Weak localization and Berry flux in topological crystalline insulators with a quadratic surface spectrum

TL;DR

This paper investigates how the topology of quadratic band crossings in topological crystalline insulators influences weak localization effects and proposes using WL measurements to detect Berry flux.

Contribution

It provides a detailed analysis of WL corrections in surface states with quadratic band crossings, linking Berry flux to observable conductivity signatures.

Findings

Negative WL correction sign dictated by quadratic band topology

Explicit Berry flux dependence of WL conductivity derived

Potential method to measure Berry flux via WL experiments

Abstract

The paper examines weak localization (WL) of surface states with a quadratic band crossing in topological crystalline insulators. It is shown that the topology of the quadratic band crossing point dictates the negative sign of the WL conductivity correction. For the surface states with broken time-reversal symmetry, an explicit dependence of the WL conductivity on the band Berry flux is obtained and analyzed for different carrier-density regimes and types of the band structure (normal or inverted). These results suggest a way to detect the band Berry flux through WL measurements.