QUANTUM TRANSPORT IN TOPOLOGICAL SYSTEMS

Abstract

Topological phases are states of matter characterized not by symmetry-breaking order parameters, but by topological numbers whose values remain invariant under smooth changes of the system parameters such as sample thickness and gate voltage. This robustness establishes topological matter as a candidate for next-generation devices such as low-dissipation spintronics components and far-infrared optical modulators. In this thesis, we study the quantum transport of various topological states. We first considered the Hofstadter model driven by a periodic field. Upon applying the Floquet sum rule, robust quantized conductance plateaus as large as $8e^2/h$ were found, and algorithms for the calculations of the local current and density of states were proposed. We then extended the method to tackle superconductivity to investigate the transport in several Floquet quantum anomalous Hall-topological superconductor heterostructures. Distinctive higher half-integer conductance plateaus were identified as signatures for the scattering between multiple chiral Majorana and Dirac modes. Next, we studied how topological phases as diverse as Weyl semimetals and second-order Chern insulators may arise from gapping a nodal loop semimetal and discussed the corresponding transport signatures. Lastly, we explored the possibility of high harmonic generation with nodal Hopf and chain semimetals, by means of the semiclassical Boltzmann equation.