[Paper Review] Microwave spectroscopy of interacting Andreev spins

Jaap J. Wesdorp, F. J. Matute-Cañadas+14 more|arXiv (Cornell University)|Aug 23, 2022

Physics of Superconductivity and Magnetism4 citations

TL;DR

This study demonstrates microwave spectroscopy of interacting Andreev bound states in an InAs/Al nanowire Josephson junction using a flux-tunable superconducting circuit under magnetic fields up to 1 T. It identifies spin-polarized triplet Andreev states via field-dependent avoided crossings, observes direct magnetic field-driven spin-flip transitions, and measures a gate-tunable anomalous phase shift up to 0.7π, revealing key spin-triplet physics and supercurrents in hybrid nanowire systems.

ABSTRACT

Andreev bound states are fermionic states localized in weak links between superconductors which can be occupied with spinful quasiparticles. Microwave experiments using superconducting circuits with InAs/Al nanowire Josephson junctions have recently enabled probing and coherent manipulation of Andreev states but have remained limited to zero or small fields. Here we use a flux-tunable superconducting circuit in external magnetic fields up to 1T to perform spectroscopy of spin-polarized Andreev states up to ~250 mT, beyond which the spectrum becomes gapless. We identify singlet and triplet states of two quasiparticles occupying different Andreev states through their dispersion in magnetic field. These states are split by exchange interaction and couple via spin-orbit coupling, analogously to two-electron states in quantum dots. We also show that the magnetic field allows to drive a direct spin-flip transition of a single quasiparticle trapped in the junction. Finally, we measure a gate- and field-dependent anomalous phase shift of the Andreev spectrum, of magnitude up to approximately $0.7π$. Our observations demonstrate new ways to manipulate Andreev states in a magnetic field and reveal spin-polarized triplet states that carry supercurrent.

Motivation & Objective

• To probe the spin-resolved many-body spectrum of Andreev bound states in hybrid nanowire Josephson junctions under high magnetic fields.
• To identify signatures of spin-triplet pairing and exchange interactions in the Andreev spectrum.
• To demonstrate direct magnetic field control of single-quasiparticle spin-flip transitions in a superconducting circuit platform.
• To measure and analyze gate- and field-dependent anomalous phase shifts in the Andreev spectrum.

Proposed method

• Employed a flux-tunable superconducting circuit with an InAs/Al nanowire Josephson junction to achieve high-energy resolution microwave spectroscopy.
• Applied external magnetic fields up to 1 T to tune the Zeeman splitting and probe spin-dependent Andreev states.
• Used microwave absorption spectroscopy to resolve individual Andreev levels and their magnetic field dispersion.
• Performed tight-binding simulations without interactions and developed a minimal model including spin-orbit coupling, Zeeman effect, and electron-electron exchange interaction.
• Analyzed the spectra to identify singlet-triplet avoided crossings and extract the anomalous phase shift.
• Utilized parity-selective measurements to distinguish between even- and odd-parity Andreev states.

Experimental results

Research questions

• RQ1 How do spin-orbit coupling and electron-electron interactions manifest in the magnetic field dependence of Andreev bound states?
• RQ2 What signatures in the microwave spectrum indicate the presence of spin-triplet pairing in an InAs/Al nanowire Josephson junction?
• RQ3 Can a direct spin-flip transition of a single quasiparticle trapped in an Andreev state be driven by an external magnetic field?
• RQ4 What is the origin and magnitude of the gate-tunable anomalous phase shift observed in the Andreev spectrum at high fields?
• RQ5 How do the interactions between Andreev states lead to hybridization between singlet and triplet states?

Key findings

• The microwave spectrum reveals a clear singlet-triplet avoided crossing in the Andreev levels, indicating hybridization between spin-singlet and spin-triplet states due to spin-orbit coupling and exchange interaction.
• Spin-polarized triplet Andreev states are identified through their distinct magnetic field dispersion, with a splitting consistent with exchange interaction in the junction.
• A direct magnetic field-driven spin-flip transition of a single quasiparticle is observed, enabling control of a single Andreev state's spin without requiring a second bound state.
• Anomalous phase shifts of up to approximately 0.7π are measured, which are gate-tunable and attributed to the many-body Andreev spectrum at high fields.
• The spectrum becomes gapless beyond ~250 mT, indicating a transition to a non-superconducting or topologically distinct phase.
• The results confirm that both spin-orbit coupling and electron-electron interactions are essential for understanding the many-body Andreev spectrum in hybrid nanowire junctions.