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PhD Projects
Project Title Supervisor(s) Institution
Low-temperature Magneto-Kerr Microscopy Cole, Dr. Jamie and Prof. Huxley, Andrew Edinburgh
Quantum and classical in adiabatic computation

Green, Prof. Andrew, Serafini, Dr. Alessio, Warburton, Dr. Paul

UCL
Experimental and Theoretical Investigation of Spatially Modulated Magnetic Phases Near to Quantum Criticality Green, Prof. Andrew (UCL)
Huxley, Prof. Andrew (Edinburgh)
St Andrews
Exotic Kondo effects in tunable nanostructures Hooley, Dr. Chris St Andrews
Non-equilibrium and Non-adiabatic Effects in Bose-Einstein Condensates Hooley, Dr. Chris St Andrews
Measurement of Physical Properties at Very High Pressures Kamenev, Dr. Konstantin and Prof. Andrew Huxley Edinburgh
Quantum Simulation with Matter-light Systems Keeling, Dr. Jonathan St Andrews
Nonequilibrium Physics in Many-body Quantum Optics Systems Keeling, Dr. Jonathan St Andrews
A New Approach to Inelastic Electron Scattering King, Dr. Phil St Andrews
Imaging and Manipulating Spins and Pseudospins in 2D Materials King, Dr. Phil St Andrews
Tuning Many-Body Quantum Systems Through Electrostatic Surface Control King, Dr. Phil St Andrews
Controlling Emergent Quantum Phases Through Strain-tuning of Electronic Structure

Mackenzie, Prof. Andy (St Andrews & MPI Dresden), King, Dr. Phil (St Andrews), Hicks, Dr. Clifford (MPI Dresden)

St Andrews/MPI Dresden
Novel Quantum Order in Vector Magnetic Fields Mackenzie, Prof. Andy St Andrews/MPI Dresden
Mesoscopic Unconventional Superconductors and Fermi Liquids Mackenzie, Prof. Andy (St. Andrews)
St Andrews/MPI Dresden
Topological Superconductivity Mackenzie, Prof. Andy and Davis, Prof. Séamus St Andrews and Cornell
Characterisation of Triplet Superconductivity by Tunneling Spectroscopy Wahl, Dr. Peter St Andrews
Competing and Co-existing Orders in Fe-based Superconductors Wahl, Dr. Peter St Andrews
Setup of a Combined STM/AFM for the Study of Layered Oxide Materials Wahl, Dr. Peter St Andrews
Superconductivity in Non-centrosymmetric Materials Wahl, Dr. Peter St Andrews
Magnetic Measurements to Probe Unconventional Superconductors Yelland, Dr. Ed and Prof. Andrew Huxley St Andrews

 

lowtempmagnokerr

Low-temperature Magneto-Kerr Microscopy

Dr. Jamie Cole and and Prof. Andrew Huxley (Edinburgh)

A magneto-Kerr microscope will be built to work at progressively lower temperatures, ulimately down to 0.1 K. The microscope will then be used to image domain structures in ferromagnetic superconductors (URhGe and UCoGe). The images will be used to position contacts to make transport measurements across single domain walls and to test for the presence of Josephson currents (Shapiro steps etc). The microscope will also be used to look for surface currents around domain edges that are signatures of topologically protected states associated with some non-conventional order parameters (with applications in quantum computing). The microscope will also be used to image vortices to look for new behaviours predicted at domain walls. The above project will be based in Edinburgh but with some measurements making use of facilities in St Andrews.

Category: Experimental Hard Condensed Matter
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lowtempmagnokerr

Quantum and classical in adiabatic computation

Prof. Andrew Green, Dr. Alessio Serafini, Dr. Paul Warburton (UCL)

Adiabatic quantum computation (AQC) has been proposed for the efficient solution of computationally-complex optimization problems. Recent demonstrations of AQC have led to controversy about the degree of quantum mechanics that is involved. The student will develop a set of test problems that may be used to quantify this – a set of target Hamiltonians that require different degrees of entanglement in order to optimize them by adiabatic means. The experimental input would be from D-Wave systems, with simulations using tensor networks compared to runs on their machines.

