Andreev-enhanced conductance quantization and gate-tunable induced superconducting gap in germanium

Abstract

Ge/SiGe quantum well heterostructures confining a high-mobility two-dimensional hole gas (2DHG) have emerged as a compelling platform for hybrid superconductor(S)-semiconductor(Sm) quantum devices. Here, we investigate the low-temperature transport properties of split-gate quantum point contacts (QPC) defined in one such heterostructure and positioned at different distances from an aluminum superconducting contact. We observe ballistic one-dimensional transport evidenced by conductance quantization with at least four clearly visible plateaus. Andreev reflection at the S/Sm interface induces a 40% enhancement of the conductance steps relative to the normal-state conductance staircase measured under a 100-mT out-of-plane magnetic field. This result is in excellent agreement with the theoretical expectation for an interface transparency of 0.88. By operating the QPCs in the tunneling regime, we probe the local density of states of the proximitized 2DHG. We report direct experimental evidence of an induced superconducting gap, demonstrating that its magnitude can be tuned by a gate voltage acting on the carrier density in the 2DHG.

Figures (14)

• Figure 1: (a) False-colored scanning-electron micrograph (SEM) of device D1 (scale bar: 1µm). (b) Top-view device schematic with simplified measurement circuitry. (c) Cross-sectional schematic taken along the dashed line in (b). (d) Linear conductance, $G$, vs QPC gate voltage, $V_{\mathrm{qpc}}$. Cyan solid line: normal-state conductance, $G_{\mathrm{N/Sm}}(V_{\mathrm{qpc}})$, measured at a perpendicular magnetic field $B_{\perp}$=100mT. Black solid line: Andreev-enhanced conductance, $G_{\mathrm{S/Sm}}(V_{\mathrm{qpc}})$, measured at zero magnetic field. Black dashed line: measured Andreev-enhanced conductance scaled by the theoretically expected ratio $G_{\mathrm{S/Sm}}/G_{\mathrm{N/Sm}} = 2\tau/(2 - \tau)^2$ for a fitted transmission coefficient $\tau = 0.88$. $G_{\mathrm{N/Sm}}$ and the scaled $G_{\mathrm{S/Sm}}$ exhibit overlapping plateaus well aligned with a set of horizontal thin lines positioned at integer multiples of $\tau G_0$, again with $\tau = 0.88$. (e) Color plot of $dI/dV_{\mathrm{sd}}(V_{\mathrm{qpc}}, V_{\mathrm{sd}})$ with dashed lines indicating where the bias voltage matches the Al superconducting gap. (f) Solid lines: $dI/dV_{\mathrm{sd}}(V_{\mathrm{sd}})$ obtained from (e) by averaging line-cut traces from the central regions of the first and second plateau indicated by colored bands. The ensemble of line-cuts used for this averaging are overlayed as light grey lines. We also plot as dashed traces the line-cut averages calculated from similar $dI/dV_{\mathrm{sd}}(V_{\mathrm{qpc}}, V_{\mathrm{sd}})$ measurements in the absence of superconductivity at $B_{\perp}$=100mT.
• Figure 2: Tunnel spectroscopy of the induced superconducting gap in device D2, hosting QPCs at different distances from a same superconducting contact. (a) False-colored SEM image of D2 (scale bar: 1µm) and simplified measurement circuitry. The image shows two QPCs, labeled as left and right QPC, respectively at distances $d_{\mathrm{L}} \sim$ 300nm and $d_{\mathrm{R}} \sim$ 0nm from the upper Al contact. (b) and (c) show color plots of the differential conductance, $dI/dV_{\mathrm{sd}}$, for the left and right QPC, respectively. The $dI/dV_{\mathrm{sd}}$ of the left (right) QPC is individually measured as a function of $V_{\mathrm{sd}}$ and the respective QPC gate voltage $V_{\mathrm{L}}$ ($V_{\mathrm{R}}$), while the right (left) QPC is pinched off. This is achieved with $V_{\mathrm{C}} =$ 0.15V ($V_{\mathrm{C}} =$ 0.35V) and $V_{\mathrm{R}} =$ 1V ($V_{\mathrm{L}} =$ 1V). (d) Representative line-cuts from (b) and (c).
• Figure 3: Parent and induced superconducting gaps (generically, $\Delta$) extracted from tunnel spectroscopy of the local density of states in device D2 as a function of the accumulation gate voltage, $V_{\mathrm{acc}}^{\mathrm{S}}$. The induced gap $\Delta^{*}_{\mathrm{R}}$ and the parent gap $\Delta^{\mathrm{Al}}$ are measured using the right QPC, while the induced gap $\Delta^{*}_{\mathrm{L}}$ is measured using the left QPC. All data points are obtained by fitting the $dI/dV_{\mathrm{sd}}$ tunneling characteristics to a broadened Bardeen-Cooper-Schrieffer density of states. Inset: two representative $dI/dV_{\mathrm{sd}}$ traces measured with the left QPC at $V_{\mathrm{acc}}^{\mathrm{S}} = -2$ and -1.6V, corresponding to strong and weak hole accumulation, respectively.
• Figure S1: Hall bar measurement of (a) the carrier density ($\rho_{_{\mathrm{2D}}}$) and (b) the mobility ($\mu$) as a function of gate voltage for a Hall bar device similar to D1 that has not undergone an oxygen treatment step (blue) and for D2 that has undergone oxygen treatment (red).
• Figure S2: Device D1 two-point resistance measured as a function of gate voltage $V_{\mathrm{acc}}^{\mathrm{S}}$ or $V_{\mathrm{acc}}^{\mathrm{N}}$) with zero voltage applied to the other gates. In the strong accumulation regime the resistance saturates at 8.85kΩ for zero applied magnetic field (a,b) and 9.04kΩ for a 100mT perpendicular magnetic field (c).