Full electrostatic control of quantum interference in an extended trenched Josephson junction

Hybrid semiconductor/superconductor devices constitute an important platform for a wide range of applications, from quantum computing to topological-state-based architectures. Here, we demonstrate full modulation of the interference pattern in a superconducting interference device with two parallel islands of ballistic InAs quantum wells separated by a trench, by acting independently on two side gates. This so far unexplored geometry enables us to tune the device with high precision from a SQUID-like to a Fraunhofer-type behavior simply by electrostatic gating, without the need for an additional in-plane magnetic field. These measurements are successfully analyzed within a theoretical model of an extended tunnel Josephson junction, taking into account the focusing factor of the setup. The impact of these results on the design of novel devices is discussed.

Figure 1

(a) Pseudocolor scanning electron micrograph of the measured device (top view): the superconductor is shown in blue, the N region in green, the hole in the 2DEG in red, and the side gates in yellow. Standard current-bias four-wire setup is sketched. The resistance of each line is omitted (2.1 $\mathrm{k}\mathrm{\Omega }$, mostly originating from the RC filters). (b) Schematic drawing of the heterostructure: the 2DEG is confined in the InAs region (blue); the Si-doped region is marked red; below there is the buffer region in order to accommodate the lattice mismatch between InAs and GaAs. (c) $I_{\text{SD}}-V_{\text{SD}}$ curves of the measured device. The red (black) arrows show the direction of the up (down) sweep. From this measurement, a switching current $I_{\text{SW}}=(95\pm 1)$ nA and a retrapping current $I_{\text{RT}}=(77\pm 1)$ nA are deduced. $T=315$ mK, $B=-0.21$ mT, $V_{\text{LG}}=V_{\text{RG}}=0$ V. (d) Maximum switching current $I_{\text{SW}}$ (blue) and normal resistance $R_N$ (black) as a function of gate voltage $V_G$ ($V_G=V_{\text{LG}}=V_{\text{RG}}$) at $T=315$ mK. The side gates offer a strong modulation of the supercurrent by squeezing simultaneously the two arms of the hybrid device. (e) Maximum switching current $I_{\text{SW}}$ (blue) and maximum retrapping current $I_{\text{RT}}$ (black) as a function of temperature, for $V_G=0$ V.

Figure 2

Differential resistance of the device as a function of the injected source-drain current and magnetic field in three different configurations of symmetric gate voltage: (a) $V_{\text{LG}}=V_{\text{RG}}=0$ V; (b) $V_{\text{LG}}=V_{\text{RG}}=-12.5$ V; (c) $V_{\text{LG}}=V_{\text{RG}}=-22.5$ V. The dark blue region is the Josephson regime. As the gate voltage becomes more negative, the magnetic interference pattern changes toward a SQUID-like. $T=315$ mK.

Figure 3

Differential resistance of the device as a function of the injected source-drain current and magnetic field in three different configurations of asymmetric gate voltage: (a) $V_{\text{LG}}=-60$ V and $V_{\text{RG}}=0$ V; (b) $V_{\text{LG}}=0$ V and $V_{\text{RG}}=-25$ V; (c) $V_{\text{LG}}=0$ V and $V_{\text{RG}}=-60$ V. The center of the pattern in (b) presents a slight shift of $-0.2$ mT with respect to $B=0$, consistent with the residual magnetization of the cryostat. $T=315$ mK.

Figure 4

(a) Contribution to the total supercurrent from left arm (red) and right arm (black) when the same voltage is applied to both gates ($V_{\text{LG}}=V_{\text{RG}}$). The inset shows the schematics of the device with the same color scheme as in Fig. 1. (b), (c) Same as before, but with asymmetric gating: (b) LG biased, RG grounded, (c) LG grounded, RG biased. $T=315$ mK.

Figure 5

Supercurrent density (black) and focusing factor (blue) as a function of position. LA and RA are the widths of the left and right interferometer arm, respectively, while $J_{\text{LA}}$ and $J_{\text{RA}}$ are the corresponding supercurrent densities. The focusing factor profile was used for all simulations presented in Fig. 6, while the supercurrent density profile is the one used for $V_{\text{LG}}=V_{\text{RG}}=0$ V [Fig. 6].

Figure 6

Supercurrent as a function of the applied external magnetic field $B$. Experimental data are plotted in red, while the results of the simulations are plotted in black. (a) Corresponds to the measurement shown in Fig. 2 ($V_{\text{LG}}=V_{\text{RG}}=0$ V), (b) to Fig. 3 ($V_{\text{LG}}=-60$ V and $V_{\text{RG}}=0$ V), and (c) to Fig. 3 ($V_{\text{LG}}=0\mathrm{V}$ and $V_{\text{RG}}=-25$ V). The insets sketch the supercurrent density (black) and focusing factor (blue) used for the simulations as a function of position (same axes as in Fig. 5).