Nonlinear transport and noise thermometry in quasiclassical ballistic point contacts

We study nonlinear transport and nonequilibrium current noise in quasiclassical point contacts (PCs) defined in a low-density, high-quality two-dimensional electron system in GaAs. At not too high bias voltages $V$ across the PC, the noise temperature is determined by a Joule heat power and is almost independent on the PC resistance that can be associated with a self-heating of the electronic system. This commonly accepted scenario breaks down at increasing $V$, where we observe extra noise accompanied by a strong decrease of the PC's differential resistance. The spectral density of the extra noise is roughly proportional to the nonlinear current contribution in the PC, $\delta S\approx 2F^{*}\left|e\delta I\right|\sim V^2$, with the effective Fano factor $F^{*}<1$, indicating that a random scattering process is involved. A small perpendicular magnetic field is found to suppress both $\delta I$ and $\delta S$. Our observations are consistent with a concept of a draglike mechanism of the nonlinear transport mediated by electron-electron scattering in the leads of quasiclassical PCs.

Figure 1

Experimental layout. The PC constriction is formed with the help of split gates on the surface of the crystal. Current $I$ flows through the sample and drives the electronic distribution out of equilibrium. On top of the trivial self-heating of the 2DES, sketched by a color gradient, we are looking for a contribution of $e-e$ scattering of counterpropagating beams to current and noise (white circles mimic scattering electrons). The momentum space distributions at points A and B are sketched in the lower part of the figure. In the former case, the distribution is anisotropic with a bump of size $\left|eV\right|/v_F$ and a higher local temperature $T_A$, while in the latter case the distribution is locally equilibrium with a lower temperature $T_B$. The noise measurement scheme used for sample II is given on the left hand side.

Figure 2

Nonlinear transport regime in a quasiclassical PC. $R_{\mathrm{diff}}$ (lines, scale on the left) and $T_N$ (symbols, scale on the right) are plotted as a function of the bias voltage on the PC in sample I. The solid line and circles are taken in the absence of magnetic field, whereas the dashed line and triangles correspond to a perpendicular $B$ field of 67 mT.

Figure 3

Noise dependence on Joule heat power $\left(J\right)$. Square of the noise temperature is plotted against $J$ for the two samples. Open symbols correspond to sample I and $R_0\approx 2\text{k}\Omega$. Solid symbols correspond to sample II and $R_0\approx 0.5\text{k}\Omega$ (circles), $1.5\text{k}\Omega$ (triangles), and $3.4\text{k}\Omega$ (squares). In sample I the upper (lower) trace corresponds to $V<0$ $\left(V>0\right)$, whereas in sample II the bias symmetry is preserved. Dashed lines are extrapolations of the linear dependencies $T_N^2-T_0^2\propto J$ at small $J$, where the equilibrium temperature is $T_0=0.1$ K for sample I and $T_0=0.5$ K and $R_0\approx 1.5\text{k}\Omega$ for sample II. The data for sample I are shifted vertically for clarity, with the zero level indicated by a solid line. In this plot, the data for sample I were obtained in a separate run, compared to Fig. 2. We believe that a difference of 15% in $T_N$ between the data sets at $R_0\approx 2\text{k}\Omega$ is an artifact owing to a long-term drift of the gain of the cryogenic amplifier, which was not figured out during the experiment. Inset: $R_{\mathrm{diff}}$ vs $V$ for sample II (dashed lines, $T_0=0.5$ K) and $R_0\approx 1.5$, 2, and 3.4 $\mathrm{k}\Omega$ from bottom to top and for sample III (solid lines, $T_0=0.1$ K) and $R_0\approx 1.2$, 2.3, and 3.3 $\mathrm{k}\Omega$ from bottom to top. The data are vertically shifted for clarity.

Figure 4

Extra noise vs extra current. The spectral density $\delta S$ of the extra noise is plotted as a function of the nonlinear current contribution $\delta I$ for both polarities of $V$. Open symbols correspond to sample I and $R_0\approx 2\text{k}\Omega$ $(0.5\mathrm{mV}\le \left|V\right|\le 1$ mV). Solid symbols correspond to sample II and $R_0\approx 1.5\text{k}\Omega$ (triangles, $0.4\mathrm{mV}\le \left|V\right|\le 0.7$ mV), $2\text{k}\Omega$ (circles, $0.4\mathrm{mV}\le \left|V\right|\le 0.6$ mV), and $3.4\text{k}\Omega$ (squares, $0.5\mathrm{mV}\le \left|V\right|\le 0.9$ mV). Dashed lines are guides with a slope of $F^{*}=0.9$. For sample I, the data are obtained in the same run as in Fig. 2 and the scales on both axes are reduced by a factor of 2.