Transverse rectification in density-modulated two-dimensional electron gases

We demonstrate tunable transverse rectification in a density-modulated two-dimensional electron gas (2DEG). The density modulation is induced by two surface gates, running in parallel along a narrow stripe of 2DEG. A transverse voltage in the direction of the density modulation is observed, i.e., perpendicular to the applied source-drain voltage. The polarity of the transverse voltage is independent of the polarity of the source-drain voltage, demonstrating rectification in the device. We find that the transverse voltage $U_y$ depends quadratically on the applied source-drain voltage and nonmonotonically on the density modulation. The experimental results are discussed in the framework of a diffusion thermopower model.

Figure 1

(a) Schematic picture of the rectifier and the experimental setup. The rectifier is measured in the push-pull configuration, i.e., half of the source-drain voltage $U_{\mathrm{sd}}$ is applied at one terminal and the other half is applied at the second terminal. The source-drain voltages and the gate voltages $U_{\mathrm{g}1}$ and $U_{\mathrm{g}2}$ are both referenced to the ground potential. The transverse voltage $U_y^{\exp }$ is measured between the left and right voltage probe. The 2DEG defined by an etched mesa is indicated in blue, the metallic gate electrodes in red. The carrier density in the area marked by the blue rectangle is sketched in (b) for $U_{\mathrm{g}1}<U_{\mathrm{g}2}<0\mathrm{V}$, which gives a ratchet-type potential landscape. Here, $E_F$ marks the Fermi energy and CB denotes the conduction band (dark-blue curve).

Figure 2

(a) Dependence of the transverse voltage $U_y^{\exp }$ on the source-drain voltage $U_{\mathrm{sd}}$. The gate voltage $U_{\mathrm{g}2}$ is applied from $-0.3\mathrm{V}$ (black trace) to $+0.3\mathrm{V}$ (dark green trace) in steps of $0.05\mathrm{V}$, while gate 1 remains grounded ($U_{\mathrm{g}1}=0\mathrm{V}$). The yellow trace shows the transverse voltage for $U_{\mathrm{g}2}=0\mathrm{V}$. The dashed, black line is an exemplary parabolic fit for $U_{\mathrm{sd}}\le 25\mathrm{mV}$. (b) Transverse voltage $U_y^{\exp }$, when the role of the gates is switched, i.e., the gate voltage $U_{\mathrm{g}1}$ is varied, while gate 2 remains grounded.

Figure 3

(a) Rectification efficiency $a_U^{\exp }$ as a function of $U_{\mathrm{g}2}$ for $U_{\mathrm{g}1}=0\mathrm{V}$, where $a_U^{\exp }$ is the coefficient of an $a_U^{\exp }{U}_{\mathrm{sd}}^2$ fit on the traces shown in Fig. 2 for $U_{\mathrm{sd}}$ smaller than $25\mathrm{mV}$. (b) Contour plot of the rectification efficiency $a_U^{\exp }$ as a function of $U_{\mathrm{g}1}$ and $U_{\mathrm{g}2}$. The black dashed line represents $U_{\mathrm{g}1}=U_{\mathrm{g}2}$ and the gray dashed line shows the cross section, which is plotted in (a). The distance between the contour lines is $0.10{\mathrm{V}}^{-1}$ with additional contour lines at $\pm 0.05{\mathrm{V}}^{-1}$. (c) $a_U^{\exp }$ in dependence on $U_{\mathrm{g}2}$ for $U_{\mathrm{g}1}=-0.3\mathrm{V}$. This trace matches the cross section of the contour plot in (b) at $U_{\mathrm{g}1}=-0.3\mathrm{V}$.

Figure 4

Temperature dependence of the rectification efficiency $a_U^{\exp }$ (left axis). The black, red, and green traces show $a_U^{\exp }$ as a function of the temperature $T$ for $U_{\mathrm{g}2}=-0.3$, $-0.2$, and $-0.1\mathrm{V}$, respectively. The blue trace shows the temperature dependence of the mobility $\mu$ measured on the reference sample B (right axis).

Figure 5

Schematic sketch of the rectifier. The system is divided into four regions: the two stripes of the electron channel plus the two voltage probes. The current-free voltage probes have carrier density $n_0$; the two stripes have (tunable) carrier concentrations $n_1$ and $n_2$.

Figure 6

Energy dependence of the elastic scattering time ${\tau }_{\mathrm{e}}$ (blue) and the inelastic scattering time ${\tau }_{\mathrm{i}}$ (red). The first data points match $U_{\mathrm{g}2}=-0.2\mathrm{V}$ and the gate voltage increases by $0.05\mathrm{V}$ for each data point. The lines correspond to the linear fits of the data.

Figure 7

Heating correction to the temperature of the electron system for $I_{\mathrm{sd}}=5\mu \mathrm{A}$, $U_{\mathrm{g}1}=0\mathrm{V}$, and three different values for $U_{\mathrm{g}2}$: $U_{\mathrm{g}2}=-0.2\mathrm{V}$ (blue), $U_{\mathrm{g}2}=-0.15\mathrm{V}$ (green), and $U_{\mathrm{g}2}=-0.1\mathrm{V}$ (red). The horizontal dashed lines are the heating temperatures for channels with infinite width for the gate voltage $U_{\mathrm{g}2}$ of corresponding color. The gray region shows the electron transport channel and the vertical dashed lines separate the two stripes with different carrier density from the voltage probes left and right of the channel.

Figure 8

(a) Calculated rectification efficiency $a_U^{\mathrm{theo}}$ as a function of $U_{\mathrm{g}2}$ for $U_{\mathrm{g}1}=0\mathrm{V}$. (b) Contour plot of the calculated rectification efficiency $a_U^{\mathrm{theo}}$ as a function of $U_{\mathrm{g}1}$ and $U_{\mathrm{g}2}$. The distance between the contour lines is $0.1{\mathrm{V}}^{-1}$ with additional contour lines at $\pm 0.05{\mathrm{V}}^{-1}$. (c) $a_U^{\mathrm{theo}}$ in dependence on $U_{\mathrm{g}2}$ for $U_{\mathrm{g}1}=-0.3\mathrm{V}$. This trace matches the cross section of the contour plot in (b) at $U_{\mathrm{g}1}=-0.3\mathrm{V}$.

Figure 9

Comparison between the measured and the calculated rectification effect: (a) Dependence of the measured transverse voltage $U_y^{\exp }$ (blue dots) and the calculated transverse voltage $U_y^{\mathrm{theo}}$ (red trace) on the heating current $I_{\mathrm{sd}}$ for $U_{\mathrm{g}1}=0\mathrm{V}$ and $U_{\mathrm{g}2}=-0.2\mathrm{V}$. (b) Dependence of the measured rectification efficiency $a_U^{\exp }$ (blue dots) and the calculated rectification efficiency $a_U^{\mathrm{theo}}$ (red trace) on $U_{\mathrm{g}2}$.