Category: Theoretical and Experimental Hard Condensed Matter
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newquantumstates

Experimental and Theoretical Investigation of Spatially Modulated Magnetic Phases Near to Quantum Criticality

Prof. Andrew Green and Prof. Andrew Huxley (Edinburgh or St Andrews)

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)

Category: Experimental Hard Condensed Matter
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exotickondoeffects

Exotic Kondo Effects in Tunable Nanostructures

Dr. Chris Hooley (St. Andrews)

When a magnetic impurity (such as iron) is placed in a good metal, it causes anomalously strong scattering of the conduction electrons below a certain characteristic temperature. This effect is called the Kondo effect, and the associated temperature is therefore called the Kondo temperature. We now understand that what the magnetic impurity is trying to do is to bind the conduction electrons into a spin-singlet, and at sufficiently low temperatures, this is achieved. In 1998, the effect was observed for the first time in nanophysical systems, with a quantum dot playing the role of the magnetic impurity, and the two electrical leads playing the role of the conduction sea. Quantum dot systems are, however, much more tunable than the metals and impurities offered to us by chemistry: even the dimensionality of the leads can in principle be altered. This is an exciting prospect, since we know that in one dimension the interacting electron system adopts an unusual strongly correlated state called a Luttinger liquid, and that the theory of the Kondo effect with Luttinger liquid leads is quite different to that in the normal metal case. This theoretical project aims to address the following questions:

  • Can the Luttinger-liquid Kondo effect be realised in quantum dot systems?
  • How do its properties relate to those of the soft-gap Anderson model?
  • What is its behaviour at bias voltages well above the Kondo scale?
  • Does it have a critical point, and if so, can this be characterised?

Established relations with several experimental groups active in the field (e.g. the Grayson group at the Walter Schottky Institute, the Marcus group at Harvard, and the Kouwenhoven group at Delft) are expected to provide fruitful and up-to-date experimental information. The majority of the work will consist of pen-and-paper calculations, perhaps supplemented by some computational analysis.

Category: Theoretical Hard Condensed Matter
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bose einstein

Non-equilibrium and Non-adiabatic Effects in Bose-Einstein Condensates

Dr. Chris Hooley (St. Andrews)

When a gas of bosonic atoms is cooled to very low temperatures, it undergoes a phase transition in which a macroscopic fraction of the atoms enters the lowest single-particle state of the system. This effect, called Bose-Einstein condensation, was predicted in 1924, but not directly observed until 1995 - the main difficulty being, of course, that gases don't tend to stay gaseous down to microkelvin temperatures unless cooled with great care! To this end, ingenious devices involving electromagnetic trapping and laser- and evaporative cooling have been devised. Recent experiments involve subjecting the atom cloud to laser standing waves (so-called “optical lattices”) as well as the background trapping potential that stops the atoms from leaving the system. One of the most exciting opportunities presented by these set-ups is the opportunity to study quantum processes far from equilibrium: since the characteristic time-scales of the Bose gas are rather long, it's easy to make a “sudden” change in the laser field. Indeed, the study of such non-equilibrium effects is vital, as they are in fact the key to measuring the properties of such gases in the first place (via “time-of-flight” experiments). This theoretical project aims to put our understanding of non-equilibrium processes in trapped Bose- and Fermi gases on a firmer footing, addressing such issues as:

  • atom-atom correlations during cloud expansion;
  • anti-bound states from sudden quenching of the condensate;
  • growth models for low-temperature Bose-Einstein fluids;
  • measuring the BCS state for fermions.

Established relations with several experimental groups active in the field (e.g. the Inguscio group in Florence, the Hinds group at Imperial, and the Schmiedmayer group at Heidelberg) are expected to provide fruitful and up-to-date experimental information. The majority of the work will consist of pen-and-paper calculations, perhaps supplemented by some computational analysis.

Category: Theoretical Hard and Soft Condensed Matter
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Measurement Physical

Measurement of Physical Properties at Very High Pressures

Dr Konstantin Kamenev and Prof. Andrew Huxley (Edinburgh)

High pressures are often needed to tune materials to quantum critical points at which new state formation occurs. The application of magentic field and the rotation of pressurised samples in the field can provide additional tuning. Rotation in a field is also essential for quantum oscillation studies to map out Fermi-surfaces. The project will develop pressure cells and instrumentation for these measurements and use this to study various quantum critical phenomena. It will build on (i) further development of miniature turnbuckle diamond anvil cells to be used on our low-temperature high-field rotatable platform and (ii) new designs for the piezo-electric rotators to rotate the cells at very low temperature. The emphasis here will be on developing apparatus and making measurements such as Hall resistivity and susceptibility. The use of designer diamonds will be explored. The project affords the possibility of making exciting discoveries probing materials where new state formation is expected to be induced with pressure and field as well as acquiring valuable transferrable skills in CAD (computer aided design) and FEA (finite element analysis) calculations. The project would be based in the new CSEC building and PhD registration could be in either physics or engineering schools depending on the preference of the candidate.

