Quantized nonlinear transport and its breakdown in Fermi gases with Berry curvature

TL;DR

The paper addresses whether Berry curvature on the Fermi surface alters quantized nonlinear transport in 2D noninteracting Fermi gases. Using a semiclassical Boltzmann framework in a three-terminal setup, it derives that the homogeneous nonlinear response is quantized and proportional to the Euler characteristic of the Fermi sea, $G(\omega_1,\omega_2)=\frac{\omega_1+\omega_2}{i\omega_1\omega_2}\frac{e^3}{h^2}\chi_F$, with Berry curvature contributions canceling in translation-invariant systems. It then analyzes a slowly varying trap, showing that Berry curvature induces an anomalous velocity which splits the response into a quantized topological part and a nonquantized Berry-curvature–dependent part, leading to breakdown of quantization except at trap extrema where $\nabla_{\bf r}U_{\bf r}=0$. The results point to ultracold-atom experiments as a platform to observe both the quantized nonlinear transport and its breakdown, enabling direct probes of Fermi-sea topology and Berry curvature effects in topological bands.

Abstract

Quantized transport not only exist in gapped topological states but also in metallic states. Recently, Kane proposed a quantized nonlinear conductance in ballistic metals whose value is determined by the Euler characteristic of the Fermi sea [Phys. Rev. Lett. 128, 076801 (2022)]. In this paper, we consider two-dimensional noninteracting fermionic systems whose Fermi surface has nonvanishing Berry curvature. We find that the Berry curvature at the Fermi surface does not affect the quantized nonlinear transport for translationally invariant systems. When spatial inhomogeneity is introduced, such quantization breaks down due to the combined effect of Berry curvature and the gradient of local potential. Such breakdown of quantization can be observed in trapped ultracold atoms with topological bands.

Figures (1)

• Figure 1: a: Illustration of three-terminal second-order nonlinear AC conductance measurement. The three terminals intersect at a single point and the frequency-dependent conductance is proportional to the Euler characteristic of the Fermi sea. b: This measurement is equivalent to a thought experiment with consecutive voltage pulses $V_1$ and $V_2$ applied in the left- and lower-half planes, respectively, which leads to quantized charge transport $Q$ to the first quadrant given by the Euler characteristic.