of £14000 (tax free) per annum as well as an enhanced travel budget. All PhDs will have internal and external mentors from other centres.

At St Andrews, PhD projects are available on themes associated with major advances in Electron Magnetic Resonance and Dynamic Nuclear Polarisation and are likely to involve collaborations with other centres and other interdisciplinary groups.

PhD topics are likely to involve a combination of instrumental, methodological and computational techniques that would normally be associated with Basic Technology programs.

Representative PhDs from all 6 centres are listed on www.imr-cdt.ac.uk, but other PhD topics may be available on request.

For PhDs at St Andrews, applications can be made directly to St Andrews or via Warwick where the DTC program is administered.
Interacting spin lattices of exciton-polariton condensates

One of the most interesting concepts in condensed matter is the so-called “frustration”, where a few spins in the system cannot find an orientation to fully satisfy all the interactions with its neighbouring spins. Frustration is a complex and not well-understood phenomenon with interdisciplinary applications to artificial neural networks as well as material science. The classic example is 3 spins a triangular geometry with antiferromagnetic coupling between the nearest neighbours. We have recently introduced exciton-polariton (polariton) condensates as a new platform to study such spin interactions [1-3]. Polariton condensates are macroscopic quantum states with picosecond dynamics and unique spin properties arising from their nonlinearities. You will experimentally study the spin properties of coupled polariton condensates in 2-dimensional optical lattices in various geometries, specifically the phenomenon of frustration. Your project will also involve a fair amount of programming, and numerical simulations in a collaboration with our theorists.

[1] Physical Review X 5, 031002 (2015)
[2] Physical Review Letters 116, 106403 (2016)
[3] Physical Review Letters 119, 067401 (2017)

Industry link: Hitachi (http://www.hit.phy.cam.ac.uk/)
Investigating novel superconducting ground states in nanofabricated hybrid ferromagnetic-superconducting materials and devices using advanced neutron, muon and synchrotron techniques
Lee, Prof Steve - sl10@st-andrews.ac.uk

The search for novel quantum states of matter in artificial thin-film structures, in which superconducting (S) and ferromagnetic (F) materials are juxtaposed, has reached an exciting and timely stage of development. In the last year a series of new landmark experimental results seem set to herald a period of rapid expansion of interest and activity in the field. This was the pioneering observation by several groups of spin-triplet supercurrents traversing relatively thick F layers [1-3], believed theoretically to be signatures of a novel equal-spin spin-triplet and possibly ‘odd frequency’ superconducting state. This achievement represent the culmination of several years of breakthrough experiments [1-7] in a field whose modern era began almost most a decade ago, with the experimental discovery of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) [8] type states in S-F-S structures [10]. What both the FFLO [8] and the odd-frequency pairing phenomena [9] have in common is that they were predicted to occur theoretically in bulk systems [8,9] but only in state-of-the-art artificial thin-film structures were they finally demonstrated to exist [1-7,10-13]. Modern thin-film growth and large area lithographic patterning open-up an enormous range of further possibilities for engendering novel quantum states of matter via the controlled interaction S and F order on the nanoscale. This capability also offers the promise of designing and engineering hybrid metamaterials (in a similar spirit to electromagnetic metamaterials) with tailored quantum properties. Concurrently there is enormous interest in spintronics, the manipulation of electronic spin for application in novel electronic devices. The structures investigated within this programme marry the fields of mesoscopic superconductivity, novel strongly correlated electron physics and spintronics. By introducing quantum coherence phenomena into spintronic types devices, this also opens up the possibility of non-locality and entanglement, with possible application long-term in quantum computation.

Professor Steve Lee leads an EPSRC funded Critical Mass Grant award (St Andrews, Leeds, Bath, Royal Holloway, ISIS, with partners in PSI ( Swizterland), Cambridge, and Leiden ) that underpins an international research programme that brings together a team with a wide range of relevant expertise to explore the physics of such systems. We make use of some of the most powerful probes in condensed matter physics (scattering and surface probe techniques) in order to throw new light onto the physics of artificial S-F metamaterials, with particular emphasis on spatially–resolved measurements. This combines with state-of-the-art facilities for materials growth and patterning and world leading instrumentation for measurement. The programme is also informed by cutting-edge theory. There are significant opportunities for research students within this collaboration, with excellent access to world leading research facilities (such as Diamond, ISIS, ILL, PSI, SLS). Due to the strong interactions between nodes there is also significant scope for student mobility in order to enhance training and experience. This is all underpinned by access to excellent graduate training bot via the SUPA Graduate School and the additional benefits of the Doctoral Training Centre in condensed matter physics based at St Andrews, Edinburgh and Heriot Watt.

