Transport in topological insulators with bulk-surface coupling: Interference corrections and conductance fluctuations

Motivated by the experimental difficulty to produce topological insulators (TIs) of the ${\text{Bi}}_{2}{\text{Se}}_{3}$ family with pure surface-state conduction, we study the effect that the bulk can have on the low-temperature transport properties of gated thin TI films. In particular, we focus on interference corrections, namely weak localization (WL) or weak antilocalization (WAL), and conductance fluctuations (CFs) based on an effective low-energy Hamiltonian. Utilizing diagrammatic perturbation theory, we first analyze the bulk and the surface separately and subsequently discuss WL/WAL and CFs when a tunneling-coupling is introduced. We identify the relevant soft diffusion modes of t…