Topological Invariants of Interacting Gapped Quantum Materials and Transport Phenomena

Citation

Spodyneiko, Lev (2021) Topological Invariants of Interacting Gapped Quantum Materials and Transport Phenomena. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/fmt8-qb23. https://resolver.caltech.edu/CaltechTHESIS:06012021-025758430

Abstract

In this thesis we study transport properties of interacting lattice system focusing, on those which become topologically protected at low temperatures for gapped Hamiltonians. We prove the vanishing of the net energy currents in equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We derive Kubo-like formulas for the thermal and thermoelectic Hall conductances of arbitrary 2d lattice systems which are free from ambiguities associated with the definition of magnetizations. We use these formulas to define a relative topological invariant of gapped 2d lattice systems at zero temperature.

We define and study analogs of the Thouless charge pump and Berry Curvature for many-body gapped systems in spatial dimension D. We show how to attach a topological invariant to a D-dimensional family of such systems. For a large class of families we argue that this topological invariant is an integer.

Thesis Files