Impurity as a probe of Berry curvature and wavefunction winding in gapped two-band models
Abstract
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.
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BibTeX
@misc{nabil2026impurity,
title = {{Impurity as a probe of Berry curvature and wavefunction winding in gapped two-band models}},
author = {Reda Nabil and Pascal Simon and Andrej Mesaros},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08447},
eprint = {2609.08447},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05771729v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Impurity as a probe of Berry curvature and wavefunction winding in gapped two-band models
AU - Reda Nabil
AU - Pascal Simon
AU - Andrej Mesaros
PY - 2026
DA - 2026/09/08
PB - HAL
DO - 10.48550/arxiv.2609.08447
UR - https://hal.science/hal-05771729v1
AB - 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.
ER -