[1] J.W.A. Robinson et al., Science 329 59 (2010).
[2] T.S. Khaire et al., PRL 104, 137002 (2010).
[3] M.S. Anwar et al., PRB 82, 100501 (2010).
[4] R.S. Keizer et al., Nature 439 825 (2006).
[5] J. Wang et al., Nat. Phys. 6 389 (2010).
[6] I. Sosnin et al., PRL 96 157002 (2006).
[7] D. Sprungmann et al., PRB 82, 060505 (2010).
[8] P. Fulde and R.A. Ferrell, PRB 135 A550 (1964);
A.I. Larkin and Y.N. Ovchinnikov, Zh. Eksp.
Teor. Fiz. 47, 1136 (1964).
[9] V.L. Berezinskii, JEPT Lett. 20, 287 (1974).
[10] V.V. Ryazanov et al., PRL 86, 2427 (2001); T. Kontos et al., PRL 89, 137007 (2002).
[11] A.I. Buzdin et al., JETP Letters 35, 178 (1982);
[12] F.S. Bergeret et al., PRL 86, 4096 (2001); Rev. Mod. Phys. 77, 1321 (2005).
[13] M. Eschrig et al., PRL 90, 137003 (2003); M. Eschrig and T. Löfwander, Nature Phys. 4 138 (2008).


Local control and manipulation of electronic properties of transition metal oxide surfaces
Wahl, Prof Peter - gpw2@st-andrews.ac.uk

Transition metal oxides host a wide range of physical properties and functionalities, making them an ideal platform for implementing potential future devices. The aim of this project is to establish novel ways to manipulate the local properties of transition metal oxides by using a scanning tunneling microscope to enable writing device structures at the atomic scale into the surface of the material. To establish the properties of these written device structure, you will first use scanning tunneling spectroscopy, but later also explore possibilities to contact the written structures macroscopically to study transport through these and enable actual device operation.
While initial studies will be performed on bulk material, at later stages of the project, thin-film samples grown by reactive oxide molecular beam epitaxy will be used.
Mesoscopic unconventional superconductors and Fermi liquids
Mackenzie, Prof Andy - apm9@st-andrews.ac.uk

This project is offer in conjunction with Prof. Amir Yacoby at Harvard.

In this project, we aim to bridge the gap between two fields in which huge progress has been made over the past twenty years. In mesoscopic physics, the aim is to work with samples that are specially fabricated so that their physical size becomes comparable with one or more of the fundamental length scales of the underlying physics. In a metal this might be the mean free path, and in a superconductor it might be the coherence length or the penetration depth. So far, the vast majority of research into mesoscopic physics has been performed on traditional materials in which the electron-electron interactions are relatively weak. In parallel with these developments, equally rapid progress has been made on research into new materials with very strong electron-electron interactions, which lead to high quasiparticle masses and an exciting variety of metallic, superconducting and magnetic ground states. For technical reasons the two fields have advanced in parallel, with little cross-fertilisation of ideas and techniques. The goal of this jointly supervised project is to combine the different expertise of our two groups to bring strongly interacting electrons into the mesoscopic regime. You will work both in St Andrews and at the spectacular new Harvard Nanoscience Center, performing pioneering experiments on the fabrication and measurement of correlated electron mesoscopic devices.

(Jointly affiliated to both University of St Andrews and Max Planck Institute for the Chemical Physics of Solids, Dresden)



Novel Quantum Order in Vector Magnetic Fields
Mackenzie, Prof Andy - apm9@st-andrews.ac.uk

Strongly interacting electron systems are one of the best hosts for study of the quantum many-body problem. Experimental discoveries made in the past decade show that, in the cleanest materials, a variety of subtle collective states form at low temperatures. Some of these are metallic but involve the development of a preferred direction, driven not by the crystal symmetry but by the electron-electron interactions themselves. To study anisotropic responses like these, careful experiments are necessary – they can easily be missed if the correct probes are not used. Many of the states discovered so far have a coupling to externally applied magnetic fields, so these fields can be used to ‘train’ the systems’ response functions. This has highlighted the need to develop better and better ‘vector magnets’ in which the field vector can be changed via computer-controlled energisation of multiple superconducting coils. On this project you will have access to world-leading instruments capable of generating 1, 1 and 9 tesla along the x, y and z axes. This will enable you to study transport and thermodynamic quantities that cannot be accessed in standard instruments. Using this unique instrumentation, you will have the chance to investigate a range of the most exciting new strongly correlated materials in a fast-moving field of modern research.

