Interfering trajectories in a ballistic Andreev cavity

Abstract

The conventional description of transport through the interface between a normal conductor and a superconductor reduces the system to a one-dimensional problem treating Andreev reflection based on a zero-dimensional Sharvin type point-contact model, and effectively neglects all considerations of device geometry. While this has been successful in systems where conductance in the normal material is in the diffusive transport regime, such an over-simplification of the problem fails in other transport regimes. In particular, when transport is ballistic as in a typical semiconductor-superconductor hybrid structure, geometrical effects are inherently important, and a proper description must consider a one-dimension contact injecting into a two-dimensional ballistic cavity. We present the first study of this regime and explore the bias-voltage dependence of Andreev transport in a cavity-type device comprised of a high mobility HgTe quantum well side-contacted by one superconducting and one normal contact, each creating a one-dimensional interface. The enhanced conductance from Andreev transport features two finite bias conductance peaks, observed at energies within the energy gap of the superconductor. Interestingly, these two peaks respond differently to the application of a perpendicular-to-plane magnetic field. Using a semi-classical model for the quantum transport within the cavity, we are able to attribute each peak to a different class of ballistic trajectories. One class is dominated by normal reflection, and its interference condition is independent of magnetic field, whereas the other one contains retro-reflected Andreev processes at the superconductor interface. These create closed trajectories that are strongly suppressed by magnetic field due to Aharonov-Bohm and Doppler shift effects.

Figures (8)

• Figure 1: (a) Schematic of the side-contacted device geometry. The HgTe quantum well (in red) is embedded between (Cd,Hg)Te layers (in blue) grown on a (Cd,Zn)Te substrate (in dark blue). $N$ and $S$ represent the normal contact (Au) and the superconducting contact (MoRe), respectively. The length ($L$) and width ($W$) of the device are indicated in the schematic. (b) Nomarski microscopy image of the device and simplified schematic of the measurement circuit.
• Figure 2: Bias-voltage dependence of d$I$/d$V$ for zero gate-voltage measured at 25 mK and 13 K. (Inset: Plot of base temperature d$I$/d$V$ after removing the antisymmetric background.)
• Figure 3: (a) $H_{z}$ dependence of d$I$/d$V$ vs $V_{b}$ from 0 to $2\;\text{mT}$ in steps of $50\;\mu\text{T}$ (with self-gating background removed; see main text). The device length is $1000\;\text{nm}$. (b) Schematic of the 4 possible transport processes in the simplified one dimensional picture. (c) Extension of schematic processes to two dimensions. Process (1) and (2) are open trajectories with no magnetic field dependence, whereas the enclosed area of process (3) couples strongly to $H_z$ (see text.) (d) Model curves of d$I$/d$V$ vs $V_{b}$ as a function of $H_{z}$, and corresponding to the results of a, with parameter $\gamma = 0.5$ (a phenomenological parameter describing the transparency of the interface; see text for details).
• Figure 4: Two additional devices. The top row shows measured data for a device with length $650\;\text{nm}$ (a) and $860\;\text{nm}$ (b). (c) and (d) show the corresponding model calculations. A value of $\gamma = 0.4$ is used in both cases.
• Figure S1: Conductance in units of $e^{2}/h$ vs inverse of applied magnetic field H$_{z}$ measured at 4 K. Data points in red are read by eye as minimums, and used to extract SdH period using a linear fit shown in blue.