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

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.