Evidence for charging effects in CdTe/CdMgTe quantum point contacts

Here we report on fabrication and low-temperature magnetotransport measurements of quantum point contacts patterned from a novel two-dimensional electron system—CdTe/CdMgTe modulation doped heterostructure. From the temperature and bias dependence we ascribe the reported data to evidence for a weakly bound state which is naturally formed inside a CdTe quantum constriction due to charging effects. We argue that the spontaneous introduction of an open dot is responsible for replacement of flat conductance plateaus by quasiperiodic resonances with amplitude less than $2e^2/h$, as found in our system. Additionally, below 1 K a pattern of weaker conductance peaks, superimposed upon wider resonances, is also observed.

Figure 1

Longitudinal ${\rho }_{xx}$ and Hall ${\rho }_{xy}$ resistances versus perpendicular magnetic field $B$ for two-dimensional electron gas in CdTe/CdMgTe quantum well (at temperature $1.4$ K). Inset shows a Dingle plot of the reduced SdH oscillations amplitude $r=\Delta {\rho }_{xx}/\mathcal{X}{\rho }_0$, where ${\rho }_0={\rho }_{xx}\left(0\right)$ and $\mathcal{X}$ is the function of temperature and inverse magnetic field, defined in Ref. 4.

Figure 2

The zero-bias differential conductance $G=dI/dV$ (in $G_0=2e^2/h$ units) as a function of gate voltage $V_{\text{g}}$ for temperatures $T$ from $0.330$ to $1.745$ K. The inset displays an electron micrograph of a typical device, electrical contacts are shown schematically, side gates are marked with $g1$ and $g2$. $V_{\text{g}}$ have been applied symmetrically, i.e., $V_{\text{g}}=V_{\text{g1}}=V_{\text{g2}}$.

Figure 3

(a) Oscillating part of the zero-bias conductance, defined as $\Delta G=G\left(T\right)-G(T=1.745\text{K})$ as a function of temperature $T$, vs gate voltage $V_{\text{g}}$. Black line corresponds to $T=0.33$ K, red (or gray) line corresponds to $T=1.34$ K, all intermediate temperatures are the same as in Fig. 2. (b) The absolute values of $\Delta G$ as a function of temperature plotted vs $T^{-3/2}$. Data marked with blue (dark gray) symbols and lines have been obtained for two maxima of $\Delta G$, data marked with red (gray) symbols and lines, for two strongest minima. Corresponding gate voltages are indicated with small dots in (a).

Figure 4

(a) $G\left(V_{\text{g}}\right)$ for $T=0.27$ K at various in-plane magnetic fields $B_{\parallel }$, from 0 (bottom) to $7.3$ T (top), collected at different cooldown cycle than data shown in Fig. 2. For clarity curves are shifted vertically by offset of $0.3G_0$. (b) Conductance $\Delta G$ oscillations as a function of $V_{\text{g}}$ and $B_{\parallel }$, data are obtained from $G\left(V_{\text{g}}\right)$ curves by subtracting a smooth background from each. Labels $\mathsf{A}$ and $\mathsf{B}$ mark up first two conductance resonances for $V_{\text{g}}>-2.25$ V, which are split in magnetic field to spin-up and spin-down components (also indicated, negative Landé factor is assumed). Labels $\alpha$, $\beta$, and $\gamma$ denote weaker resonances for $V_{\text{g}}<-2.25$ V, which are not split.

Figure 5

(a) $G\left(V_{\text{g}}\right)$ and $\partial G/\partial V_{\text{g}}$ for $T=0.3$ K at various source-drain voltages $V_{\text{SD}}$, from $2.6$ (left) to $1.9$ mV (right) with $0.1$-mV steps. Curves are successively shifted horizontally by $0.1$ V for clarity. (b) Transconductance $\partial G/\partial V_{\text{g}}$ as a function of $V_{\text{g}}$ and $V_{\text{SD}}$. Dashed lines indicate shift of plateaulike regions. Data differ with previous on pinch-off voltage, because they have been measured for a subsequent cooldown cycle.

Figure 6

(a) Model of the external confining potential $V_{\mathrm{conf}}$ for CdTe quantum point contact. Shape of the device in $(x,y)$ plane is shown on the left. On the right $V_{\mathrm{conf}}\left(y\right)\sim y^4$ is plotted at the constriction of $W_0$ width (narrower curve) and also far away from it (wider curve), $E_{\mathrm{g}}$ is the energy gap. (b) Local density of electrons $n(x,y)$ calculated self-consistently at $T=0$ in Hartree approximation for two values of $W_0$. Note different scalings on $x$ and $y$ axes. White curves represent cross sections of electron density taken along $y=0$ line.