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 -

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).
Superconductivity in Non-Centrosymmetric Materials and Structures
Wahl, Prof Peter -

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 -

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

[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 -

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 -
Wahl, Prof Peter -

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 -

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 -

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).
Coherent many-body dynamics between a quantum system and its environment
Braunecker, Dr Bernd -

Decoherence, the enemy of any quantum processing, is the uncontrolled decay of a well defined quantum superposition. It occurs because any quantum system is always embedded in a wider environment with a macroscopic number of degrees of freedom. The interaction with these degrees of freedom causes a destructive interference and a nicely prepared quantum superposition dissipates somewhere in the environment. Large efforts are thus made throughout the world to isolate the system from its environment, to use special driving protocols that reverse some of the destructive interference, etc.

However, the concept of "bad" can also be reversed into something "good". It is indeed interesting to ask how exactly decoherence builds up, if we can use this to learn something about the system and the environment, and even if there is a way to use this knowledge for quantum information processing. Indeed the quantum fluctuations that eventually turn into decoherence initially build up an entanglement with the environment. The main questions underlying this PhD project are how this happens, how it can be followed in time, and if we can use it in a controlled way.

As a first example we have worked out in detail how a spin decays in a metal [1]. The stationary properties of such a system are known since very long and the analysis of the thermal decay is on the basis of magnetic resonance techniques such as NMR or MRI. However, mostly left aside was the regime of very short time scales in which the spin and a part of the metallic environment have a joint coherent evolution, and in which coherent excitations in the metal act back on the spin dynamics. The coherent many-body effect of a local excitation, such as from a spin flip, on the environment runs under the name of orthogonality catastrophe or Fermi edge singularity, is on the basis of the Kondo effect, and we have worked on extending the techniques to access this physics for various situations over many years. In [1] we have now set up the approach allowing us to systematically investigate the backaction on the spin as well. This proposed PhD work will build on these foundations and make the transition to including strongly correlated many-body environments. The goal is to provide a framework for the characterisation of correlated systems through probing localised spins, which is de facto an extension of the foundations of NMR to strongly interacting systems in which temporal correlations are as important as the spatial correlations that alone are addressed in current theories. Through the tremendous progress made in material design, low temperature physics and quantum control such a theoretical foundation is becoming more and more necessary.

[1] S. Matern, D. Loss, J. Klinovaja, B. Braunecker, Phys. Rev. B 100, 134308 (2019) [arXiv:1905.11422]
Controlling emergent quantum phases through strain-tuning of electronic structure
Hicks , Dr Clifford -
King, Prof Phil -
Mackenzie, Prof Andy -

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 ( 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 -

Quantum simulation offers the possibility to create physical phenomena that are hard to access or control otherwise. Notorious is particularly many-body physics with strong correlations. Remarkably some types of such physics can be created in dissipative quantum circuits, in which the type of correlation physics appears through a nonlinear interaction of the electron transport with electromagnetic environment fluctuations. For weakly transmitting conductor such physics is understood since a long time [1]. But the potential of the quantum simulation appears only for highly transmitting circuits in which the transmission time is comparable with the environment's reaction time, called the dynamical Coulomb blockade regime, for which much less is known. Although for specific conditions important advances have been made over the last years [2], recent experimental progress has shown that there is still much unclear especially when there is strong backaction of the environment [3]. In this PhD project we will access this physics through analytical and numerical non-perturbative many-body modelling, including bosonisation [4] and recently developed mappings on scattering boundary value problems [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); A. Anthore, Z. Iftikhar, E. Boulat, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, and F. Pierre, Phys. Rev. X 8, 031075 (2018).
[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 -

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, 154112 (2018)
[3] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Nature Communications 9 3322 (2018)
Engineering non-equilibrium material states with cold atoms in optical cavities
Keeling, Dr Jonathan -

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. Kollar, 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 -

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 -

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 -

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 -

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
Holographic traps and guides for superfluidity studies and atom interferometry
Cassettari, Dr Donatella -

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.

Holographic traps for the efficient production of Bose-Einstein condensates
Cassettari, Dr Donatella -

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.


Investigating novel superconducting ground states in nanofabricated hybrid ferromagnetic-superconducting materials and devices using advanced neutron, muon and synchrotron techniques
Lee, Prof Steve -

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 -

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 -

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 -

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 -

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 -
Turnbull, Prof Graham -

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 -

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 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 -

Topological quantum phases have risen to a very active field of research recently, triggered mostly by the realisation that "ordinary" semiconductor nanostructures can 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 [1-5]. 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 [6].

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] C. J. F. Carroll and B. Braunecker arXiv:1709.06093
[6] P. Simon, B. Braunecker, and D. Loss, Phys. Rev. B 77, 045108 (2008) [arXiv:0709.0164]
Strong light-matter coupling with Rydberg polaritons
Ohadi, Dr Hamid -

Joint PhD studentship between Scotland and Australia

Dr Hamid Ohadi (University of St Andrews, UK) (
A/Prof Thomas Volz (Macquarie University, Sydney, Australia)

Exploiting the laws of quantum mechanics for the benefit of humanity in the so-called "second quantum revolution" is one of the key goals of 21st-century physics. Unlike the first quantum revolution, which simply made use of the wave-particle duality that quantum mechanics dictates, the second quantum revolution harnesses entanglement, superposition and quantum measurement for creating new technologies. Ultimately, the quantum correlations at the heart of these phenomena require strong interactions between individual quantum particles. Many different quantum systems are currently being explored for applications, and photons, the quantum particles of light, are one of the most promising candidates for applications such as quantum information processing and quantum sensing. While they are easy to create, manipulate and detect, their biggest drawback, however, is the lack of direct interactions in vacuum. Yet, photons can be made to interact by binding them to matter. Photons propagating in an optically active material can couple strongly to the excitations of that material to the point where the photon and the material are entangled and form new hybrid particles that are half-matter and half-light. These chimeres are called ‘polaritons’ and have been at the forefront of modern quantum photonics research for the past two decades. While many spectacular results have been demonstrated so far, the ideal single-photon non-linear system has not been found to date.

