Joule heating and electronic Gurzhi effect in hydrodynamic differential transport in an electron liquid

Abstract

We perform a differential resistance study in the hydrodynamic regime of electron liquid in GaAs/AlGaAs quantum wells. At zero magnetic field ($B$) a Lorentzian profile occurs in the nonlinear transport driven by a U-turn (ac) current loop, in (ac + dc) measurements a minimum deepens with the external dc current bias ($j_{dc}$). Our analysis shows that the observed electronic transport valley induced by $j_{dc}$ is attributed to Joule heating effect on the electron temperature ($T_{e}$) of electron liquid. Quantitatively, we demonstrate that the viscosity resistivity ($Δρ$) is proportional to $T^{-2}$ and is consistent with the dc-current induced electronic Gurzhi effect in various configurations of measurement.

Figures (6)

• Figure 1: (Color online). Panel (a): Differential (longitudinal) resistance $R^{\ast}_{xx}$ measured at 1.6 K using U-shape configuration. (b): The first derivative of resistivity $R^{(1)}=(R^{\ast}_{xx}(I)-R^{\ast}_{xx}(0))/2I_{dc}$ with respect to dc current. (c): Fitting curves of the traces in panel (a) via the superposition of two Lorentzian profiles.
• Figure 2: (Color online). Panel (a): Lorentzian Fitting parameter: $\tau_{2, ee}$ versus applied dc current. The red dashed fitting curve shows that $\tau_{2, ee}$ follows the form of Eq.(4), in which $\theta$ is a coefficient. (b): Normalized differential resistance($d\rho_{xx}/di$) at different dc current. Both $B$-field and dc current are normalized by parameter $B_0=me\tau_2$ and $i_0$. (c), (d): 3D calculated contour plot of resistance $\rho$ and differential magnetoresistance $d\rho_{xx}/di$ are obtained via Eq. (\ref{['eq6']}), respectively.
• Figure 3: (Color online). Panel (a): Second momentum relaxation rate ($1/\tau_{2, ee}$) (black solid triangles) and its parabolic fitting curve versus dc current ($j_{dc}$) in the U-shape measurement of Structure I at 1.6 K. (b): Slip length $l_s$ (black solid squares) and viscosity $\eta$ (red open circles) obtained from U-shape measurements of Structure-I at 1.6 K.
• Figure 4: (Color online). Panel (a): $T$-dependent resistance with a U-turn current configuration of measurement of Structure I at zero dc-current. (b): $T$-dependent resistance with an external U-turn current configuration of Structure I at a bias of $I_{dc} = 2\ \mu$A. (c): $T$-dependent slip length $l_{s}$ (black solid squares) and viscosity $\eta$ (red solid circles). (d): Calculated momentum relaxation rate $1/\tau$ (black solid triangles) and second momentum relaxation rate $1/\tau_{2}$ (red open circles) versus $T$, along with theoretical values (highlighted by dashed lines).
• Figure 5: (Color online). The equivalent current densities at various temperatures (black solid squares) are estimated via equal second momentum rates with Eq. (5) and (8), and the heating effect from $j_{dc}$ versus $T_{e}$ (red solid circles) is deduced with Eq. (11).