Transport studies in a gate-tunable three-terminal Josephson junction

Josephson junctions with three or more superconducting leads have been predicted to exhibit topological effects in the presence of few conducting modes within the interstitial normal material. Such behavior, of relevance for topologically protected quantum bits, would lead to specific transport features measured between terminals, with topological phase transitions occurring as a function of phase and voltage bias. Although conventional, two-terminal Josephson junctions have been studied extensively, multiterminal devices have received relatively little attention to date. Motivated in part by the possibility to ultimately observe topological phenomena in multiterminal Josephson devices, as well as their potential for coupling gatemon qubits, here we describe the superconducting features of a top-gated mesoscopic three-terminal Josephson device. The device is based on an InAs two-dimensional electron gas proximitized by epitaxial aluminum. We map out the transport properties of the device as a function of bias currents, top gate voltage, and magnetic field. We find a very good agreement between the zero-field experimental phase diagram and a resistively and capacitively shunted junction computational model.

Figure 1

(a) False-color scanning electron microscope image of gated three-terminal junction with measurement schematic. Blue areas are aluminum and grey areas are etched to the insulating buffer layers to create the device mesas. The Ti/Au top gate (yellow) overlays the 200-nm-wide Y-shaped junction formed by selectively etching the Al layer only (dotted lines). (b) Cross-sectional view along the purple horizontal line in (a) (not to scale). (c) Gate dependence of the switching current when biasing between terminals 1 and 2 showing pinch-off occurring at $V_g\sim -4.5$ V. (d) Two-terminal $I_1$ vs $V_1$ curve with $I_2=0$ showing hysteresis.

Figure 2

(a) $d{V}_1/d{I}_1$ as measured at $B=0$, $V_g=-2$ V. The five distinct transport regions are indicated by the letters A–E. (b) $d{V}_2/d{I}_2$ from the same data as (a). The dotted yellow line indicates $I_2=-2I_1$, and the dotted blue line $I_1=-2I_2$. (c) Schematic depictions of the junction states corresponding to each of the lettered regimes from (a). Dashed (solid) lines indicate superconducting (resistive) legs of the trijunction.

Figure 3

(a), (b) $d{V}_1/d{I}_1$ at two different gate voltages. (c) Dependence of retrapping current ($I_{1,\mathrm{rt}}$) and switching current ($I_{1,\mathrm{sw}}$) on gate voltage, with $I_2=0$. Inset shows the ratio $I_{1,\mathrm{sw}}/I_{1,\mathrm{rt}}$ vs $V_g$. (d), (e) $d{V}_1/d{I}_1$ vs $I_1$ and $I_2$ at two different values of the perpendicular magnetic field.

Figure 4

(a) Three-junction RCSJ network used in simulations. (b), (c) Simulated plots of $d{V}_1/d{I}_1$ and $d{V}_2/d{I}_2$ with large synthetic capacitance, which reproduce the main features in Figs. 2 and 2(b), respectively. There are additional very narrow superconducting arms along the lines $I_1=0$, $I_2=0$, and $I_1=-I_2$, which we do not see in the data. These features could be completely suppressed in the measurements by heating, in the same way that the experimentally visible superconducting arms are narrowed. (d) Simulation with same parameters as (b) and (c), but with $C_i=0$, showing that the central region becomes elliptical when hysteresis is absent and the three critical currents are relatively close in magnitude. (e) $d{V}_1/d{I}_1$ with reduced $I_{c,i}$ to simulate gating effects [cf. Fig. 3]. (f) Further reduction of critical currents compared to (e), cf. Fig. 3. In (e) and (f) $I_{c,2}$ is reduced more than the other two critical currents to account for the observed gating asymmetry, and $C_i$ are set to zero to account for the small hysteresis observed in this regime [cf. Figs. 3–3].