Category: Experimental Hard Condensed Matter
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unconventional superconductors

Quantum Simulation with Matter-light Systems

Dr. Jonathan Keeling (St Andrews)

Quantum simulation aims to build controllable quantum systems that can experimentally determine the behaviour of particular theoretical models of interacting quantum systems. Potentially this allows one to experimentally test how to design materials with particular desired properties (superconductivity, magnetism etc.)

There has been significant progress recently in building coupled matter-light systems that can act as quantum simulators. In particular, experiments on superconducting circuit arrays, experiments on Rydberg states of atoms, and experiments on ultracold atoms in optical cavities all show the possibility to design and tune model Hamiltonians. All these systems however face losses; photons leak out, and so the system is in a non-equilibrium steady state.

We will theoretically explore how these losses affect the possibility to use these systems as quantum simulators. This can involve a wide range of modelling approaches, from Keldysh field theory to numerics based on matrix product operators.

Category: Theoretical Hard Condensed Matterback to top

 

Many Body Quantum Optics

Nonequilibrium Physics in Many-body Quantum Optics Systems

Dr. Jonathan Keeling (St. Andrews)

The aim of this project is to explore phase transitions in non-equilibrium quantum systems, and in particular, those involving many body quantum optics that is readily accessible to current or future experiments with cold atoms or superconducting qubits.

The last few years have seen a growing range of experimental systems in which collective quantum optical effects can be studied, and which prompt important questions about the differences between "quantum" phase transitions in open and closed quantum systems, and whether open quantum systems can ever be described as displaying a quantum phase transition. In particular, experiments by the group of Esslinger in ETH have shown how cold atoms in an optical cavity subject to an external coherent pump can undergo a transition to a superradiant phase.

This project will consider related problems, in which different aspects of quantum phase transitions in non-equilibrium systems become accessible.

Theory of Condensed Matter - Dr Keeling, St Andrews

Category: Theoretical Hard Condensed Matter
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Many Body Quantum Optics

A New Approach to Inelastic Electron Scattering

Dr. Phil King (St Andrews)

A key goal of condensed matter physics is to develop a thorough understanding of the microscopic properties of materials to enable the rational design of new compounds with desired characteristics. A major challenge, however, is that their particles often do not act independently, but collectively. In this project, you will initially develop a state-of-the-art instrument to probe the inelastic scattering of low-energy electrons, creating new opportunities for studying the dispersions and lifetimes of collective excitations in solids with unprecedented resolution. You will apply this to investigate exotic metals known to exist at the surface of a special type of insulator called a topological insulator, providing new insights on their collective excitation spectra and many-body interactions.

Category: Experimental Hard Condensed Matter
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Many Body Quantum Optics

Imaging and manipulating spins and Pseudospins in 2D Materials

Dr. Phil King (St Andrews)

Work on graphene, an atom-thick layer of carbon, has spurred enormous interest in related families of two-dimensional materials. These can possess a host of attractive properties such as semiconducting band gaps and strong spin-orbit interactions. An example of particular current interest is the transition-metal dichalcogenides (TMDs) such as MoS2 or WSe2. Excitingly, for electrons residing in degenerate conduction and valence band extrema at different positions in the Brillouin zone (so-called distinct valleys), the spin and valley degrees of freedom have been found to be strongly entangled [1], raising tantalising prospects for their use in exotic new schemes of electronics and quantum computing. We have recently used spin- and angle-resolved photoemission spectroscopy (ARPES) to visualise such spin-valley locking, directly observing for the first time how this becomes further entangled with a layer pseudospin in bulk TMDs [2]. In this project, you will employ ARPES measurements in our state-of-the-art spectroscopy lab in St Andrews to uncover the diverse electronic structures and many-body interactions of a range of 2D materials, and will investigate methods to manipulate and exploit their valley and layer degrees of freedom. You will also perform complementary measurements, for example using spin-resolved and nanoscale ARPES, at synchrotron light sources in the UK and abroad.

