[Paper Review] Supercurrent parity-meter in a nanowire Cooper-pair transistor

Ji‐Yin Wang, Constantin Schrade+14 more|arXiv (Cornell University)|Jul 18, 2021

Physics of Superconductivity and Magnetism5 citations

TL;DR

This paper demonstrates a supercurrent parity-meter in an InSb-Al hybrid nanowire Cooper-pair transistor (CPT) by inducing subgap states via a parallel magnetic field. The supercurrent exhibits a parity-dependent phase offset that distinguishes even and odd charge ground states on the superconducting island, persisting even when a subgap state approaches zero energy, enabling parity readout via supercurrent interferometry for topological qubit applications.

ABSTRACT

We study a Cooper-pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably,this phase offset persists when a subgap state approaches zero energy and, based on theoretical considerations, permits parity measurements of subgap states by supercurrent interferometry. Such supercurrent parity measurements could, in a new series of experiments, provide an alternative approach for manipulating and protecting quantum information stored in the isolated subgap levels of superconducting islands.

Motivation & Objective

• To investigate whether a Cooper-pair transistor (CPT) with a superconducting island in an InSb-Al nanowire exhibits a parity-dependent phase offset in its Josephson relation when subjected to a magnetic field.
• To determine if such a phase offset persists when a subgap state approaches zero energy, enabling robust parity measurement.
• To explore the tunability of the phase offset via plunger gate voltage and magnetic field, and its implications for quantum information manipulation.
• To demonstrate that supercurrent interferometry can serve as a viable method for reading out the parity of low-energy subgap states in superconducting islands.
• To provide a new experimental platform for manipulating and protecting quantum information stored in isolated subgap states of nanowire-based CPTs.

Proposed method

• The experiment uses a superconducting quantum interference device (SQUID) incorporating an InSb-Al hybrid nanowire Cooper-pair transistor (CPT) with a superconducting island formed by two Josephson weak links.
• A magnetic field applied parallel to the nanowire induces subgap states in the superconducting island, which mediate supercurrent via coherent co-tunneling of Cooper pairs.
• The Josephson relation is measured as $ I = (-1)^{n_0} I_c an( heta) imes ext{sign}( ext{Re}[ ext{Tr}(G_{ ext{eff}})]) $, where $ n_0 $ is the electron number parity, and the phase offset $ heta $ arises from interference between tunneling paths.
• The phase offset $ heta $ is extracted from the SQUID’s current-phase relation by measuring switching currents $ I_{ ext{sw}} $ as a function of applied flux $ heta $, with distinct phase shifts observed between even and odd Coulomb valleys.
• Tunability of the phase offset is achieved via plunger gate voltage $ V_P $, which controls the electron number on the island, and via magnetic field $ B_ ext{parallel} $, which modifies subgap state energies and wavefunction overlap.
• Theoretical modeling supports that the phase offset arises from broken time-reversal and mirror symmetries due to spin-orbit coupling and magnetic field, leading to a non-zero $ heta_0 $ in the Josephson relation $ I = I_c an( heta) imes ext{Re}[ ext{Tr}(G_{ ext{eff}})] $.

Figure 1: (Color online) a , False-color micrograph of the measured NbTiN (green) SQUID device comprising an InSb-Al NW CPT in the right arm and an InSb nanowire reference junction in the left arm. Top gates (L, R, REF) define tunable JJs, and a plunger gate (P) controls the electron number on the S

Experimental results

Research questions

• RQ1 Does the Josephson relation in a nanowire-based Cooper-pair transistor exhibit a parity-dependent phase offset when subgap states are induced by a magnetic field?
• RQ2 Can such a phase offset persist when a subgap state approaches zero energy, indicating robustness for quantum information applications?
• RQ3 How is the phase offset tunable via plunger gate voltage and magnetic field, and what does this reveal about subgap state hybridization and coupling?
• RQ4 Can supercurrent interferometry be used to distinguish even and odd charge ground states in a superconducting island with isolated subgap levels?
• RQ5 What is the role of spin-orbit coupling and broken symmetries in generating the observed phase offset in the supercurrent response?

Key findings

• A measurable phase offset $ heta_0 $ in the supercurrent is observed between even and odd Coulomb valleys of the superconducting island, confirming parity-dependent Josephson coupling.
• The phase offset persists when the lowest-energy subgap state approaches zero energy, indicating robustness against level degeneracy and enabling parity readout near the topological regime.
• The phase offset is tunable with both plunger gate voltage $ V_P $ and magnetic field $ B_ ext{parallel} $, demonstrating control over the subgap state hybridization and Josephson coupling strength.
• The phase offset decreases with increasing magnetic field, indicating enhanced energy splitting between the lowest and higher subgap states, which suppresses the parity-dependent supercurrent contribution.
• The observed phase offset is consistent with theoretical predictions for spin-orbit coupled systems under magnetic fields, where time-reversal and mirror symmetries are broken.
• The system exhibits a $ 2e $-periodic charging energy for the island, confirming the presence of a Coulomb-blockaded superconducting island, while the supercurrent shows $ e $-periodic features due to subgap state occupancy.

Figure 2: (Color online) a , Differential conductance, $\text{d}I/\text{d}V$ , versus source-drain voltage $V$ and plunger gate voltage $V_{P}$ . At zero parallel magnetic field, the differential conductance shows a Coulomb diamond pattern with a $2e$ -periodicity. At $B_{\parallel}=100\,$ mT, the $