Viscous Electron Flow and Nonlinear Magnetotransport in 2D Channels

Technical Summary: Viscous Electron Flow and Nonlinear Magnetotransport in 2D Channels

Problem Statement
The hydrodynamic regime of electron transport, characterized by collective fluid-like behavior where the electron-electron mean free path ($l_{ee}$) is shorter than the momentum-relaxing mean free path ($l$), has been extensively studied in the linear response regime. However, accessing the nonlinear domain in electronic systems remains challenging due to the typically low Reynolds numbers ($Re \sim 10^{-2}$) of state-of-the-art devices. While classical fluids exhibit rich nonlinear effects at high velocities, electronic systems require alternative pathways to observe such phenomena. Recent theoretical work suggests that strong magnetic fields and correlated electron interactions could induce nonlinear behavior through "extended collisions" of electron pairs on cyclotron orbits, leading to non-Newtonian viscosity and memory effects. A significant challenge in experimental verification is disentangling these correlation-driven mechanisms from conventional current-induced electron heating, which also modifies scattering rates and can mimic nonlinear flow effects.

Methodology
The authors investigated nonlinear magnetotransport in high-purity GaAs two-dimensional electron gas (2DEG) channels. The study utilized Hall-bar devices fabricated from high-quality GaAs quantum wells (nominal width 14 nm, electron density $\approx 9.0 \times 10^{11} \text{ cm}^{-2}$, mobility $2 \times 10^6 \text{ cm}^2/\text{Vs}$). The devices featured narrow channels ($W = 6 \, \mu\text{m}$) with ten voltage probes to facilitate multiterminal measurements.

Experiments were conducted in a variable temperature insert cryostat. The differential resistance ($r_d = dV_{xx}/dI_{dc}$) was measured as a function of magnetic field ($B$) and direct current bias ($I_{dc}$) at low temperatures ($T = 2.5 \text{ K}$). The measurement configuration involved driving current between specific contacts (9 and 8) and measuring voltage across others (3 and 4) to enhance hydrodynamic effects.

Theoretical analysis involved two primary components:

1. Heating Effects: A model based on Poiseuille flow in a magnetic field (Ref. [12]) was used to describe the linear regime and electron heating. This model accounts for viscous relaxation and ballistic scattering, allowing the extraction of electron temperature ($T_e$) as a function of $I_{dc}$ by fitting the broadening of magnetoresistance peaks.
2. Nonlinear Correlation Effects: The authors applied a theoretical framework (Ref. [26]) describing "extended collisions" where electron pairs form correlated states on cyclotron orbits. This model introduces a non-local-in-time memory effect into shear stress relaxation, resulting in a velocity-gradient-dependent (non-Newtonian) viscosity. The model utilizes dimensionless parameters: $r$ (ratio of pair correlation lifetime to quasiparticle scattering time) and $\tilde{\nu}$ (scaled nonlinearity parameter).

Key Results

• Non-Monotonic Magnetoresistance: The differential magnetoresistance ($r_d$) exhibits a pronounced non-monotonic behavior at high currents, characterized by a distinct peak whose position shifts to higher magnetic fields as $I_{dc}$ increases. This contrasts with the monotonic Lorentzian profile observed in the linear regime.
• Electron Heating: Analysis of the zero-field resistivity and peak broadening confirms that the applied DC current significantly increases the electron temperature ($T_e$), reaching up to $\approx 40 \text{ K}$. The dependence of $T_e$ on $I_{dc}$ follows a quadratic trend ($I_{dc}^2$) at low currents, deviating at higher currents due to efficient electron-phonon energy loss.
• Non-Newtonian Viscosity: By comparing experimental data with the theoretical model of Ref. [26], the authors demonstrate that the observed nonlinearity is a composite effect. The shift in the peak position is attributed to electron heating (which alters the relaxation time $\tau_{2,ee}$), while the enhancement of the peak amplitude is driven by correlation-induced non-Newtonian viscosity.
• Parameter Extraction: The data is consistently described by a correlation parameter $r \approx 2.1\text{--}2.4$. The dimensionless nonlinearity parameter $\tilde{\nu}$ extracted from the fit ($4\text{--}6$) is significantly smaller than the value calculated from the applied electric field ($\approx 10^4$). The authors attribute this discrepancy to an overestimation in the theoretical characteristic distance for paired electrons, suggesting that only nearby pairs ($|r_1 - r_2| \sim a_B$) contribute significantly to scattering cross-section changes in screened Coulomb interactions.

Significance and Claims
The paper establishes the nonlinear transport regime as a powerful probe for dissecting the interplay between correlated electron states and momentum relaxation. The primary significance of the work lies in:

1. Confirmation of Non-Newtonian Behavior: The findings provide compelling evidence for a non-Newtonian electron fluid in GaAs quantum wells, where effective shear viscosity depends on the flow gradient due to electron-electron correlations.
2. Mechanism Separation: The study successfully separates the contributions of current-induced heating and correlation-driven memory effects. It demonstrates that heating shifts the magnetoresistance peak, while nonlinear hydrodynamic effects enhance its amplitude.
3. Experimental Validation of Theory: The results validate the theoretical framework of "extended collisions" and memory effects in electron hydrodynamics, showing good agreement with experimental data when appropriate corrections for interaction ranges are applied.
4. New Frontier: The work opens an experimental avenue for investigating quantum hydrodynamics and the potential onset of electronic turbulence in condensed matter systems, moving beyond the linear Stokes-Ohm regime.

The authors conclude that their findings confirm the existence of a non-Newtonian electron fluid and establish a refined framework for interpreting nonlinear transport where memory effects and energy relaxation govern hydrodynamic behavior.