[1] Xu et al., Nature Phys. 10 (2014) 343
[2] Riley et al., Nature Phys. 10 (2014) 835

Category: Experimental Hard Condensed Matterback to top

 

Many Body Quantum Optics

Tuning Many-Body Quantum Systems Through Electrostatic Surface Control

Dr. Phil King (St Andrews)

Control of the source-drain conductivity of a semiconductor transistor by applying a small external voltage (so-called field-effect doping) underpins almost all current electronic devices. However, the transistor is widely accepted to be approaching its physical limits of performance. A new approach is required. In this project, you will investigate the potential of correlated electron materials – compounds where there are strong interactions between the constituent particles and which often exhibit emergent phases such as superconductivity and magnetism – for such applications. You will develop schemes to mimic field-effect doping in ultra-high vacuum while still leaving the sample surface accessible for advanced spectroscopic measurements [1,2]. In particular, you will employ angle-resolved photoemission (ARPES) to simultaneously uncover how the electronic structure and many-body interactions evolve with such doping. ARPES measurements will be performed using our state-of-the-art system in St Andrews, as well as synchrotron light sources in the UK, Europe, and the USA.

[1] Meevasana, King et al., Nature Materials 10 (2011) 114
[2] King et al., Nature Communications 5 (2014) 3414

Category: Experimental Hard Condensed Matter
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Many Body Quantum Optics

Controlling Emergent Quantum Phases Through Strain-tuning of Electronic Structure

Prof. Andy Mackenzie (St Andrews & MPI Dresden), Dr. Phil King (St Andrews), Dr. Clifford Hicks (MPI Dresden)

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 within the UK, Europe and the USA. 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 Dr. King), and will also undertake experiments at national and international facilities. Thus, a willingness to travel is an essential prerequisite. Collaborations in this area are also envisaged with the STM group of Dr. Peter Wahl in St Andrews.

Category: Experimental Hard Condensed Matter
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unconventional superconductors

Novel Quantum Order in Vector Magnetic Fields

Prof. Andy Mackenzie (St. Andrews & MPI Dresden)

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 xy 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.

Category: Experimental Hard Condensed Matter 
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unconventional superconductors

Mesoscopic Unconventional Superconductors and Fermi Liquids

Prof. Andy Mackenzie (St. Andrews) and Prof. Amir Yacoby (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.

Category: Experimental Hard Condensed Matter
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Topological Superconductivity

Topological Superconductivity

Prof. Andy Mackenzie and Prof. Séamus Davis (St. Andrews and Cornell)

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 and at Cornell. Part of the work will be performed using the atomically resolved STM spectroscopy pioneered by one of us (JCD). Initially the thrust will be on the candidate topological superconductor Sr2RuO4, but others will also be considered as the field advances. The project is ambitious, and would be best suited to a candidate with both experimental and theoretical aptitude.


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Many Body Quantum Optics

Characterisation of Triplet Superconductivity by Tunneling Spectroscopy

Dr. Peter Wahl (St Andrews)

In spin-triplet superconductors, cooper pairs are formed by electrons whose spins are aligned parallel. Examples of superconductors, where the electron pairing occurs with equal spins are Sr2RuO4 and some of the heavy fermion superconductors (e.g. ferromagnetic superconductors). In most of these materials, the superconducting order parameter and the properties of the superconducting state are only poorly understood. Part of the experimental challenge is that superconductivity typically only emerges at temperatures on the order of 1K.  The properties of these superconductors are often intriguing and surprising, e.g. in ferromagnetic superconductors the material is at the same time magnetic and superconducting. Even without applied magnetic field, the superconductor can be expected to be in a vortex state due to the magnetization of the material itself. 
During the first time of this project, the focus of your work will be to establish the sample preparation and to identify a triplet superconductor which is suitable for studies by spectroscopic imaging STM. In parallel, you will be trained to operate our spectroscopic imaging STM, which is mounted in a dilution refrigerator and can reach a base temperature of 7mK. 

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Many Body Quantum Optics

Competing and Co-existing Orders in Fe-based Superconductors

Dr. Peter Wahl (St Andrews)

The iron-based superconductors, an only recently discovered family of materials which become superconducting at temperatures up to ~50K, have almost all complex phase diagrams as a function of doping with structural and magnetic phase transitions. Superconductivity in these materials, similarly to high-temperature copper based superconductors, is most likely not mediated by phonon coupling, but rather either by some magnetically mediated coupling or due to electron correlations. In this regard, the importance of the magnetic and structural phases in these materials for superconductivity, and whether they coexist or compete with superconductivity become important questions. In this project, the aim is to determine the importance and possibly the origin of symmetry breaking electronic ordering for superconductivity. A nematic state in an iron-based superconductor has been first observed by STM in CaFe1.94Co0.06As2[1]. By spectroscopic imaging STM, you will attempt to search for ordering phenomena in the electronic excitations and study their dependence on temperature and magnetic field, in order to elucidate their relation to superconductivity.

