[Paper Review] Phase-engineering the Andreev band structure of a three-terminal Josephson junction

M. Coraiola, D. Z. Haxell+12 more|arXiv (Cornell University)|Jan 1, 2023

Physics of Superconductivity and Magnetism63 references9 citations

TL;DR

This study demonstrates phase-engineered control of Andreev bound states in a three-terminal Josephson junction using tunnelling spectroscopy in an InAs/Al heterostructure. By independently tuning two superconducting phase differences via flux-bias lines, the authors observe hybridization between two discrete Andreev levels, evidenced by avoided crossings and anisotropic band structures in the 2D phase space, validated by a numerical model. This establishes a platform for engineering synthetic Andreev matter and topological states in multiterminal hybrid nanostructures.

ABSTRACT

In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries.

Motivation & Objective

• To realize and probe a phase-controllable three-terminal Josephson junction (3TJJ) in an InAs/Al heterostructure with independent control over two superconducting phase differences.
• To investigate the formation of hybridized Andreev bound states—termed an 'Andreev molecule'—through spatial overlap and coupling of discrete Andreev levels.
• To map the two-dimensional Andreev band structure in phase space and identify signatures of hybridization such as avoided crossings and anisotropic dispersion.
• To validate experimental observations with a theoretical model based on coupled quantum dots coupled to superconducting leads with tunable phase differences.
• To establish a foundation for future exploration of spin-resolved levels, fermion parity transitions, and Weyl-like band structures in multiterminal geometries.

Proposed method

• Fabricated a three-terminal Josephson junction in an InAs/Al heterostructure using selective Al etching to define three superconducting terminals (L, M, R) connected via a common node D, forming two closed superconducting loops.
• Employed flux-bias lines to inject currents (IL, IR) that generate tunable external magnetic fluxes (ΦL, ΦR) threading the left and right loops, enabling independent control over the phase differences ϕL and ϕR.
• Used a superconducting probe lead (S) to perform DC tunnelling spectroscopy, measuring differential conductance (G) as a function of bias voltage (VSD) and phase differences (ΦL, ΦR).
• Implemented a switch junction (via gate voltage VSwitch) to electrostatically toggle between three-terminal (ON) and two-terminal (OFF) configurations, enabling comparative studies.
• Applied a numerical model based on two coupled quantum dots (QDs) representing Andreev levels, each coupled to two superconducting leads with phases ϕL, ϕR, ϕM, and tunable hybridization (t) and transmission (Γ).
• Performed current-to-flux remapping using Eqs. 13 and 14 to convert measured current injections (IL, IR) into effective phase differences (ΦL, ΦR), enabling accurate phase-space mapping.

Experimental results

Research questions

• RQ1 Can Andreev bound states in a three-terminal Josephson junction be hybridized through phase engineering, and what signatures emerge in the 2D phase space?
• RQ2 How do avoided crossings and band structure anisotropies in the phase space reflect the hybridization of two discrete Andreev levels?
• RQ3 To what extent can the observed band structure be explained by a theoretical model of coupled Andreev levels in a synthetic 2D phase space?
• RQ4 What role does Josephson-like mutual inductive coupling between the two loops play in shifting the phase-dependent resonances?
• RQ5 Can the system be used to engineer synthetic Andreev matter with tunable topological or non-trivial fermionic properties?

Key findings

• Tunnelling spectroscopy revealed two distinct Andreev bound states in the 3TJJ, each dispersing with one of the two phase differences (ϕL and ϕR), forming a 2D band structure in the phase space.
• Avoided crossings were observed in the differential conductance maps, indicating level repulsion and hybridization between two Andreev levels with spatial overlap.
• The band structure exhibited anisotropic dispersion: the slope of resonance lines varied with the state of the switch junction, confirming finite Josephson-like mutual inductive coupling between the two loops.
• Phase shifts of up to ΔΦL ≈ 0.3Φ0 and ΔΦR ≈ 0.2Φ0 were measured when switching the junction state, consistent with the finite mutual inductance and flux quantization.
• The experimental data matched well with numerical simulations based on a two-level quantum dot model with tunable hybridization (t ≈ 0.01Δ) and finite normal reflection amplitudes.
• The system demonstrated a phase-controlled Andreev molecule, where hybridization between two discrete Andreev levels leads to a synthetic band structure unattainable in two-terminal junctions.