Non-Hermitian quantum geometric tensor and nonlinear electrical response

Abstract

We demonstrate that the non-Hermitian quantum geometric tensor (QGT) governs nonlinear electrical responses in systems with a spectral line gap. The quantum metric, which is the symmetric component of the QGT and takes complex values in non-Hermitian systems, generates an intrinsic nonlinear conductivity independent of the scattering time. In contrast, the full complex-valued QGT induces a distinct conductivity that depends explicitly on the wavepacket width. Using one- and two-dimensional non-Hermitian models, we establish a direct link between nonlinear dynamics and the QGT, thereby connecting quantum state geometry to observable transport phenomena. Crucially, we reveal that the finite wavepacket width fundamentally alters non-Hermitian transport -- a mechanism strictly absent in Hermitian systems. This framework elucidates non-Hermitian response theory by revealing how the complex geometry of quantum states, captured by the QGT, and the wavepacket width jointly encode transport in open and synthetic quantum matter.

Figures (5)

• Figure 1: (Color online) Schematic of the non-Hermitian SSH lattice model.
• Figure 2: SODCc in the non-Hermitian SSH model. (a) Band dispersion for $t_2/t = 1.1$. (b) Intrinsic contribution (order $\tau^0$) and the coefficient of the $\tau^2$ term in the SODCc. (c) Ratio of the intrinsic contribution to the total SODCc as a function of $T$ for $t_2/t = 1.1$; (d) the same ratio as a function of $t_2/t$ for $T = 0.1$. Other parameters: $t_1/t = t_2/t + i\,0.2$.
• Figure 3: SODCc at the boundary of a Chern insulator. (a) Band dispersion of the Hamiltonian in Eq. (\ref{['chern']}). (b) Ratio of the intrinsic contribution to the total SODCc as a function of temperature $T$. The parameters are $m = -1.9$ and $\eta = 1/\sqrt{80}$.
• Figure 4: Band dispersion (a), (c) SODCc $\sigma_{xyy}$ as a function of $T$, and momentum-space distributions of the Berry curvature (b) and the $xy$-component of the QM, $G_{xy}$ (d), for parameters $m = 0.8$, $\gamma = 0.5$.
• Figure 5: Band dispersion (a), SODCc $\sigma_{xxx}$ as a function of $W$ (b), and momentum-space distributions of typical components of the QGT (c-f). Parameters: $m = 0.8 - 0.02i$, $\gamma = 0.5$.