High-magnetic fields to explore phase diagrams of novel superconductors

To understand the practical applications of novel superconductors, it is essential to explore their three-dimensional phase diagrams, defined by temperature, magnetic field, and critical currents. These diagrams can be constructed using various experimental techniques, including resistivity measurements to test the zero-resistance state and critical currents, torque measurements to probe irreversibility fields, and tunnel diode oscillator studies to determine penetration depth. Magnetization measurements can detect upper and lower critical fields, assess pinning forces, and estimate critical currents using the Bean model, with corrections for demagnetizing effects.

This project aims to construct detailed superconducting phase diagrams of novel crystalline superconducting materials, including iron-based and candidate topological superconductors (such as FeSe1-xSx and FeSe1-xTex systems). Experiments will be conducted as a function of temperature and magnetic field, both in Oxford (up to 21T) and at high-field facilities in Europe and the USA (up to 90T). Upper critical fields will be modeled using single-band and multi-band approaches, as applied to other iron-based superconductors. Additionally, superconducting fluctuations will be investigated through torque magnetometry and paraconductivity studies.

This project can be extended to explore superconducting wires and tapes relevant for practical applications using the facilities of the Oxford Centre for Applied Superconductivity in Oxford which include a probe for critical current studies up to 500 A in 14T at 4.2K.

For further reading please consult relevant papers:

1. Ultra-high critical current densities, the vortex phase diagram and the effect of granularity of the stoichiometric high-Tc superconductor, CaKFe4As4
https://arxiv.org/abs/1808.06072

2. Competing pairing interactions responsible for the large upper critical field in a stoichiometric iron-based superconductor, CaKFe4As4
https://arxiv.org/abs/2003.02888

3. Multi-band description of the upper critical field of bulk FeSe
https://arxiv.org/abs/2311.04188

Developing tunable superconducting devices based on thin flakes of iron-chalcogenide superconductors

Iron-chalcogenide superconductors are versatile materials composed of conducting two-dimensional iron planes separated by van der Waals layers of chalcogens. When FeSe is grown as a monolayer on a suitable substrate, it exhibits the highest critical transition temperature among two-dimensional systems, exceeding that of liquid nitrogen [1]. Furthermore, ionic-liquid gating of FeSe films induces electron doping, enhancing superconductivity four-fold to around 45 K [2]. Thin flakes of FeSe also demonstrate a superconducting diode effect, where zero-resistance states appear non-reciprocally during current injection [3].

This project aims to explore the superconducting and electronic behaviour of dimensional devices based on thin flakes of highly crystalline iron chalcogenides (FeSe1-xSx and FeSe1-xTex). Different ionic substrates and electrochemical gating will be used to tune carrier concentrations and enhance superconductivity. These studies will help establish the link between superconducting phases, electron doping, and competing nematic and magnetic phases, as well as identify signatures of topological behaviour and the superconducting diode effect. The student will investigate phase diagrams and normal electronic manifestations in novel superconducting thin flake devices, tuned via flake thickness and electrochemical gating. The project will involve device preparation, critical current measurements, magnetotransport, and Hall effect studies to explore electronic properties and superconducting phase diagrams under high magnetic fields and low temperatures. Experiments will search for quantum oscillations in the best candidate systems with large mean free paths, utilizing high magnetic field facilities in Europe and the USA. The thin flakes will be exfoliated from existing single crystals using previously developed methods [4,5]. Sample preparation will include designing appropriate lithographic patterns via optical and e-beam lithography, mechanical exfoliation, and using a glove box to handle air-sensitive samples. This project could also be extended to include simulations of current distributions in devices using finite element analysis, to better quantify and understand current distribution.

For further reading consult:

1. Superconductivity above 100 K in single-layer FeSe films on doped SrTiO3,
https://doi.org/10.1038/nmat4153

2. Interplay between superconductivity and the strange-metal state in FeSe
https://doi.org/10.1038/s41567-022-01894-4

3. Field-free superconducting diode effect in layered superconductor FeSe
https://arxiv.org/abs/2409.01715

4. Suppression of superconductivity and enhanced critical field anisotropy in ultra-thin flakes of FeSe,
https://www.nature.com/articles/s41535-020-0227-3

5. Unconventional localization of electrons inside of a nematic electronic phase,
https://www.pnas.org/doi/10.1073/pnas.2200405119

Strain-tuning of Superconducting and Competing Electronic Phases in Iron-Chalcogenide Superconductors

Uniaxial pressure is a powerful tuning parameter of correlated electronic phases of matter and relevant in superconducting applications. This technique can enhance superconductivity, it provides a unique insight into the behaviour of nematic electronic states giving access to the anisotropic Fermi surfaces, via the nematic susceptibility, and it can break the translational symmetry to stabilize novel topological phases of matter [1,2]. This project will use applied strain to tune the superconducting and the electronic structure. This will help develop a strategy about how to enhance superconductivity, and identify whether the pairing interaction is related to the nematic or magnetic fluctuations [3]. Additionally, elastocaloric effect can be used to probe second-order phase transitions to study the nature of complex pairing symmetries in iron-based superconductors [4].

