Shot-noise and conductance measurements of transparent superconductor/two-dimensional electron gas junctions

We have measured the conductance and shot noise of superconductor-normal metal (S-N) junctions between a niobium (Nb) film and a two-dimensional electron gas (2DEG), formed in an InAs-based semiconductor heterostructure. Adjacent to the junction, the 2DEG is shaped into a sub-micrometer beam splitter. The current shot noise measured through one arm of the beam splitter is found to be enhanced due to Andreev reflection. Both noise and conductance measurements indicate that the Nb-2DEG interface is of high quality with a transparency approaching $\approx 60\text{–}70\%$. The present device can be seen as a quasi-ballistic S-N beam-splitter junction.

Figure 1

(a) Schematic side view of the Nb contact to the InAs semiconductor heterostructure and the corresponding energy band diagram. (b) Longitudinal $\left(R_{xx}\right)$ and Hall $\left(R_H\right)$ resistance measured on this heterostructure. (c) SEM picture of a sample (top view) with a diagram of the measurement setup. The sample is current biased through a series resistor and the voltage fluctuations are measured with the aid of two sets of amplifiers whose outputs are cross correlated. $S$ denotes the power spectral density in units of ${\mathrm{V}}^2∕\mathrm{Hz}$.

Figure 2

(a) Example of a measurement of the equilibrium (thermal) voltage noise (spectral density $S_V$) versus temperature $T$ used to deduce the calibration parameters. Here, the frequency and sample resistance were $f=110\mathrm{kHz}$ and $R\simeq 2\mathrm{k}\Omega$, respectively. The thermal noise is linearly dependent on $T$ and the slope (Ref. 64) yields the attenuation factor $A$ of the signal. (b) The attenuation $A$ as a function of $\omega R$ follows the dependence expected for a simple RC network, i.e., $A\left(\omega \right)={[1+{\left(\omega RC\right)}^2]}^{-1}$.

Figure 3

Temperature dependent resistance $R\left(T\right)$. Circles correspond to the measurements, whereas the curves are calculated using the BTK model together with a classical series resistor $R_S=0$ (solid), $R_S=500$ (dashed), and $R_S=1000\Omega$ (dotted). $\Delta$ was fixed to 1.14 meV and the barrier transparency $\Gamma \approx 0.72$ and channel number $N\approx 9$ were deduced so that the theoretical $R\left(T\right)$ matches the experiment one in the normal state and the superconducting state at the lowest temperature. The inset shows the superconducting transition of the Nb film measured with two probes on a structured device. The transitions of the Nb film and the submicron Nb contact are marked by arrows.

Figure 4

Voltage dependent differential resistance $dV∕dI\left(V\right)$ measured at $T=270\mathrm{mK}$. Circles correspond to the measurements, whereas the curves are calculated using the BTK model together with a classical series resistor $R_S=0$ (solid), $R_S=500$ (dashed), and $R_S=1000\Omega$ (dotted). The parameters are similar to the ones used in Fig. 2. The full arrows point to the gap value $\Delta$ estimated from the transition temperature $T_c$ using the standard BCS relation $\Delta =1.76k_B{T}_c$, whereas the open arrows point to $\Delta =1.9k_B{T}_c$, where the factor 1.9 is known for bulk Nb.

Figure 5

Power spectral density $S_I$ of the current noise of a submicrometer S-N junction as a function of applied current $I$. $S_I$ is extracted from the measured voltage noise $S_{V_1,V_2}$ between the superconductor and one of the normal reservoirs [see Fig. 1c] according to the Eq. (1). A clear crossover from a large Fano factor $F_S$ at small bias currents to a reduced Fano factor $F_N$ for large currents is observed. This crossover coincides with gap $\Delta$ of the superconductor (open arrows).

Figure 6

Fano factors versus perpendicular magnetic field $B$ (symbols). The dashed curves are guides to the eyes. As $B$ is increased, the enhancement of the Fano factor in the superconducting relative to the normal state (i.e., the ratio $F_S∕F_N$) diminishes and fully disappears for $B\gtrsim 3\mathrm{T}$. Note, that $F_N$ also slightly decreases as the field increases. Inset: The power spectral density $S_I$ of the current noise as a function of the bias current $I$ for $B=0$, 1, 2, and 4 T. The curves are shifted vertically for clarity. The crossover (arrows) between the superconducting and normal state shifts to lower voltages for increasing magnetic field as expected.

Figure 7

Illustration of the two basic models which we have used to analyze our data. (a) is based on a wire and (b) on a cavity. The models are considered in different regimes, but always in the limit of zero temperature. In (a) we distinguish between the ballistic $(l_e⪢L)$, intermediate $(l_e\sim L)$, and diffusive $(l_e⪡L)$ regime, whereas in (b) the cavity is assumed to be either open on both sides (no barrier) or only open on one side with a tunneling barrier on the other side, described by its transparency $\Gamma$.