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Stephen Spurrier

 Stephen Spurrier

Stephen Spurrier

Member of Girton College
PhD student in Prof Cooper's group

Office: 524 Mott Bld
Phone: +44(0)1223 3 37459
Email: snms2 @
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TCM Group, Cavendish Laboratory
19 JJ Thomson Avenue,
Cambridge, CB3 0HE UK.

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My research concerns exploring topological aspects of condensed matter systems, both in the context of cold atoms and electronic systems, often using a blend of analytical and numerical techniques. The projects I have worked on or are currently working on fall under the following broad research areas:
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In Plain English

After the discovery of X-ray diffraction it was generally considered that ordered materials (those which displayed sharp Bragg peaks in their diffraction patterns) were periodic and a simple theorem known as the `crystallographic restriction theorem' ensured that the only allowed rotational symmetries of a periodic structure are 1-,2-,3-,4- and 6-fold. Despite this, in 1983, Dan Schectman discovered that the X-ray diffraction pattern of an aluminium alloy remarkably displayed both sharp Bragg peaks but with a crystallographically disallowed 5-fold rotational symmetry. These and similar materials were soon termed `quasicrystals', and their structure was found to be related to aperiodic tilings such as the well-known Penrose tiling.

In recent years there has been a growing interest in the `simulation' of models from condensed matter by using systems of so-called `ultracold atomic gases'. Here the atoms play the role of electrons and an `optical lattice' potential created from the interference of overlapping laser beams, models the background ionic lattice. The key advantage of these systems is that the optical lattice is highly controllable and free from defects that can obscure various quantum phenomena. By simply arranging the lasers to have a rotational symmetry that is disallowed for a periodic structure one can then extend the control available in cold-atom systems to simulate quasicrystals. In my research I have been exploring novel theoretical questions that were previously less relevant in condensed matter quasicrystals (and therefore remained uninvestigated), but which are now highly relevant for their optical lattice analogues.