This project aims to take a big leap forward and study a new exciting contender for inducing strong photon-photon interactions in a semiconductor system. Very recently, polaritons formed from electron hole pairs, i.e. excitons, in traditional semiconductor GaAs have been demonstrated to exhibit non-classical correlations at the single quantum level [1,2]. However, these correlations are weak due to the relatively weak interactions between the GaAs excitons. There are several avenues to induce even stronger interactions but almost all of them involve excitonic states that have a much larger interaction radius than the ground state GaAs excitons. A particularly interesting class of excitons are Rydberg excitons that in analogy to the hydrogen atom correspond to highly-excited excitons with large principal quantum numbers (and large spatial extent). Cuprous Oxides are known to have stable bulk Rydberg excitons with principal quantum numbers beyond n=20. Spectroscopy experiments have revealed effects due to exceptionally strong exciton-exciton interactions [3]. However, to date no light-matter interface with a 2D cuprous oxide film has been formed. This project will address this open problem and unlock the potential of the cuprous oxide material to form strongly interaction Rydberg polaritons.

The cotutelle project within the St-Andrew-Macquarie partnership will be conducted in two steps: In the first step, the semiconductor devices will be fabricated at the University of St Andrews. There will be two types of devices, one that will consist of a 2-dimensional microcavity formed by two highly reflective mirrors encapsulating a cuprous oxide thin film and a second type which is missing one of the mirrors and can be combined with an external mirror to form a fully-tunable system. Photons confined in the microcavity will strongly couple to the Rydberg excitons in the cuprous oxide film to form Rydberg polaritons. The second part of the project will be carried out at Macquarie University in Sydney. There the properties of the cuprous oxide polariton system will be explored with the expectation to demonstrate strong quantum correlations and photon blockade. If successful, the results will be a real breakthrough for quantum polaritonics and its perspective for real-world applications, such as networked non-linear cavities for quantum simulation with light.

Informal enquiries should be sent to Dr Hamid Ohadi (

[1] G. Munoz-Matutano et al, Nature Materials 18, 213–218 (2019).
[2] A. Delteil et al, Nature Materials 18, 219-222 (2019).
[3] Kazimierczuk et al, Nature 514, 343 (2014).
Strong matter-light coupling with novel materials
Keeling, Dr Jonathan -

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. Kena-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 -

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 -

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.

[1] I. Aharonovich. D. Englund and Milos Toth, Nature Photonics 10 631 (2016)
[2] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Nature Communications 9 3322 (2018)
[3] R. P. Feynman, and F. L. Vernon, Jr., Ann. Phys. 24 118 (1963)
[4] N. Makri and D. E. Makarov. The Journal of Chemical Physics J. Chem. Phys. 102 4600 (1995)
[5] R. Orús, Annals of Physics 349 117 (2014)
Topological physics beneath magnetic structures and interfaces on superconductors
Braunecker, Dr Bernd -

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 -

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 control of correlated states in 2D materials
King, Prof Phil -

In recent years, it has become possible to fabricate materials down to just a single atom in thickness. Compared to their bulk counterparts, this nanostructuring approach can drive a host of major changes in their material properties, from electronic transport and optical activity to the way in which electrons in these systems interact with each other and the underlying crystal lattice in which they reside. A way to further control these interactions is via ultrafast (fs) laser excitation. Importantly, such excitation can now be combined with a precise probe of how the electron motion in solids is modified, via time- and angle-resolved photoemission spectroscopy (TR-ARPES). In this project, you will fabricate crystals in the two-dimensional limit using ultra-high vacuum-based growth techniques, and study the resulting electronic properties of the materials using both static and TR-ARPES techniques. A particular initial focus will be in the optical control of correlated and magnetic orders in these systems. This PhD project forms part of an ambitious research programme to be undertaken jointly between the Electronic Structure of Quantum Materials group at the University of St Andrews, Scotland (, and the Artemis program at the U.K Central Laser Facility, Rutherford Appleton Laboratory, in Oxfordshire ( Your project will exploit a unique UK capability for integrated materials synthesis and electronic structure study in St Andrews (, and the recently-upgraded state-of-the-art capabilities for TR-ARPES at the Rutherford Appleton Lab ( You will be based in St Andrews for approximately half of the project, and in Oxfordshire for the other half, and will additionally attend synchrotron beamtimes at leading international facilities; a willingness to travel is thus an essential pre-requisite! Candidates should have a degree in physics or a related discipline. Laboratory experience with ultra-high vacuum techniques, synchrotron or laser science, or crystal growth is helpful but not required. For more information, contact or
Ultrafast Photophysics of Organic Semiconductors
Samuel, Prof Ifor -

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.