Nonequilibrium Exchange Nonlinear Hall Effect

Abstract

Quantum geometric electronic responses are often viewed through a non-interacting lens: independent quasiparticles accumulate Berry phases as they move through a static crystal and background potential. Here we argue that the combined action of electron-electron interactions and an out-of-equilibrium many-body state can produce striking departures from this familiar picture. We demonstrate how nonequilibrium exchange interactions produce a nonequilibrium collective quantum geometry distinct from that of its equilibrium ground state. We find this manifests as an exchange induced nonlinear Hall effect with nonlinear Hall current signals competitive with that of well-known non-interacting mechanisms. This highlights the critical role electron interactions and nonequilibrium states can play in the nonlinear response of quantum matter.

Figures (3)

• Figure 1: Nonequilibrium collective quantum geometry (a) Bloch wavefunction variation with $\mathbf{k}$ characterizes its momentum-space quantum geometry; e.g., Berry phase across small (red) loops track momentum-space Berry curvature. (c) In non-interacting materials, these are locked to the equilibrium state, e.g., equilibrium spin density in a PT symmetric antiferromagnet vanishes. (b) When pushed out-of-equilibrium by an applied electric field, a collective quantum geometry develops, mirroring the nonequilibrium state e.g., tracked by (d) a nonequilibrium spin density.
• Figure 2: Spin Dependent SBP distributions. SBP $S^{\eta\alpha} (\mathbf{k})$ tensor distributions obtained from Eq. (\ref{['eq:deltaA']}); here we have used $H_{\rm PT}^{(0)}$, see text. Note that $S^{1x}(\mathbf{k})$ and $S^{2y} (\mathbf{k})$ vanishes for $H_{\rm PT}^{(0)}$. The in plane contributions are monopolar $S^{2x}(\mathbf{k})$ and $S^{1y}(\mathbf{k})$ [panel (a) and (c)] while the spins induced in $\hat{z}$ direction are dipolar $S^{3x} (\mathbf{k})$ and $S^{3y} (\mathbf{k})$ [panel (b) and (d)]
• Figure 3: ENH in noncentrosymmetric materials. (a) ENH second-order conductivity $\sigma_{\rm ENH}^{(\rm T)}$ (red) and BCD $\sigma_{\rm BCD}$ (blue) for a non-magnetic noncentrosymmetric $H_{\rm T}^{(0)} (\mathbf{k})$ (see text). (b) The ratio of $\sigma_{\rm ENH}^{(\rm T)}$ to $\sigma_{\rm BCD}$ grows with interaction strength and chemical potential becoming competitive at larger chemical potentials and interaction strength. The relaxation time scale for plots (a) and (b) are chosen to be $\tau=0.5\ \text{ps}$. (c) Contrasting $\sigma_{\rm ENH}^{(\rm PT)}$ (red) and $\sigma_{\rm INH}$ (blue) for a PT-symmetric magnetic $H_{\rm PT}^{(0)}(\mathbf{k})$ (see text). (d) Ratio of $\sigma_{\rm ENH}^{(\rm PT)}$ against $\sigma_{\rm INH}$ indicates ENH is competitive across a wide parameter space. Other model parameters are $\Delta = 50\, {\rm meV}$, $v_{x,y} = 4 \times 10^5 \, {\rm m} {\rm s}^{-1}$, $\alpha/\hbar v = 0.1$, $q_s=0.2\ \text{nm}^{-1}$ for both $H_{\rm T}^{(0)}$ and $H_{\rm PT}^{(0)}$ in panel (a) and (c) respectively.