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Higher-order bulk photovoltaic effects, quantum geometry, and application to p-wave magnets

Motohiko Ezawa

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Phys. Rev. B 112, 155308 – Published 27 October, 2025

DOI: https://doi.org/10.1103/zt2c-v7ly

Abstract

The injection and shift currents are generalized to the ℓth-order injection and shift currents for the longitudinal conductivities in the two-band model, where ℓ is the power of the applied electric field. In addition, the formulas for the higher-order injection current are expressed in terms of the quantum metric, and those for the higher-order shift current are expressed in terms of the higher-order quantum connection. Then, they are applied to p-wave magnets, which are well described by the two-band Hamiltonian as far as low-energy physics is concerned. It is shown that the injection and shift currents are zero. On the other hand, the ℓth-order injection and shift currents with odd ℓ are nonzero when the direction of the spin-splitting vector of the p-wave magnet points to an in-plane direction.

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Phys. Rev. B 112, 155308– Published 27 October, 2025
  • Received 2 July 2025
  • Revised 2 September 2025
  • Accepted 7 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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