Firstly, the student will perform transport and magnetotransport measurements under strain in high magnetic fields and it will establish how the superconducting phase diagrams are affected by applied strain. These studies will be extended in magnetic fields up to 90T to assess the changes in the Fermi surface under applied strain. Additionally, the student will develop capabilities to measure elastocaloric effect to determine the changes in temperature to an oscillating uniaxial stress at the superconducting phase transitions. The strain will be applied using both piezostacks and Razorbill cells to tune electronic nematic phases and to assess the strain dependence of critical temperature. The student will use finite element analysis software to simulate the expected strain transmission for the different experimental strain design and cells. The student will be able to perform first-principle calculations to simulate the changes in the electronic structure under strain.

Experiments in high magnetic fields will be performed at international high-magnetic field facilities in Europe and USA. As applied strain is relevant for technological applications, during the project the student could also test the strain variation of the critical currents of wires and tapes used in superconducting applications. Experiments will be performed in the Oxford Centre for Applied Superconductivity (CfAS).

For further reading consult:

1. Emergence of the nematic electronic state in FeSe
https://doi.org/10.1103/PhysRevB.91.155106

2. Strain tuning of nematicity and superconductivity in single crystals of FeSe,
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.205139

3. Iron pnictides and chalcogenides: a new paradigm for superconductivity,
https://www.nature.com/articles/s41586-021-04073-2
https://arxiv.org/abs/2201.02095

4. AC elastocaloric effect as a probe for thermodynamic signatures of continuous phase transitions, https://doi.org/10.1063/1.5099924

Thin film growth of novel superconductors for quantum devices

Superconducting materials hold great promise for a range of quantum technologies owing to their inherently low dissipation and the ability to exploit their unique physics at junctions with non-superconducting materials to make qubits.

Typically, superconducting quantum devices are fabricated using aluminium technology because it is possible to relatively easy to control the growth of a uniform aluminium oxide layer to act as the tunnel junction. However, aluminium is a relatively poor superconductor, with a critical temperature of around 2 Kelvin, and there are limitations in terms of the quality of the aluminium oxide layer. This collaborative project with Oxford Instruments Plasma Technology will explore the potential of a variety of other superconducting materials such as (Nb,Ti)N that can be grown in the form of thin films by complementary physical vapour deposition (Oxford Materials) and atomic layer deposition (Oxford Instruments).

The research project will involve the growth and characterisation of superconducting films to assess how chemistry and microstructure correlate with superconducting properties, and performance in quantum devices (Oxford Physics). By improving understanding of what materials parameters ultimately control device performance, the aim is to be able to assess the potential of different superconducting materials and growth conditions without the need for fabricating complex devices and testing them at millikelvin temperatures.

In-situ radiation damage in high temperature superconducting magnet materials for fusion reactors

Nuclear fusion reactors require high magnetic fields to confine the intensely hot plasma in which the deuterium–tritium reaction takes place. The next generation of fusion reactors relies on state-of-the-art high-temperature superconductors (HTS) to achieve these very high magnetic fields, the superconductor of choice being (RE)Ba₂Cu₃O₇ (where RE = rare earth element). In operation in a fusion device, the HTS magnet windings are exposed to high energy neutrons, which cause severe degradation of superconducting properties and, ultimately, a total loss of superconductivity long before any structural damage becomes visible under atomic resolution electron microscopy. As a safe experimental proxy for neutron damage, we have pioneered in-situ measurements of the effects of ion-beam irradiation (with protons, He⁺, and O₂⁺) on the superconducting performance of REBCO tapes. Building on this foundation, we are now conducting state-of-the-art in-situ experiments using both fission and fusion-spectrum neutrons.

The student will work closely with collaborators at the UK Atomic Energy Authority and Birmingham University and become an expert in the measurement of superconducting properties under irradiation, and will join in with experiments on the beamlines at the Diamond Light Source to explore the damage mechanisms specific to each kind of irradiation that control the properties of these complex materials.

In situ cryogenic irradiation experimental setup.

