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

TL;DR

This paper extends the theory of bulk photovoltaic effects to higher orders, linking them to quantum geometric quantities, and applies the framework to $p$-wave magnets where certain currents vanish or emerge depending on magnetic orientation.

Contribution

It introduces formulas for higher-order injection and shift currents in terms of quantum metric and connection, and applies these to $p$-wave magnets revealing their behavior.

Findings

Higher-order injection and shift currents are expressed via quantum geometry.

In $p$-wave magnets, these currents vanish for even orders.

Odd-order currents are nonzero when the Néel vector points in-plane.

Abstract

The injection and shift currents are generalized to the $\ell $th-order injection and shift currents for the longitudinal conductivities in the two-band model, where $\ell $ 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 the higher-order shift current in terms of the higher-order quantum connection. Then, they are applied to $p$-wave magnets. It is shown that the injection and shift currents are zero. On the other hand, the $\ell $th-order injection and shift currents with odd $\ell $ are nonzero when the direction of the N\'{e}el vector of the $p$-wave magnet points to an in-plane direction.