  1. T.-M. Chuang, M.P. Allan, J. Lee, Y. Xie, N. Ni, S.L. Bud’ko, G.S. Boebinger, P.C. Canfield, and J.C. Davis,Science 327, 181 (2010).

Category: Experimental Hard Condensed Matterback to top

 

Many Body Quantum Optics

Setup of a Combined STM/AFM for the Study of Layered Oxide Materials

Dr. Peter Wahl (St Andrews)

In this project, the setup of a new combined STM/AFM is envisioned. The study of correlated electron materials by spectroscopic imaging STM has become a valuable tool, especially to study excitations at low energies and in magnetic fields. Adding force detection has a number of advantages, besides obtaining an additional observable the force allows to independently define the tip-sample distance. The is particularly beneficial when studying poorly conducting or even insulating samples, such as e.g. oxide heterostructures, which are often capped by insulating layers.

Your part in this project will be to implement force detection in an existing STM head (for a description, see, e.g., Ref. 1) and make it work in a cryogenic environment. In parallel, the sample preparation to study layered oxide materials in STM will be established. The aim of the project is to investigate the properties of 2D electron gases at the interface in layered oxide heterostructures by tunneling spectroscopy. It has been shown in the past that in these heterostructures, electronic correlation effects can be taylored such that the interfacial electron gas becomes, e.g., superconducting or exhibits magnetic ordering [2]. Observation of the electronic states of the two-dimensional electron gas in tunneling spectroscopy would open the possibility to study the properties on the nanometer scale.

  1. S.C. White, U.R. Singh and P. Wahl, A stiff STM head for measurement at low temperatures and in high magnetic fields, Rev. Sci. Instr. 82, 113708 (2011).
  2. J. Mannhart and D. Schlom, Science 327, 1607 (2010).

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Many Body Quantum Optics

Superconductivity in Non-Centrosymmetric Materials

Dr. Peter Wahl (St Andrews)

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. Measurements will be performed using the low temperature (down to 20 millikelvin) and high magnetic field (up to 17 Tesla) experimental facilities at St Andrews; these will include measurements of bulk properties like electrical resistivity, specific heat and torque magnetometry, as well as various microscopic characterization techniques. Materials that can be prepared with the necessary very clean surfaces will be further studied by low temperature scanning tunneling microscopy and spectroscopy to establish the gap structure from tunneling spectroscopy.
Candidates for this project should be adaptable to learning a wide range of different experimental techniques and be able to connect the results from these techniques using advanced data analysis and modeling.

Further Reading:
S.S. Saxena and P. Monthoux, Symmetry not required, Nature 427, 799 (2004)
E. Bauer, Non-centrosymmetric Superconductors, Springer (2012)
Y.L. Chen et al., Discovery of a single topological Dirac fermion in the strong inversion asymmetric compound BiTeCl, Nat. Phys. 8, 704 (2013)

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Magnetic Measurements

Magnetic Measurements to Probe Unconventional Superconductors

Dr. Ed Yelland and Prof. Andrew Huxley (St. Andrews)

Magnetism and superconductivity are intimately connected in many so-called heavy fermion metals. A particularly dramatic case is URhGe, where two distinct superconducting regions exist – one coexisting with ferromagnetism, and the other at extremely strong applied magnetic fields that are sufficient to destroy conventional forms of superconductivity. This project will involve developing sensitive heat capacity and magnetic measurement apparatus that will operate at extremes of low-temperature and high-magnetic field, and apply them to study URhGe and other related materials. The aims are both to gain a deeper understanding of how magnetic pairing may lead to superconductivity and to drive the search for new superconducting materials. The project is an integral part of a major research effort to study quantum criticality and unusual quantum ordered phases using a variety of magnetic, electrical and thermal measurement techniques. The apparatus in St Andrews includes a state-of-the-art dilution refrigerator (commissioned December 2007) with a base temperature 10 millikelvin and equipped with a 17 tesla magnet. The focus for the project is on magnetic measurements including heat capacity, torque magnetometry, field gradient magnetometry and a.c. susceptibility. By combining torque and field-gradient results, the vector magnetic moment can be determined as a function of magnetic field. This will give a complete phenomenological (Ginzburg-Landau) description of the magnetism in the region superconductivity occurs, and will provide detailed information about the nature of the magnetic interactions that are important for superconductivity. Another important component of the work will be to use quantum oscillations in the different measurements to study the Fermi surface and how it changes approaching and crossing quantum phase transitions.

Category: Experimental Hard Condensed Matter
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