(Jointly affiliated to both University of St Andrews and Max Planck Institute for the Chemical Physics of Solids, Dresden)
Path integrals over matrix product states: applications and extensions
Hooley, Dr Chris - cah19@st-andrews.ac.uk

The realisation that the ground states of short-range quantum spin systems can generically be represented by matrix product states is an important recent development in theoretical physics [1]. With the aim of integrating the insights of matrix product states with the powerful tools of quantum field theory, some colleagues and I recently developed a path integral over one-dimensional versions of such states [2].

The aim of this project is threefold: first, to explore the extension of this matrix-product-state path integral to higher-dimensional systems; second, to investigate the nature and physical meaning of instanton processes in such path integrals; and third, to develop further applications of the matrix-product-state path integral to open questions in the physics of frustrated magnetism.

[1] R. Orús, Ann. Phys. 349, 117 (2014).

[2] A.G. Green, C.A. Hooley, J. Keeling, and S.H. Simon, arXiv:1607.01778 (2016).

Category: Theoretical Hard Condensed Matter
Polaritons in organic semiconductor microcavities
Samuel, Prof Ifor - idws@st-andrews.ac.uk
Turnbull, Prof Graham - gat@st-andrews.ac.uk

When light is confined on the nanoscale it is possible to observe light-matter interactions that are not normally observed in bulk materials. One example is the strong coupling of photons and excitons in wavelength-scale microcavities which leads to a number of unusual phenomena [1,2]. The modes of the cavity couple with the exciton to make a hybrid-light-matter state called a polariton. One can make polaritons lasers that emit coherent light [3] and it has been shown that polaritons can form a Bose-Einstein condenstate [4].

This project will explore the properties of polaritons in microcavities based on organic semiconductors [2,4-6]. It will involve the fabrication of microcavities that include J-aggregate dyes or semiconducting polymers to explore how the energy states of organic materials can be modified when coupled to the cavity modes, and be applied in photonic devices including lasers and LEDs.

[1] C. Weisbuch et al., Phys. Rev. Lett. 69, 3314 (1992)
[2] D.G. Lidzey et al., Nature 395, 53 (1998)
[3] S. Christopoulos et al., Phys. Rev. Lett. 98, 126405 (2007)
[4] J D Plumhof, T Stöferle, L Mai, U Scherf & R F Mahrt, Nature Materials 13, 247–252 (2014)
[5] T. Schwartz, J. A. Hutchison, C. Genet, and T. W. Ebbesen, Phys. Rev. Lett. 106, 196405 –(2011)
[6] S Kéna-Cohen*, S A. Maier and D D. C. Bradley, Advanced Optical Materials 1, 827–833, (2013)
Quantum Electronic States in Delafossite Oxides
King, Prof Phil - pdk6@st-andrews.ac.uk

As part of a generously-funded ERC research project, we are seeking ambitious and motivated PhD students to join a major research initiative aimed at investigating Quantum Electronic States in Delafossite Oxides (QUESTDO). One of the most active challenges of modern solid state physics and chemistry is harnessing the unique and varied physical properties of transition-metal oxides. While little-studied to date, initial work suggests that the delafossite oxide metals are a particularly rich member of this materials class. They exhibit a wide array of fascinating properties, from ultra-high conductivity [1,2] to unconventional magnetism [3], with the potential to host strongly spin-orbit coupled states at their surfaces and interfaces [4]. You will seek to understand, and control, the delicate interplay of frustrated triangular and honeycomb lattice geometries, interacting electrons, and effects of strong spin-orbit interactions in stabilising these. Projects are available: (i) utilizing laboratory-, laser-, and synchrotron-based angle-resolved photoemission to probe their intriguing bulk and surface electronic structures and many-body interactions; (ii) developing the epitaxial growth of delafossites by reactive-oxide molecular-beam epitaxy, using a state-of-the-art system recently installed in St Andrews; or (iii) working jointly between us and our research partners at the Max-Planck Institute for the Chemical Physics of Solids, Dresden, pursuing either single-crystal growth of new delafossites, or density-functional theory calculations of their electronic structures, combined with experimental studies in our group. For further information, or to discuss research possibilities, please contact philip.king@st-andrews.ac.uk. As part of this project, you will undertake experiments at national and international facilities. Thus, a willingness to travel is an essential prerequisite.

