Intrinsic nonlinear conductivity induced by quantum geometry in altermagnets and measurement of the in-plane N\'{e}el vector

TL;DR

This paper demonstrates that the in-plane Néel vector in altermagnets can be measured via quantum-metric induced nonlinear conductivity, with analytic formulas showing divergence at the Dirac point.

Contribution

It introduces a method to measure the in-plane Néel vector using nonlinear conductivity induced by quantum geometry in altermagnets, providing explicit formulas.

Findings

Quantum-metric induced nonlinear conductivity is proportional to the in-plane Néel vector.

The nonlinear conductivity diverges at the Dirac point, indicating strong effects.

The quantum-metric induced nonlinear conductivity dominates at the Dirac point.

Abstract

The $z$-component of the N\'{e}el vector is measurable by the anomalous Hall conductivity in altermagnets because time reversal symmetry is broken. On the other hand, it is a nontrivial problem how to measure the in-plane component of the N\'{e}el vector. We study the second-order nonlinear conductivity of a system made of the $d$-wave altermagnet with the Rashba interaction. It is shown that the quantum-metric induced nonlinear conductivity and the nonlinear Drude conductivity are proportional to the in-plane component of the N\'{e}el vector, and hence, the in-plane component of the N\'{e}el vector is measurable. We obtain analytic formulas of the quantum-metric induced nonlinear conductivity and the nonlinear Drude conductivity both for the longitudinal and transverse conductivities. The quantum-metric induced nonlinear conductivity diverges at the Dirac point, while the nonlinear Drude conductivity is always finite. Hence, the quantum-metric induced nonlinear conductivity is dominant at the Dirac point irrespective of the relaxation time.