Shift photoconductivity in the Haldane model
arXiv:2305.17035 · doi:10.1103/PhysRevB.108.155419
Abstract
The shift current is part of the second-order optical response of materials with a close connection to topology. Here we report a sign inversion in the band-edge shift photoconductivity of the Haldane model when the system undergoes a topological phase transition. This result is obtained following two complementary schemes. On one hand, we derive an analytical expression for the band-edge shift current in a two-band tight-binding model showing that the sign reversal is driven by the mass term. On the other hand, we perform a numerical evaluation on a continuum version of the Haldane model. This approach allows us to include off-diagonal matrix elements of the position operator, which are discarded in tight-binding models but can contribute significantly to the shift current. Explicit evaluation of the shift current shows that while the model predictions remain accurate in the deep tight-binding regime, significant deviations arise for shallow potential landscapes. Notably, the sign reversal across the topological phase transition is observed in all regimes, implying it is a robust effect that could be observable in a wide range of topological insulators.
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