Impurity as a probe of Berry curvature and wavefunction winding in gapped two-band models

RESUMO

We explore the possibility of using quasiparticle interference near impurities to extract non-local properties of bands. Focusing on the minimal two-band description of a system with multiple valleys, we show that the local density of states (LDOS) induced by non-magnetic impurities can effectively probe both the Berry curvature and the wavefunction winding, locally in each valley. We analyze gapped models based on Dirac, semi-Dirac, quadratic touching, and higher-order touching energy dispersions, in presence of a point-like potential scatterer. We find that for strong enough impurity potentials the LDOS along a contour around the impurity unambiguously shows the wavefunction winding number, in contrast to the case of gapless Dirac-like dispersions where the winding can be precluded by LDOS oscillations in the radial direction. We also establish a general connection between, on the one hand, the Berry curvature as a function of momentum locally in a valley, and on the other hand, the wavefunction winding number and the energy dispersion parameters, making hence the local Berry curvature directly observable from spectroscopic LDOS information.