[1] Kushwaha et al., Science Advances 1 (2015) 1500692
[2] Moll et al., Science 351 (2016) 1061
[3] Ok et al., Phys. Rev. Lett. 111 (2013) 176405
[4] Sunko et al., Nature 549 (2017) 492
Self-sustained topological phases in quasi-1D and 2D structures
Braunecker, Dr Bernd - bhb@st-andrews.ac.uk

Topological quantum phases have risen to a very active field of research recently, triggered mostly by the realisation that "ordinary" semiconductor nanostructures could be fine tuned to exhibit topological properties which are very attractive for quantum information storing and processing. With the link to semiconductors a major step forward has been taken towards a quantum technological implementation of such states, yet to obtain robust and scalable quantum systems the requirement of fine tuning has to be dropped.

Self-sustained topological phases provide such stable and robust systems, and exhibit a multitude of fascinating new physical properties that emerge as an effect of strongly interacting particles in a condensed matter system. We have already demonstrated that such phases spontaneously appear in hybrid magneto-electronic systems in one dimension [1-4]. Yet in 1D the number of topological states is restricted, and to obtain more exotic topological states extensions to higher dimensions must be made. It is, however, mandatory to maintain then the 1D self-sustaining mechanisms to avoid producing only conventional phases [5].

In this PhD project, we will take a systematic approach towards such self-sustained topological phases by enhancing the complexity of the systems step by step while maintaining full control over the strongly correlated electron state. We will investigate the influence of the lattice structure (square, honeycomb, kagome), anisotropies and frustration, as well as the crucial renormalisation of the system properties by electron interactions.

[1] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. Lett. 102, 116403 (2009) [arXiv:0808.1685]
[2] B. Braunecker, P. Simon, and D. Loss, Phys. Rev. B 80, 165119 (2009) [arXiv:0908.0904]
[3] B. Braunecker and P. Simon, Phys. Rev. Lett. 111, 147202 (2013) [arXiv:1307.2431]
[4] B. Braunecker and P. Simon, Phys. Rev. B 92, 241410(R) (2015) [arXiv:1510.06339]
[5] P. Simon, B. Braunecker, and D. Loss, Phys. Rev. B 77, 045108 (2008) [arXiv:0709.0164]
Strong matter-light coupling with novel materials
Keeling, Dr Jonathan - jmjk@st-andrews.ac.uk

Polaritons are quasiparticles resulting from strong coupling between matter and light. Strong coupling occurs for photons confined in a microcavity, so that rather than photon emission being an irreversible loss process, photons that are emitted into the cavity can subsequently coherently excite the material again. This leads to new normal modes, polaritons. [1]

Historically, much of the work on these quasiparticles made use of strong coupling to electronic excitations in inorganic semiconductors, such as GaAs or CdTe. However, recently there has been a lot of interest in polaritons formed from a wide variety of materials, including organic molecules (ranging from small molecules to organic polymer chains), as well as very recent developments for materials such as transition metal dichalcogenides, and hybrid organic-inorganic perovskits. These molecular systems have very strong matter-light coupling, and so the physics can be seen at room temperature. [1,2]

One significant area of research concerns polariton condensation and lasing. Polaritons are bosons, and so Bose-Einstein condensation can be (and has been) seen. Because polaritons are part photon, they have a very low effective mass, leading to a very high transition temperature, indeed with organic materials, this can occur up to room temperature.

Another area of increasing experimental interest is in using strong coupling to change material properties. In the context of organic molecules, this has included the idea of changing chemical reaction rates by strong coupling.

