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:
Ultracold atoms: Developed a theory of the dynamics of atoms in two-dimensional shallow quasicrystalline optical lattices. Studied Bloch oscillations, Berry curvature and Chern number defined over a pseudo-Brillouin-zone. Key finding of an unusual 'spiral holonomy' in the effective band structure.
Quantum oscillations: Provided the first account of quantum oscillations in two or three dimensional 'weakly coupled' quasiperiodic materials---a key example being 30° twisted bilayer graphene. Found that these reveal a 'spiral Fermi surface' characterised by a nontrivial topological invariant.
Artificial gauge fields: Explored ways of engineering topologically nontrivial phases in quasicrystalline optical lattices via the breaking of time reversal symmetry, approaches included Floquet engineering and coupling of internal states.
Topological insulators: Investigating possible higher order topological phases in materials with non-Bravais lattice rotational symmetries.
Spiral Fermi Surfaces in Quasicrystals and Twisted Bilayer Graphene:
Signatures in Quantum Oscillations
Stephen Spurrier and Nigel R. Cooper,arXiv:1811.03652