We study a wide class of free-fermion systems on a hypercubic lattice in spatial dimensions d ≥ 1. When the system is insulating, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analogue ...

Two-dimensional transition metal trichalcogenides (TMTCs) feature covalently bonded metal-chalcogen layers separated by the van der Waals (vdW) gap. Similar to dichalcogenides (TMDCs), TMTCs often host charge density waves (CDWs) and superconductivity, but unlike TMDCs, atomic chains in crystal structure give rise quasi one-dimensional (quasi 1D) conduction. ZrTe3 features CDW below TCDW = 63 K...

The purpose of this thesis is to study the long term behavior of time-inhomogeneous Markov chains. We analyze under what conditions they converge, in what sense they converge and what the rate of convergence should be. A Markov chain is a random process with the memoryless property: the next state only depends on the current state, and not on the sequence of events that preceded it. Time-inhomo...