Viscous Electron Flow and Nonlinear Magnetotransport in 2D Channels

TL;DR

This work addresses nonlinear magnetotransport in a viscous 2D electron fluid in GaAs quantum wells. By combining magnetotransport measurements in long, narrow channels with a theory that separates correlation-driven memory effects (non-Newtonian viscosity) from current-induced heating, the authors show a nonmonotonic differential magnetoresistance whose peak is shaped by extended electron collisions and shifts with heating. They extract a hydrodynamic regime characterized by $l_{ee} < W < l$ and find $r \approx 2.1$–$2.4$ in the nonlinear model, demonstrating that nonlinear transport can diagnose correlated electron states and momentum relaxation in 2D fluids. The results advance understanding of quantum hydrodynamics in solids and suggest pathways toward observing electronic pre-turbulent dynamics.

Abstract

We examine nonlinear transport in a viscous two-dimensional electron fluid within narrow GaAs channels. The differential magnetoresistance shows nonmonotonic behavior, a signature of electron pairing in the hydrodynamic regime. Theoretical models that account for both the influence of these interactions on shear stress relaxation and viscosity changes from electron heating show good agreement with the data. The nonlinear regime thus reveals how such correlated states govern the hydrodynamic behavior of the electron fluid. Our findings establish the nonlinear transport regime as a powerful probe for dissecting the complex interplay of correlated electron states and momentum relaxation in the hydrodynamic flow of an electron fluid.

Figures (8)

• Figure 1: (Color online) Image of the central part of the Hall bar with 10 contacts. (b) Hydrodynamic velocity flow in configuration, when current is directed between contacts 9 and 8. Sketch of the velocity flow profile in a device within a channel of narrow width of $W = 6 \mu m$.
• Figure 2: (Color online) (a) Temperature-dependent magnetoresistivity of narrow GaAs channel, sample A. (b) Temperature-dependent magnetoresistivity calculated from equation \ref{['magnetoresistance']}, sample A .
• Figure 3: (Color online) Evolution of differential magnetoresistance $r_d$ with increasing dc bias for sample A (a) and sample B (c). Magnetoresistivity calculated from equation \ref{['magnetoresistance']} for sample A (b) and sample B (d).
• Figure 4: (Color online) The characteristic lengths $l$, $l_2$ as a function of temperature for two reference samples; (black -Sample A, red- sample B). Horizontal line- the width of the sample W.
• Figure 5: (Color online) (a) Comparative analysis of the fitting parameter $\l_{2}$ for Sample A, showing its dependence on temperature (circles) and DC bias current (solid line). (b) Comparative analysis of the fitting parameter $\l_{2}$ for Sample B, showing its dependence on temperature (circles) and DC bias current ( solid line). (c) The extracted electron temperature as a function of DC current for Samples A and B, as determined from the analyses presented in (a) and (b).The solid lines show the expected trend for a quadratic dependence ($\sim I_{DC}^2$).