Anomalous Knudsen effect signaling long-lived modes in 2D electron gases

Abstract

Proper analysis of electron collisions in two spatial dimensions leads to the conclusion, that the odd harmonics of the electron distribution function decay much slower than the even ones at finite temperatures. The number of long-lived odd harmonics quickly shrinks with increasing temperature. Focusing on a channel geometry with boundary scattering, we show that such behavior of the odd decay rates leads to a characteristic behaviour of the conductance that we dub anomalous Knudsen effect: it initially grows with temperature but then starts to decrease, forming a peak. Further increase of the temperature forces the conductance to grow again due to the Gurzhi effect, associated with the crossover from ballistic to hydrodynamic transport. The simultaneous observation of the Gurzhi dip preceded by the anomalous Knudsen peak constitutes a particular signature of the long-lived modes in 2D electron transport at low temperatures.

Figures (4)

• Figure 1: Normalized conductance $G/G_{T=0}$ as a function of temperature for different fixed values of the impurity scattering rate $\gamma_i$: $(a,b)$ for the Soffer parameter $\alpha=0.8$; $(c,d)$ for the Soffer parameter $\alpha=20.0$. Panels $(a,c)$ compare the computed conductances for the collision kernel with the scattering times given by Eqs. \ref{['tau-even']} and \ref{['tau-odd']} (solid lines) and for the collision kernel with the mode-independent scattering times $1/\tau_{ee}^{(n\geqslant2)} \equiv 1/\tau_{ee}^{(\mathrm{even})}$ (dash-dotted lines). Panel $(b)$ zooms in on the part of panel $(a)$ highlighted by dashed rectangle and compares solid lines of panel (a) with the perturbative result of Eq. \ref{['Xi-first-order']} obtained using Eqs. \ref{['tau-even']} and \ref{['tau-odd']} (dashed lines). Analogously, panel $(d)$ zooms in on panel $(c)$. The corresponding values of $\gamma_i$ are colour-coded.
• Figure 2: Normalized real part of the conductance $\mathop{\mathrm{Re}}\nolimits{[G(\omega)]}/\mathop{\mathrm{Re}}\nolimits{[G_{T=0}(\omega)]}$ as a function of temperature for different fixed values of the ac drive frequency $\omega$: $(a,b)$ for the Soffer parameter $\alpha=0.8$; $(c,d)$ for the Soffer parameter $\alpha=20.0$. Panels $(a,c)$ compare the computed conductances for the collision kernel with the scattering times given by Eqs. \ref{['tau-even']} and \ref{['tau-odd']} (solid lines) and for the collision kernel with the mode-independent scattering times $1/\tau_{ee}^{(n\geqslant2)} \equiv 1/\tau_{ee}^{(\mathrm{even})}$ (dash-dotted lines). Panel $(b)$ zooms in on the part of panel $(a)$ highlighted by dashed rectangle and compares solid lines of panel (a) with the perturbative result of Eq. \ref{['Xi-first-order']} obtained using Eqs. \ref{['tau-even']} and \ref{['tau-odd']} (dashed lines). Analogously, panel $(d)$ zooms in on panel $(c)$. The corresponding values of $\omega$ are colour-coded. The impurity scattering rate was fixed at $\gamma_i = 0.05$.
• Figure S1: Normalized conductance $G/G_{T=0}$ as a function of temperature for different fixed values of the impurity scattering rate $\gamma_i$ for the collision integral with the odd scattering rates given by Eq. \ref{['tau-odd']} (solid lines) and for smoothly saturating odd scattering rates $\gamma_\mathrm{ee}^{(2k+1)} = \gamma_{ee}^{(\mathrm{odd})}(2k+1)^4/\left[1 + (2k+1)^4\gamma_{ee}^{(\mathrm{odd})}/\gamma_{ee}^{(\mathrm{even})}\right]$ (dash-dotted lines): $(a)$ for Soffer parameter $\alpha=0.8$; $(b)$ for Soffer parameter $\alpha=20.0$. The difference between the solid line and the dashed-dotted line for a given choice of $\gamma_i$ is small.
• Figure S2: Normalized conductance $G/G_{T=0}$ as a function of temperature for different fixed values of the impurity scattering rate $\gamma_i$ for the collision integral with collision kernel with the mode-independent scattering times $1/\tau_{ee}^{(n\geqslant2)} \equiv 1/\tau_{ee}^{(\mathrm{even})}$