Berry phase formalism of shift currents and its usage in discovering 3D topological observables: non-E-field-driven transports at topological transitions in insulators/semi-metals.

One present-day challenge is that for D-dimensional topological materials its observable’s dimension is d=D-1, known as the principle of bulk-edge correspondence. For the higher-order topological effect, it is D-2, D-3, etc. This limits its detection and usage. In this talk, We present a result about D-dimension topological phase transition (TPT) causing observables of D-dimension. The key to the breakthrough is that without increasing the material dimension, we obtain an “extra” dimension from the time axis.

A current formalism suitable for handling situations with TPT is described. It is supposed to solve these challenges: (i) gap closing will cause divergence in Berry curvature and other observables, (ii) perturbation approaches (e.g., Fermi-golden) become invalid, (iii) occupancy will be strongly modified during transport and a linear proportionality to Fermi-distribution difference becomes invalid.

Berry phase formalism of shift currents is closely related to recent geometric pumping [1], it is inspired by Berry phase polarization theory [2] and shift current theory [3] and could be viewed as a bridge connecting the gulf between adiabatic and non-adiabatic limits. The current discovered is not E-field driven (E-field lifetime << currents lifetime) but is a coherent transport of momentum between heavier-lighter subsystems: the momentum of the lattice finds a dissipation-less way into electrons. Such currents rely on TPT and are characterized by anomalous temperature, field-strength dependence, etc. supported by models and first-principle simulations.

[1] B. Q. Song, et al. Phys. Rev. B, 105 035101 (2022)

[2] R. D. King-Smith, D. Vanderbilt, Phys. Rev. B, 47, 1651 (1993).

[3] J. Ahn, et al. Phys. Rev. X, 10, 041041 (2020)