This PhD position will be to explore theoretically models that capture the specific physics of a given material system, and ask how the physics of these materials affects, and is affected by, strong coupling to light. We will look both at the physics of Bose-Condensation, as well as modelling other possible applications of strong matter-light coupling to change material properties. We will make use of a variety of analytical and numerical techniques. For examples of our recent work see Refs. [3-5]

[1] "The new era of polariton condensates." D. W. Snoke and J. Keeling Phys. Today 70 54 (2017)
[2] "The road towards polaritonic devices." D. Sanvitto and S. Kéna-Cohen. Nat. Mater. 15 1061 (2016)
[3] "Organic polariton lasing and the weak- to strong-coupling crossover" A. Strashko, P. Kirton, J. Keeling arXiv:1808.07683
[4] "Orientational alignment in cavity quantum electrodynamics." J. Keeling and P. G. Kirton. Phys. Rev. A 97 053836 (2018)
[5] "Exact States and Spectra of Vibrationally Dressed Polaritons." M. A. Zeb, P. G. Kirton, and J. Keeling. ACS Photonics 5 249 (2018)
Subdiffusive dynamics in the approach to many-body localisation
Hooley, Dr Chris - cah19@st-andrews.ac.uk

The phenomenon of many-body localisation – the failure of ergodicity in certain disordered, interacting many-body quantum systems – has become a major topic of research over the past few years [1]. Recently attention has also become focussed on the approach to this transition from the ergodic side. In particular, it has been shown that spin and energy transport become subdiffusive before the actual many-body-localisation transition is reached [2,3].

Recent work in my research group has concentrated on how universal such subdiffusive phenomena are [4]. In particular, we have begun investigating the connection between the hydrodynamics of the weakly disordered model and the nature of the subdiffusive transport that occurs in the approach to full localisation. The aim of this project is twofold: first, to extend those numerical studies to a larger class of one-dimensional models, and second, to draw on existing literature on the nonlinear Schrödinger equation [5] to explore the development of an analytical theory of this subdiffusive regime.

[1] R. Nandkishore and D.A. Huse, Annu. Rev. Cond. Matt. Phys. 6, 15 (2015).

[2] M. Žnidaric, A. Scardicchio, and V.K. Varma, Phys. Rev. Lett. 117, 040601 (2016).

3] V.K. Varma, A. Lerose, F. Pietracaprina, J. Goold, and A. Scardicchio, J. Stat. Mech. (2017) 053101.

[4] M. Schulz, S.R. Taylor, A. Scardicchio, and C.A. Hooley, in preparation.

[5] A. Iomin, Phys. Rev. E 81, 017601 (2010).

Category: Theoretical Hard Condensed Matter
Theory of Quantum Light Sources: how can we make coherent single photons in solid state systems?
Lovett, Dr Brendon - bwl4@st-andrews.ac.uk

The generation of indistinguishable single photons on demand is a key requirement for many kinds of future quantum technologies, such as secure communication and optical quantum computing [1]. Being able to make coherent quantum light sources in solid state systems would enable us to create on-chip photonic circuits that would enable this technology. It is therefore of the utmost importance to understand what effect a solid state environment has on the fidelity of emitted photons.

In this project, you will exploit and developing a groundbreaking new technique our group has created for simulating open quantum systems [2]. Based on a combination of Feynman's path integrals [3,4] and matrix product states [5], it has already enabled calculations impossible by more traditional means. You will study how the technique might be used to calculate the photon correlation functions that characterise a single photon source, in the presence of a strongly-coupled environment of vibrational modes of the crystal. You will go on to study how a photonic cavity might be used to improve the performance of such a device.
Topological physics beneath magnetic structures and interfaces on superconductors
Braunecker, Dr Bernd - bhb@st-andrews.ac.uk

It has been known for a long time that magnetic impurities induce bound states in superconductors [1] but only in recent years it was realised that lining up such states [2] can lead to a twist in the resulting wave function that is known as a changed topological index. The study of such topological states has by now become a highly active field of research. A strong promotor is the rather recent insight that any quantum technology will have to rely on some form of topological states. In this PhD project we will investigate how topological properties appear at interfaces or magnetic structures embedded on superconductors, in a set-up where a strict dimensional decoupling as considered by most approaches is not possible. This will build on our recent work [3]. A particular emphasis will be given to interactions between the states generated by the interaction between the magnetic scatterers and the superconductor, and to particular instabilities that can lead to novel quantum phases.

