Topological Insulators: A Statistical Mechanics Approach

Topological insulators (TIs) are materials characterized by insulating bulk states and conductive surface states, protected by topological invariants rather than conventional symmetry breaking. In this seminar, we will explore the statistical mechanics underlying these phases, focusing on how quantum statistical mechanics governs the behavior of fermionic excitations in TIs. A key feature of these systems is the preservation of time-reversal symmetry, which protects surface states from backscattering and ensures their robustness even in the presence of non-magnetic impurities. We will discuss how the statistical behavior of fermions in topological insulators leads to these protected surface states, and how various thermodynamic properties provide deeper insights into their stability.