Third-order optical response in d-wave altermagnets: Analytical and numerical results from microscopic model

TL;DR

This paper provides a detailed theoretical analysis of third-order optical responses in d-wave altermagnets, highlighting their dependence on quantum geometric properties and offering analytical solutions verified by numerical calculations.

Contribution

It introduces a microscopic model-based framework for understanding third-order optospintronic responses in altermagnets, emphasizing quantum metric and connection effects.

Findings

Derived closed-form analytical solutions for third-order photoconductivities when $V_\delta=0$.

Presented perturbative analytical solutions for finite $V_\delta$ and verified them numerically.

Established a comprehensive theoretical description of third-order responses in d-wave altermagnets.

Abstract

Altermagnets represent a novel category of magnetic materials characterized by zero net magnetization yet featuring spin-split band structures, and they demonstrate distinctive orbital-spin locking phenomena. Commencing from the minimal multi-orbital tight-binding Hamiltonian of d-wave altermagnets, we conduct an analysis of the general formulas for the third-order injection and shift currents. These currents are solely determined by the quantum metric and quantum connection, being free from Berry curvature contamination. In the ideal scenario where the $\delta$-bond hopping $V_\delta$ approaches zero ($V_\delta = 0$), we derive closed-form analytical solutions for the third-order photoconductivities. For the general situation with a finite value of $V_\delta$, we present a perturbative analytical solution within the limit of $V_\delta \ll V_\pi$, and this solution is verified through numerical calculations. Our research establishes a comprehensive theoretical description of the third-order optospintronic responses in d-wave altermagnets based on a microscopic model. Moreover, it offers a viable approach for the experimental observation of pure quantum geometric effects.