[Paper Review] Universal Josephson diode effect

Margarita Davydova, Saranesh Prembabu+1 more|arXiv (Cornell University)|Jan 3, 2022

Physics of Superconductivity and Magnetism4 citations

TL;DR

This paper proposes a universal mechanism for the Josephson diode effect in short Josephson junctions driven by finite Cooper pair momentum, arising from simultaneous breaking of inversion and time-reversal symmetries. The effect originates from Doppler shifts in Andreev bound state energies and phase-independent asymmetric current from the continuum, enabling up to 40% diode efficiency with critical current asymmetry $I_{c+}/I_{c-} \approx 230\%$, robust even in disordered systems and independent of junction transparency or material details.

ABSTRACT

We propose a universal mechanism for the Josephson diode effect in short Josephson junctions. The proposed mechanism is due to finite Cooper pair momentum and is a manifestation of simultaneous breaking of inversion and time-reversal symmetries. The diode efficiency is up to 40%, which corresponds to an asymmetry between the critical currents in opposite directions $I_{c+}/I_{c-} \approx$ 230%. We show that this arises from both the Doppler shift of the Andreev bound state energies and the phase-independent asymmetric current from the continuum. Finally, we propose a simple scheme for achieving finite-momentum pairing, which does not rely on spin-orbit coupling and thus greatly expands existing platforms for the observation of supercurrent diode effects.

Motivation & Objective

• To establish a universal microscopic mechanism for the Josephson diode effect in short junctions.
• To clarify the origin of nonreciprocal supercurrents in systems with finite-momentum Cooper pairing.
• To demonstrate that the effect arises from Doppler shifts in quasiparticle energies and asymmetric continuum contributions.
• To propose a simple, material-agnostic scheme for inducing finite-momentum pairing using the Meissner effect under small in-plane magnetic fields.
• To show robustness of the diode effect against disorder and finite junction transparency.

Proposed method

• Derive an analytical expression for the Josephson current in short junctions between finite-momentum superconductors using a generalized BCS-like formalism.
• Model the superconducting order parameter as $\Delta_{1,2}(x) = \Delta e^{\pm 2iqx + i\varphi}$ to capture spatial modulation from Cooper pair momentum.
• Use a tight-binding lattice model to simulate the Josephson current and diode efficiency in disordered systems with varying disorder strength and system size.
• Perform perturbative expansion in junction transparency $T$ to isolate subleading terms that generate asymmetric current-phase relations.
• Analyze the role of Andreev bound states and continuum contributions separately to quantify their respective roles in diode efficiency.
• Use the Meissner effect in a short junction with in-plane magnetic field $B_y < B_{c1}$ to induce finite-momentum pairing without requiring spin-orbit coupling.

Experimental results

Research questions

• RQ1 What is the microscopic origin of the Josephson diode effect in short junctions with finite-momentum Cooper pairing?
• RQ2 How do Doppler shifts in quasiparticle energies and continuum contributions jointly determine the diode efficiency?
• RQ3 Can the Josephson diode effect be induced universally across all superconductors without relying on spin-orbit coupling or complex heterostructures?
• RQ4 How robust is the diode effect against disorder and finite junction transparency?
• RQ5 What is the role of system size and localization length in determining the magnitude and universality of the effect?

Key findings

• The Josephson diode effect arises universally from the Doppler shift of Andreev bound state energies due to finite Cooper pair momentum, leading to direction-dependent current-phase relations.
• The diode efficiency reaches up to 40%, corresponding to a critical current asymmetry $I_{c+}/I_{c-} \approx 230\%$.
• The phase-independent asymmetric current from the continuum plays a crucial role in determining the magnitude of the diode effect.
• The effect persists even at very low junction transparency $T \ll 1$, indicating it is not dependent on multiple scattering channels or high transparency.
• The diode effect remains robust under chemical potential disorder, with efficiency reduced by only a factor of two at $[-10\Delta, 10\Delta]$ disorder, and becomes system-length independent when $\xi_{\text{loc}} \ll L$.
• The mechanism is universal: it operates in the ballistic limit, is independent of junction parameters, and applies to all superconductors via the Meissner effect under small in-plane magnetic fields.