Predicting performance of high temperature superconductors under fusion conditions

The economic viability of a tokamak power plant (TPP) is a function of its size, toroidal field (TF) strength and availability during its operating lifetime. This optimisation has led the designers of tokamaks to adopt both a compact design and the use of coated conductors (CC) made with rare-earth barium copper oxide (REBCO) high temperature superconductor as the current carriers for their magnets. However, designing TF magnets for TPPs has some unique difficulties, notably that the properties of the superconductor at the very high magnetic field of a TF magnet (20 tesla) can only be accessed at specialist international user facilities, and that radiation emitted by fusion reactions causes damage to REBCO CCs that affect their ability to carry current.

This collaborative project between the Universities of Oxford and Cambridge and the UK Atomic Energy Authority involves using a combination of phenomenological modelling and experiments. The aim is to develop scaling relationships that will enable the prediction of superconducting performance under fusion magnet operating conditions (20 T, 20 K) from more easily accessible measurements at lower field and/or higher temperature. This will initially require comprehensive microstructural and electromagnetic characterisation of a selection of typical coated conductors (e.g. with and without artificial pinning centres) over the full range of magnetic fields, temperatures and field angles using a combination of facilities at the partner organisations and international user facilities such as the Pulsed Field Facility at Los Alamos National Laboratory. This data will be used to determine where scaling of easily accessible high temperature, low field data can be safely performed.

This will allow us to determine the optimum qualification test conditions for the coated conductor that balances the ability for testing large quantities of material quickly and cheaply, with a high degree of confidence in the extrapolation to fusion magnet operation conditions provided by the robust scaling relationships. Given that the performance of a REBCO CC is dependent on the defect structure within REBCO, the work will be extended by applying irradiation to the samples to change the defect landscape in the REBCO and assess how that changes performance. Understanding the effect of irradiation is of great importance for fusion magnets because the REBCO will be exposed to fast neutrons that seriously degrade the superconducting performance, limiting the lifetime of the magnet and determining the thickness of shielding required. Further work may include the extension of the dataset to include field angles not perpendicular to the direction of current flow and/or to include the effects of strain on REBCO performance and be combined with molecular dynamic simulations using machine learning potentials developed for magnet for REBCO materials from first-principles modelling. In addition to developing and validating scaling laws that are essential for fusion magnet design, the student will contribute to the understanding of vortex physics in HTS, which is a rich area of high scientific interest more broadly than fusion.

Pulsed magnetic field measurements on REBCO coated conductor taken at Los Alamos National Laboratory (NHMFL facility).

Understanding irradiation-induced defects in high temperature superconductors using electron and x-ray spectroscopy techniques

Rare-earth barium copper oxides (REBCO) are the only class of high-temperature superconducting (HTS) materials that have been developed into commercial wires with an engineering performance good enough for use in the high field magnet for small fusion tokamaks like the one being designed in the STEP programme. One of the critical aspects we must understand before deploying these expensive materials in a fusion reactor is how their superconducting properties are affected by exposure to high energy neutrons and a significant flux of gamma rays to ensure that they can retain adequate performance for the lifetime of the magnets. 

This project will involve using a combination of electron energy loss spectroscopy in a scanning transmission electron microscope with synchrotron x-ray absorption spectroscopy to characterise irradiation-induced point defects in REBCO.  The student will study commercial coated conductor samples and grow their own REBCO films with simpler microstructures and chemistry using our pulsed laser deposition facility.  By comparing the defects produced by different irradiating species (e.g. light ions, electrons, protons) with fast neutrons, the aim is to ascertain how reliable these alternative sources of irradiation are as proxy for the kind of neutron bombardment that will be inflicted in a fusion reactor.  This is important because neutron irradiation experiments are expensive and slow, as well as resulting in the samples becoming radioactive, which limits the number and range of experiments that can be performed. 

Electron ptychography image of He ion irradiated REBCO coated conductor taken at the ePSIC facility, Diamond Light Source and reconstructed by Dr Fred Allars.

Ultra low resistance joints for bismuth-based high temperature superconducting magnets

The next generation of ultra-high field magnets for applications in healthcare and materials characterisation will need us to take advantage of the exceptional properties of high temperature superconducting materials. One of the most challenging design features in these magnets is the requirement for joints between individual lengths of superconducting wire that allow the passage of persistent currents (resistances less than 10^-14 Ohms!) in very high magnetic fields. In collaboration with Oxford Instruments, this project will involve designing novel processes to form joints between commercial bismuth-based high temperature superconducting wires, and to measure their performance under real engineering conditions. There will be opportunities for the student to become an expert in the advanced techniques needed to correlate the microstructure formed by complex heat treatment processes with superconducting properties of materials critical for future magnet designs.