Giant Terahertz Photoconductance of Quantum Point Contacts in the Tunneling Regime

We report on the observation of the giant photoconductance of a quantum point contact (QPC) in the tunneling regime excited by terahertz radiation. Studied QPCs are formed in a $\mathrm{Ga}\mathrm{As}/(\mathrm{Al},\mathrm{Ga})\mathrm{As}$ heterostructure with a high-electron-mobility two-dimensional electron gas. We demonstrate that irradiation of strongly negatively biased QPCs by laser radiation with frequency $f=0.69\mathrm{THz}$ and intensity $50\mathrm{mW}/{\mathrm{cm}}^2$ results in two orders of magnitude enhancement of the QPC conductance. The effect increases with the dark conductivity decrease. It is also characterized by a strong polarization dependence and a drastic reduction of the signal by increasing the radiation frequency to 1.63 THz. We demonstrate that all experimental findings can be well explained by the photon-assisted tunneling through the QPC. Corresponding calculations are in good agreement with the experiment.

Figure 1

(a),(b) Sketch of Hall bar samples with two QPC structures obtained by gates placed on two parts of the sample. The size of the Hall bar is $280\times 20\mu {\mathrm{m}}^2$, the length and width of the arms of the gates are 25 and $6\mu \mathrm{m}$, respectively. The double arrow indicates the electric field vector $\mathit{E}(\omega )$ of normally incident THz radiation. The orientation of $\mathit{E}(\omega )$ with respect to the $x$ axis is described by the azimuthal angle $\alpha$, see (b). (c) Microphotograph of the gated part of the sample. (d),(e) Enlarged images of the bridged-gate QPC and a traditional split-gate QPC, respectively.

Figure 2

Dependence of the relative dark conductance $G_{\mathrm{dark}}(V_g^{\mathrm{eff}})/G_0$ on the effective gate voltage $V_g^{\mathrm{eff}}=V_g-V_g(0.1G_0)$. Here, the values of $V_g$ corresponding to $G=0.1G_0$ are $-2.23\mathrm{V}$ (bridged-gate sample A), $-2.05\mathrm{V}$ (split-gate sample B), and $-1.80\mathrm{V}$ (bridged-gate sample B). The dependencies are measured at $T=4.2\mathrm{K}$. The inset shows the temperature dependencies obtained at $V_g^{\mathrm{eff}}=-78\mathrm{mV}$ for the bridged-gate sample A and $V_g^{\mathrm{eff}}=-61\mathrm{mV}$ for the split-gate sample B.

Figure 3

Dependencies of the relative terahertz photoconductivity $G_{\mathrm{ph}}/G_{\mathrm{dark}}$ on the effective gate voltage $V_g^{\mathrm{eff}}$. Data are obtained for wafers A and B with different gate configurations by applying radiation with $f=0.69\mathrm{THz}$ and intensity $I=50\mathrm{mW}/{\mathrm{cm}}^2$. Solid curves show fits according to $G_{\mathrm{ph}}/G_{\mathrm{dark}}=A\exp (-V_g^{\mathrm{eff}}/a)$, where $A$ and $a$ are the fit parameters.

Figure 4

Dependencies of the terahertz photoconductance $G_{\mathrm{ph}}/G_0$ on the orientation of the terahertz radiation electric-field vector $\mathit{E}$ for bridged-gate samples A (blue triangles) and B (red circles). Data are obtained for the effective gate voltages $V_g^{\mathrm{eff}}=-51\mathrm{mV}$ (sample A) and $-24\mathrm{mV}$ (sample B) corresponding to the values of $G_{\mathrm{dark}}/G_0=0.0018$ and 0.003, respectively. The solid curve is a fit according to $G_{\mathrm{ph}}/G_{\mathrm{dark}}\propto (\cos \alpha {)}^2$. The inset shows the orientation of the vector $\mathit{E}$ corresponding to the signal maximum. Arrows on top illustrate the orientations of the radiation electric field vector for several values of $\alpha$.

Figure 5

(a),(b) Dependencies of the photoconductance $G_{\mathrm{ph}}/G_{\mathrm{dark}}$ on the effective gate voltage $V_g^{\mathrm{eff}}$ measured for two radiation frequencies in bridged-gate samples A and B, respectively.

Figure 6

Schematic drawings of the QPC potential barriers $U(x)$ in the plane of the QPC and their modifications upon action of the radiation electric field given by $U(x)+V(x)\cos (\omega t)$. (a) Electrostatic potential barrier in $x$ direction (solid blue curve) and radiation electric force $e{E}_{0,x}(\omega )\cos (\omega t)=[dV/dx]\cos (\omega t)$ acting on the electrons for one half of a period at $|x|<2W$ (solid magenta line). (b) Modification of the potential barrier due to the $E_x(\omega )$ component of the radiation field is shown for two instants in time, $t=0$ and $t=T/2$, shifted by half a period. (c) Electrostatic potential barrier in $x$ direction and dynamic barrier with the height $V_0$ caused by the $E_z(\omega )$ component of the radiation electric field. (d) Change of the potential $U(x)+V(x)\cos (\omega t)$ due to the $E_z(\omega )$ component shown for two instants in time, $t=0$ and $t=T/2$, shifted by half a period.

Figure 7

Calculated power dependencies of the photoconductance in a tunneling QPC in response to terahertz radiation of two frequencies. (a),(b) Dependencies on the magnitude of the radiation electric field strength $E_{0,x}^2$ and dynamic barrier amplitude $V_0^2$, respectively. Calculations are carried out using $T=0\mathrm{K}$, $E_F=27\mathrm{meV}$, $U_0=30\mathrm{meV}$, and $W=85\mathrm{nm}$. (b) The result of calculations for $f=0.69\mathrm{THz}$ and a slightly larger Fermi energy $E_F=27.5\mathrm{meV}$ (red dotted-dashed line).

Figure 8

Theoretical and experimental dependencies of (a) $G_{\mathrm{ph}}/G_0$ and (b) $G_{\mathrm{ph}}/G_{\mathrm{dark}}$ on the normalized dark conductivity $G_{\mathrm{dark}}/G_0$. The data in (a) are shown for bridged-gate sample A and split-gate sample B excited by radiation with $f=0.69\mathrm{THz}$ and intensity $I=50\mathrm{mW}/{\mathrm{cm}}^2$. Calculated curves are obtained with $U_0=30\mathrm{meV}$, $V_0=5.5\mathrm{meV}$, $W=115\mathrm{nm}$ (sample A), and 85 nm (sample B). The data in (b) are presented for bridged-gate sample A excited by radiation frequencies $f=0.69$ and 1.63 THz (intensity $I=50\mathrm{mW}/{\mathrm{cm}}^2$). Curves are calculated using $U_0=30\mathrm{meV}$, $W=115\mathrm{nm}$, and potentials $V_0=5.5\mathrm{meV}$ ($f=0.69\mathrm{THz}$) and 1 meV ($f=1.63\mathrm{THz}$). The inset shows dependencies for the bridged-gate sample B.