Gate-defined quantum point contact in an InSb two-dimensional electron gas

We investigate an electrostatically defined quantum point contact (QPC) in a high-mobility InSb two-dimensional electron gas. Well-defined conductance plateaus are observed, and the subband structure of the QPC is extracted from finite-bias measurements. The Zeeman splitting is measured in both in-plane and out-of-plane magnetic fields. We find an in-plane $g$ factor $|g_{\parallel }^{*}|\approx 40$. The out-of-plane $g$ factor is measured to be $|g_{\perp }^{*}|\approx 50$, which is close to the $g$ factor in the bulk.

Figure 1

(a) Layer structure of the quantum well (QW) heterostructure. (b) A schematic representation of the quantum point contact (QPC). The QPC is defined on a standard Hall bar geometry (light gray). The gates of the QPC (dark gray) are evaporated on the ALOx dielectric layer. The gates separation is 200 nm. The in-plane and out-of-plane magnetic field $B_{\parallel }$ and $B_{\perp }$ are defined as illustrated. The current and voltage are measured in the configuration presented here as well.

Figure 2

(a) Differential conductance $G_{\mathrm{diff}}$ as a function of $V_{\mathrm{sg}}$ at a temperature of $T=1.3\mathrm{K}$ when no magnetic field is applied. Steps of the conductance are visible. A series resistance $R_s=1.2\mathrm{k}\mathrm{\Omega }$ has been subtracted. $G_{\mathrm{diff}}=2e^2/h, 4e^2/h$, and $6e^2/h$ are labeled with dashed lines. (b) Finite bias spectroscopy showing the transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ as a function of $V_{\mathrm{sg}}$ and $V_{\mathrm{dc}}$. A correction on the voltage drop through the quantum point contact (QPC) is made with $R_s=1.2\mathrm{k}\mathrm{\Omega }$. The green dashed lines are added as guidance.

Figure 3

(a) Differential conductance as a function of both $B_{\perp }$ and $V_{\mathrm{sg}}$. The plateaus move to the correct value with the increase of $B_{\perp }$, and spin-split conductance plateaus are observable. A series resistance $R_s=1.2\mathrm{k}\mathrm{\Omega }$ has been subtracted. $G_{\mathrm{diff}}=2e^2/h$ and $4e^2/h$ are labeled with dashed lines. (b) Transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ as a function of $B_{\perp }$ and $V_{\mathrm{sg}}$. Both magnetic depopulation and spin splitting are visible. In different dark regions, the corresponding values of the conductance are labeled in the unit of $e^2/h$. (c) Finite bias spectroscopy showing the transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ as a function of $V_{\mathrm{sg}}$ and $V_{\mathrm{dc}}$ when $B_{\perp }=1.15$ T. The green dashed lines are added as guidance. (d) With a series reproduction of measurement in (c), the $B_{\perp }$ dependence of $\mathrm{\Delta }{E}_{1\uparrow \downarrow }$ and $\mathrm{\Delta }{E}_{2\uparrow \downarrow }$ is obtained. The error bars are determined by observing the height of the transconductance peaks in the cuts in the $V_{\mathrm{sg}}$ direction. The linear fit shows the out-of-plane $g$ factor with a value of $|g_{\perp }^{*}|\approx 50$.

Figure 4

Transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ as a function of $B_{\parallel }$ and $V_{\mathrm{sg}}$. The spin-degenerated conductance plateaus split according to the Zeeman effect and are labeled with the associated conductance in the unit of $e^2/h$.

Figure 5

(a) and (c) The $V_{\mathrm{sg}}$ dependence of the differential conductance $G_{\mathrm{diff}}$ and transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ when in-plane magnetic fields $B_{\parallel }=0.75$ and 1.32 T are applied, respectively. The conductance plateaus are labeled in units of $e^2/h$. (a) and (c) are the cuts of Fig. 4 along the white and green dashed line, respectively. (b) and (d) are finite bias spectroscopy showing the transconductance $d{G}_{\mathrm{diff}}/d{V}_{\mathrm{sg}}$ as a function of $V_{\mathrm{sg}}$ and $V_{\mathrm{dc}}$ with $B_{\parallel }=0.75$ and 1.32 T applied, respectively. Green dashed lines are guidance.