Transparent Semiconductor-Superconductor Interface and Induced Gap in an Epitaxial Heterostructure Josephson Junction

Measurement of multiple Andreev Reflection (MAR) in a Josephson junction made from an InAs quantum well heterostructure with epitaxial aluminum is used to quantify a highly transparent effective semiconductor-superconductor interface with near-unity transmission. The observed temperature dependence of MAR does not follow a conventional BCS form but instead agrees with a model in which the density of states in the quantum well acquires an effective induced gap, in our case, $180\mu \mathrm{eV}$, close to that of the epitaxial superconductor, indicating an intimate contact between Al and the InAs heterostructure. The carrier density dependence of MAR is investigated using a depletion gate revealing the subband structure of the semiconductor quantum well, consistent with magnetotransport experiments of the bare InAs performed on the same wafer.

Figure 1

(a) False-color scanning electron micrograph of the $S\text{−}2\mathrm{DEG}\text{−}S$ device. (b) Schematic of the second-order MAR process when a voltage $eV<\mathrm{\Delta }$ is applied across an ideal superconductor–normal-metal–superconductor ($S\text{−}N\text{−}S$) junction. (c) Cross-sectional schematic of the device in (a) (not to scale). Because of processes such as the one sketched in the schematic involving multiple Andreev reflections (ARs) and potentially also normal reflections (NRs), the part of the quantum well covered by Al gains an induced gap ${\mathrm{\Delta }}^{*}$. Andreev reflections of particles in the uncovered region happen at the vertical effective interface indicated by the gray vertical dashed line stemming from the gap ${\mathrm{\Delta }}^{*}$ in the quantum well. Right schematic indicates variation of superconducting gap $\mathrm{\Delta }(z)$ in the growth direction for the case of an effective quantum-well thickness much less than the normal-state coherence length $d_N\ll {\xi }_N$ (see text for details) in the part of the quantum well covered by Al.

Figure 2

Differential conductance (left axis) and dc voltage (right axis) at two different gate voltages. In (a), the dashed green line shows linear fit at $eV(I)\gg {\mathrm{\Delta }}_{\mathrm{Al}}$ used to extract the excess current $I_{\mathrm{exc}}$ as the intercept with the $V=0\mathrm{mV}$ (as shown in the inset). $I_c$ is the current at which the system switches to a resistive state. The dips highlighted in (b) correspond to multiple Andreev reflections of order $n$.

Figure 3

(a) Current through a $S\text{−}N\text{−}S$ junction from the simplified model of Eq. (1) in units of $g_n\mathrm{\Delta }/e$ ($g_n$ is the normal-state conductance), for several values of transmission through the junction. (b) Conductances of a $S\text{−}N\text{−}S$ junction calculated using the scattering approach for different values of the transparency $\tau$. The vertical black arrow indicates the position of the conductance dip discussed in detail in Sec. 6.

Figure 4

(a) Conductance as a function of bias voltage at two different gate voltages exhibiting resonances due to MAR. (b) Density in the 2DEG extracted from the Hall slope and power spectrum of Shubnikov–de Haas (SdH) oscillations versus gate voltage (see text for details). (c),(d) Transparency ${\tau }_i$ and number of modes $N_i$ in subband $i$ as a function of top-gate voltage $V_g$ extracted from the MAR data in (a). The red and teal points correspond to the fitting values used for the dashed curves in panel (a).

Figure 5

(a) Temperature dependence of the MAR features at $V_g=-2.2\mathrm{V}$ . Traces successively offset by $10\times 2e^2/h$. (b) Temperature dependence of the dip labeled $p_2$. Dashed purple line is Eq. (2) scaled to match $p_2$ at base temperature. The solid teal line is the temperature dependence of a BCS superconducting gap, and the dashed teal line is a rescaling of ${\mathrm{\Delta }}_{\mathrm{Al}}(T)$ to match $p_2$ at base temperature. (c) Temperature dependence of first, second, and third dip positions with multiples of ${\mathrm{\Delta }}^{*}(T)$ from (b).

Figure 6

(a) Mobility of the 2DEG as a function of top-gate voltage measured in a Hall bar. (b) Shubnikov–de Haas oscillations at two values of top-gate voltage in a Hall bar.

Figure 7

Temperature dependence of differential resistance at $V_g=0\mathrm{V}$. Curves successively offset by $25\mathrm{\Omega }$, except for $T=0.05\mathrm{K}$. Horizontal bars indicate positions of the anomalous resistance peak.

Figure 8

(a) Differential resistance of the junction as the current $I$ is swept when the gate $V_g$ is energized. (b) The value of $I_c$ and $I_c{R}_n$ extracted from (a), as a function of gate voltage.

Figure 9

Fit to experimental data at $V_g=0\mathrm{V}$ (black curve) for several values of the number of occupied subbands $M$ used in the simulation.