[Paper Review] Phase Asymmetry of Andreev Spectra From Cooper-Pair Momentum

Abhishek Banerjee, Max Geier+6 more|arXiv (Cornell University)|Jan 5, 2023

Physics of Superconductivity and Magnetism5 citations

TL;DR

This paper demonstrates a phase-asymmetric Andreev bound state spectrum in an InAs/Al superconductor-normal-superconductor Josephson junction induced by in-plane magnetic fields, arising from finite-momentum Cooper pairing due to orbital coupling. The asymmetry peaks at 0.15 T and is absent without magnetic field, providing evidence for a nonreciprocal supercurrent response without requiring spin-orbit or Zeeman coupling.

ABSTRACT

In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial InAs/Al heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field, without invoking Zeeman or spin-orbit coupling.

Motivation & Objective

• To investigate nonreciprocal Andreev bound state responses in superconducting junctions without relying on spin-orbit or Zeeman coupling.
• To determine the origin of phase asymmetry in the subgap spectrum of a Josephson junction under in-plane magnetic fields.
• To establish that orbital coupling alone can induce finite-momentum Cooper pairing leading to nonreciprocal supercurrent flow.
• To experimentally verify the spatial extent of phase-asymmetric Andreev bound states across the junction using three-terminal spectroscopy.

Proposed method

• Fabricated planar InAs/Al epitaxial Josephson junctions with a 100 nm wide normal region and 1.8 µm superconducting leads.
• Performed local and nonlocal tunneling spectroscopy to map the Andreev bound state spectrum as a function of superconducting phase difference and in-plane magnetic field.
• Used three-terminal conductance measurements to confirm the bulk nature of the phase-asymmetric states across the junction.
• Applied theoretical modeling with a Hamiltonian including orbital coupling to magnetic field, incorporating proximity-induced phase gradients.
• Simulated the energy spectrum and diode efficiency using parameters derived from material properties (g-factor, spin-orbit coupling, effective mass).
• Modeled the system with and without inductance to assess the role of kinetic inductance in modifying the phase response.

Figure 1: Device schematic and micrograph (a) Schematic of a planar Josephson junction device consisting of two superconducting leads (blue) of width $w_{s}=1.8\,\mu$ m in epitaxial contact with the underlying semiconductor (brown). The normal region between the two leads is of width $w_{n}=100$ nm,

Experimental results

Research questions

• RQ1 Can phase-asymmetric Andreev bound states be induced in a Josephson junction without spin-orbit or Zeeman coupling?
• RQ2 What is the role of orbital coupling to an in-plane magnetic field in generating finite-momentum Cooper pairing?
• RQ3 How does the phase asymmetry in the Andreev spectrum evolve with increasing in-plane magnetic field?
• RQ4 Are the nonreciprocal Andreev bound states localized at the junction edges or distributed throughout the normal region?
• RQ5 What is the maximum diode efficiency achievable via orbital coupling alone in this system?

Key findings

• Phase asymmetry in the Andreev bound state spectrum appears only under in-plane magnetic fields and reaches a maximum at 0.15 T.
• The phase-asymmetric spectrum is observed throughout the bulk of the junction, not just at the edges, as confirmed by three-terminal conductance spectroscopy.
• At zero magnetic field, the Andreev spectrum is symmetric under phase inversion, confirming the absence of intrinsic asymmetry.
• The observed phase asymmetry is attributed to finite-momentum Cooper pairing induced by orbital coupling to the in-plane magnetic field, not Zeeman or spin-orbit effects.
• Theoretical modeling reproduces the experimental phase asymmetry and diode efficiency, with peak efficiency occurring near the magnetic field where orbital phase gradient matches the superconducting gap.
• The system exhibits a nonreciprocal response in both local and nonlocal conductance, with a smaller spectral gap at one end of a flux lobe and a larger gap at the other, confirming directional supercurrent flow.

Figure 2: Nonreciprocal Andreev bound state spectrum. (a)–(e) Differential conductance measured in Device 1 as a function of $B_{\perp}$ at different value of $B_{\parallel}$ . At $B_{\parallel}=$ 0, the Andreev bound state spectrum is phase-symmetric within each flux lobe. For non-zero $B_{\paralle