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# Thomas Whitehead

**My research in plain English**

One of the most intriguing phenomena in physics is superconductivity, the proclivity of materials to enter a state with no electrical resistance at low temperatures. For many materials this is well-understood behaviour, described by a theory of 'Cooper pairs' going back sixty years. However, it is possible to imagine materials where this traditional theory would not hold; in particular, materials where there are more 'up'-spin electrons than 'down'-spin ones. I am working on a novel theory of superconductivity that might describe what would happen in these materials in terms of groups of particles, instead of just pairs.

Room 544

Mott Building

Cavendish Laboratory

J J Thomson Avenue

Cambridge

Cambridgeshire

CB3 0HE

01223 337049

I am a third year PhD student in the Theory of Condensed Matter (TCM) group of the University of Cambridge's Cavendish Laboratory, under the supervision of Dr Gareth Conduit. I am funded by the EPSRC and am a member of Jesus College.

### Current Research

The BCS theory of superconducivity has a long and successful history of describing superconducting phenomena. The conventional theory is built by combining together Cooper pairs of bound electrons from opposite sides of the (identical) Fermi seas of the up- and down-spin electrons. In imbalanced systems with different numbers of electrons for the different species this concept of Cooper pairs has previously been stretched into so-called FFLO theory, where the members of the pair just reside on the different Fermi surfaces.

However, FFLO theory has several unattractive properties. Chief amongst these is that, because there are different numbers of particles for the different species, some minority electrons will necessarily not be involved in the FFLO pairs. This wastes their potential for contributing binding energy to the system.

Our proposal for a new superconducting state extends the concept of Cooper pairs to include groups of more than two electrons. For example, if the Fermi surface for the up-spin species is twice as big as that for the down-spin species, we might include two up-spin electrons and one down-spin electron in the state, as shown in the schematic figure. We can compare the binding energy of this state to the FFLO state, and find that our proposal is energetically favourable compared to FFLO theory. The many-particle superconducting state is also under investigation, which has the interesting property of not behaving as a collection of composite bosonic particles in any limit.

*Mathematica* Path Integral Monte Carlo program

For my own edification, education, and entertainment, I have put together a *Mathematica* Package that allows the simulation of ultra-cold atomic gas experiments, at finite temperature and with finite system sizes. It is a reasonably quick, parallel bit of code whose main aim is to be easy to understand and extend. The Package, in whichever version number it currently is, should be available from here, and is distributed under GPL 3.0.

### Notes on superconductivity

I have a couple of notes on aspects of FFLO superconductivity that I have found useful during our investigation of the many-particle superconducting state. I'm making them available here in case anyone else might also find them useful: here is a run-through of the evaluation of the thermodynamic potential for 3D FFLO theory, and here is a calculation of the transition imbalance for 2D FFLO. Hopefully they are of some use!

### Previous Study

Prior to coming to Cambridge I studied for an MPhys at St Hugh's College Oxford. My final year project was investigating the motion of active nematic swimmers, supervised by Prof Julia Yeomans.

In the summer of 2013 I worked at the Met Office as part of the Atmospheric Dispersion and Air Quality group, parameterising low frequency turbulence under the supervision of Dr Helen Webster.

### Publications

*Jastrow correlation factor for periodic systems*, Physical Review B **94**, 035157 (2016).

Also available at arXiv:1607.05921 and as a pdf (© APS).

*Pseudopotential for the two-dimensional contact interaction*, Physical Review A **93**, 042702 (2016).

Also available at arXiv:1603.05001 and as a pdf (© APS).

*Pseudopotentials for an ultracold dipolar gas*, Physical Review A **93**, 022706 (2016).

Also available at arXiv:1601.07746 and as a pdf (© APS).

*Parametrizing unresolved mesoscale
motions in NAME*, Met Office Forecasting Research Technical
Report, May 2015.

### Presentations

*A multi-particle superconductor?*, Cavendish Graduate Student Conference, University of Cambridge, 1 December 2016; and Frontiers of Condensed Matter Physics, University of Bristol, 10 January 2017.

*The ν Jastrow factor*, Electronic Structure Discussion Group, TCM, University of Cambridge, 9 March 2016.

*Pseudopotentials for a dipolar ultracold atomic gas*, Electronic Structure Discussion Group, TCM, University of Cambridge, 18 March 2015; and Quantum Cambridge Winter School, St Hugh's College Oxford, 20-23 March 2015.

### Posters

*Pseudopotentials for an ultracold dipolar gas*, New States of Matter and their Excitations, Helmholtz Virtual Institute, 18 June 2015; Physics by the Lake, Cumberland Lodge, 2-15 August 2015; Jesus College Graduate Student Conference, 12 March 2016; and Long-Range Interacting Many-Body Systems: from Atomic to Astrophysical Scales, ICTP, Trieste, 25-29 July 2016.