[1] L. Yu, Acta Phys. Sin. 21, 75 (1965); H. Shiba, Prog. Theor. Phys. 40, 435 (1968); A. I. Rusinov, JETP Lett. 9, 85 (1969).
[2] F. Pientka, L. I. Glazman, and F. von Oppen, Phys. Rev. B 88, 155420 (2013); S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, and A. Yazdani.
Science 346, 6209 (2014).
[3] C. J. F. Carroll and B. Braunecker, arXiv:1709.06093.
Topological Superconductivity
Mackenzie, Prof Andy - apm9@st-andrews.ac.uk

The concepts of symmetry and symmetry breaking cut across all sub-fields of physics. Whether crystal symmetry in solids, gauge symmetry in superconductors or time reversal symmetry in ferromagnets, we have become used to defining phases of matter in terms of order parameters associated with symmetry breaking. However, not all collective quantum states can be fully characterised in terms of their symmetries. In some systems phases are classified in terms of their topological characteristics. Although this has been known for several decades, it was thought to apply in highly restricted circumstances. Exciting and rapid developments over the past five years have shown that these topologically characterised phases are likely to be much more widespread than first thought, and that, in the long term, it may be possible to exploit their properties in adventurous new technologies. Although progress has been rapid, fascinating theoretical questions remain, not least the interplay between symmetry and topology. The field is also ripe for experimental study. Superconductors are among the most fascinating candidates for topological systems. A host of intriguing theoretical proposals exist, but the extent to which they are observable in practice has yet to be determined. This project is concerned with investigating candidate topological superconductors, using a combination of the world-leading experimental facilities in St Andrews, Dresden and Cornell. The project is ambitious, and would be best suited to a candidate with both experimental and theoretical aptitude.

(Jointly affiliated to both University of St Andrews and Max Planck Institute for the Chemical Physics of Solids, Dresden)
Ultrafast Photophysics of Organic Semiconductors
Samuel, Prof Ifor - idws@st-andrews.ac.uk

This project will explore the physics of remarkable plastic-like semiconductors, such as light-emitting polymers. These materials are model one-dimensional systems and this strongly influences their physics – for example it means that excitons are strongly bound and that there is a substantial distortion of the material when it is excited. The purpose of this project is to study the nature of the excited states in these materials and how they evolve when the sample is excited by light. The initial rearrangement of the molecules occurs on a timescale of 100 femtoseconds. Remarkably we can make measurements on this timescale using advanced femtosecond lasers. We wish to explore how the excited states form and then decay, and how these processes relate to the structure of the material. The results will help understand light emission and amplification, and complementary theoretical work is underway at Heriot-Watt University by Prof. Ian Galbraith.
Under Pressure: Measuring nanometre distance changes in biomolecules
Lovett, Dr Janet - jel20@st-andrews.ac.uk

Proteins and nucleic acids (collectively: biomolecules) often function through conformational changes. Understanding these changes helps to understand how they work, which is not only interesting but also influences nanotechnology and drug discovery. One way to induce changes in proteins may be to increase the pressure they are under. We can then trap this new state through freezing and investigate the changes. A promising method for detecting the changes is to use an electron paramagnetic resonance (EPR) experiment called DEER which can measure nanometre-length distances between pairs of specifically placed molecules to map out the shape of the protein (Jeschke, Annu. Rev. Phys. Chem., 2012, 63, 419-446).

Together with our expert mechanical workshop team in St Andrews you would build a pressure cell suitable for fast freezing the high-pressure states. This is not without precedence: see Michael Lerch et al, Proceedings of the National Academy of Sciences, 2014, 111, E1201-E1210 and Lerch et al Methods in Enzymology, 2015, 564, pages 29-57, but there is still plenty to do. Completion of the first stage of the project would enable you to explore its application to biology.

A protein of particular interest in our laboratory is calmodulin which an important protein in many cellular processes as it changes its conformation in response to both calcium concentration and the presence of binding proteins.

The EPR at St Andrews is outstanding with X-band including a recent upgrade with an AWG, high powered Q-band and a homebuilt high-powered W-band spectrometer (HiPER) which is currently being upgraded to include an AWG which will further increase it’s utility and sensitivity.

The EPR groups in St Andrews and Dundee have a world-leading reputation across development and applications. We meet regularly and are also part of the Centre for Magnetic Resonance, see https://www.st-andrews.ac.uk/cmr/. The group headed by Janet Lovett currently has 4 PhD students who are based across Biology, Chemistry and Physics. The group webpages are https://www.st-andrews.ac.uk/~jel20.

The laboratory skills you would learn are to design/build equipment (based on an existing protocol), biological handling techniques, and you would become skilled in EPR experiments. You would therefore gain a broad knowledge across scientific disciplines, and a background in any science subject is useful with an enthusiasm to broaden your skills and apply them in new situations.

Informal enquiries are welcome over email (jel20@st-andrews.ac.uk) or skype and you are welcome to visit St Andrews and our well-equipped laboratories.