Doppler shift in Andreev reflection from a moving superconducting condensate in Nb/InAs Josephson junctions

We study narrow ballistic Josephson weak links in a InAs quantum wells contacted by Nb electrodes and find a dramatic magnetic-field suppression of the Andreev reflection amplitude, which occurs even for in-plane field orientation with essentially no magnetic flux through the junction. Our observations demonstrate the presence of a Doppler shift in the energy of the Andreev levels, which results from diamagnetic screening currents in the hybrid Nb/InAs banks. The data for conductance, excess, and critical currents can be consistently explained in terms of the sample geometry and the McMillan energy, characterizing the transparency of the Nb/InAs interface.

Figure 1

(Color online) (a) Scanning electron micrograph of sample No. 3 with width $W=2\mu \text{m}$ and length $L=0.6\mu \text{m}$. Regions with InAs two-dimensional electron gas are shown in yellow. Etched regions are light gray. The horizontal dark gray stripes are made from a 35-nm-thick Nb. (b) $R\left(T\right)$ for three samples with width $W=0.5,1,2\mu \text{m}$. (c) Resistance vs $1/W$ at 10 K for the $4t$ configuration with InAs leads (○) and the $2t$ configuration with Nb leads (◻). (d) Normalized supercurrent $I_C$ vs perpendicular magnetic field $B_{\perp }$ for different widths $W$. The black curve is the standard Fraunhofer pattern fitting the data for sample No. 3 $\left(W=2\mu \text{m}\right)$.

Figure 2

Critical current vs. temperature $T$ for different widths $W$ together with best fits according to our model. Inset: values of $⟨\mathcal{T}⟩$ (○) and ${\Gamma }_{McM}$ (◻) resulting from the fits.

Figure 3

(Color online) Measured differential conductance $dI/dV$ of sample No. 2a $\left(W=1\mu \text{m}\right)$ for different values of a perpendicular magnetic field $B_{\perp }=0$, 4, 10, 40, and 100 mT, from top to bottom. Arrows indicate the subharmonic gap structure induced by multiple Andreev reflections. Inset: voltages of the subharmonic gap structures for all samples. The solid line indicates the expected slope for ${\Delta }_{Nb}=1.35\text{meV}$.

Figure 4

(Color online) (a) Measured excess current of sample No. 2a vs perpendicular (○) and parallel (●) magnetic field. The solid lines result from our model including the Doppler shift ${\epsilon }_D\left(k_S\right)$ (see text) and the dashed line shows $I_{\text{exc}}$ due to the suppression of ${\Delta }_{Nb}\left(B_{\parallel }\right)$ only (Ref. 18). [(b) and (c)] One of the Nb/InAs terminals in parallel and perpendicular fields. Red arrows indicate the SC order-parameter phase gradient, ${\mathbf{k}}_S=\nabla \gamma$, with $k_S=-\pi /W\times \Phi /{\Phi }_0$ determined by the magnetic flux $\Phi$ through the bilayer for given field orientation.

Figure 5

Critical current vs $B$ for sample No. 1 at small angles $\alpha$ between $\mathbf{B}$ and 2DEG. The lines are theoretical fits (see text). The inset shows the double peak structure of ${\left|a\left(\epsilon \right)\right|}^2$ characteristic of hybrid SC and its suppression by $B_{\parallel }$.