Quantum Geometry and Nonlinear Responses in Magnetic and Topological Quantum Materials

TL;DR

This paper investigates how quantum geometry influences nonlinear transport phenomena in magnetic and topological quantum materials, providing theoretical generalizations and predicting novel effects.

Contribution

It introduces generalized quantum kinetic and Boltzmann theories for nonlinear responses and predicts new transport effects in quantum materials.

Findings

Generalized quantum kinetic theory for nonlinear responses

Predicted novel transport effects in topological materials

Extended semiclassical Boltzmann transport theory

Abstract

This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory, Kubo formulas and semiclassical Boltzmann transport theory to the nonlinear response regime, we discuss several predictions of novel transport effects and physical insights that emerge from these developments.