[论文解读] Parity-conserving Cooper-pair transport and ideal superconducting diode in planar Germanium

Marco Valentini, Olivér Sági+17 more|arXiv (Cornell University)|Jun 12, 2023

Quantum and electron transport phenomena参考文献 63被引用 11

一句话总结

本文在Al间隔层下的浅Ge量子阱中实现平面Ge空穴气体的近邻诱导超导性，实现在带门控/通量可调的SQUID中的超导二极管，以及具有sin(2φ)电流-相位关系的SQUID，并在微波驱动下观测到半整数Shapiro步。

ABSTRACT

Superconductor/semiconductor hybrid devices have attracted increasing interest in the past years. Superconducting electronics aims to complement semiconductor technology, while hybrid architectures are at the forefront of new ideas such as topological superconductivity and protected qubits. In this work, we engineer the induced superconductivity in two-dimensional germanium hole gas by varying the distance between the quantum well and the aluminum. We demonstrate a hard superconducting gap and realize an electrically and flux tunable superconducting diode using a superconducting quantum interference device (SQUID). This allows to tune the current phase relation (CPR), to a regime where single Cooper pair tunneling is suppressed, creating a $\sin \left( 2 φ ight)$ CPR. Shapiro experiments complement this interpretation and the microwave drive allows to create a diode with 100% efficiency. The reported results open up the path towards integration of spin qubit devices, microwave resonators and (protected) superconducting qubits on a silicon technology compatible platform.

研究动机与目标

• Motivate a silicon-compatible platform for hybrid superconductor–semiconductor devices with planar Ge.
• Show proximity-induced superconductivity in a Ge hole gas controlled by spacer thickness and gate tuning.
• Demonstrate a gate- and flux-tunable superconducting diode via a SQUID, inducing non-sinusoidal current-phase relations.
• Investigate the CPR harmonics and conditions under which single-Cooper-pair tunneling is suppressed.
• Explore microwave-driven Shapiro steps as evidence for higher-harmonic CPR components.

提出的方法

• Grow strained Ge/SiGe heterostructures with 18 nm Ge quantum wells separated by a SiGe spacer of thickness D (5 nm and 8 nm).
• Deposit Al ex situ to induce proximity superconductivity and characterize the induced gap Δ* via tunneling spectroscopy.
• Fabricate Josephson junctions and SQUID geometries to measure retrapping currents, CPRs, and diode efficiency η as a function of gate voltages and magnetic flux.
• Model the device CPR with higher-harmonic contributions in the junctions and include inductance to reproduce asymmetric SQUID patterns.
• Perform Shapiro-step measurements under microwave drive to identify half-integer steps consistent with sin(2φ) CPR components.]
• research_questions|

Figure 1: Proximity induced superconductivity in Planar Ge . a Heavy hole (HH) [light hole (LH)] band energies (black trace) [(grey trace)] along the growth direction $z$ simulated using NextNano. HHs are accumulated at the upper QW interface, as shown by the pink trace representing the HH wavefunct

实验结果

研究问题

• RQ1 Can proximity-induced superconductivity be robustly achieved in planar Ge hole gases using shallow QWs and thin spacers?
• RQ2 How does the induced gap Δ* depend on spacer thickness D and Al proximity?
• RQ3 Can a gate- and flux-tunable superconducting diode be realized in a Ge-based SQUID, and what CPR components are required?
• RQ4 Under what conditions can a sin(2φ) CPR dominate, enabling Cooper-pair–only transport?
• RQ5 Do Shapiro steps reveal half-integer features indicative of higher-harmonic CPRs?

主要发现

• Hard superconducting gap observed in Ge/SiGe hybrids with Δ* up to 150 μeV (sample D5) and a parent Al gap Δ ≈ 230 μeV.
• Tunneling spectroscopy shows a hard gap with suppressed subgap conductance by about two orders of magnitude for D5.
• A gate- and flux-tunable SQUID exhibits a superconducting diode effect with η up to ~15% at certain flux and gate settings.
• In the balanced junction regime, the first CPR harmonic can be quenched, yielding a sin(2φ)–dominated CPR and a sweet-spot condition where single-Cooper-pair transfer is suppressed.
• Shapiro experiments reveal half-integer steps near φ/φ0 ≈ 0.5 under microwave drive, consistent with sin(2φ) CPR contributions.
• Microwave-driven, non-volatile diode operation can achieve η ≈ 1 in certain regimes.

Figure 2: Superconducting gap tunability. a Sketch of the proximity effect. Al has a superconducting parent gap $\Delta$ and it is coupled to the Ge hole gas. The coupling $t$ , and therefore the induced gap $\Delta^{*}$ , depends on the thickness of the SiGe tunnel barrier, i.e. on D. b Top-view sk