[Paper Review] Nonreciprocal charge transport and subharmonic structure in voltage-biased Josephson diodes

Alex Zazunov, Jérôme Rech+4 more|arXiv (Cornell University)|Jul 28, 2023

Physics of Superconductivity and MagnetismPhysics and Astronomy79 references3 citations

TL;DR

This paper develops a scattering theory for voltage-biased Josephson diodes based on helical superconductors with finite Cooper pair momentum, demonstrating that multiple Andreev reflection induces a rich subharmonic structure in the DC current-voltage curve due to Doppler-shifted spectral gaps. The key result is that rectification efficiency reaches the ideal value η = 1 in the voltage-biased regime, surpassing the maximum η₀ ≈ 0.4 in current-biased cases.

ABSTRACT

We study charge transport in voltage-biased single-channel junctions involving helical superconductors with finite Cooper pair momentum. For a Josephson junction, the equilibrium current-phase relation shows a superconducting diode effect: the critical current depends on the propagation direction. We formulate a scattering theory for voltage-biased Josephson diodes and show that multiple Andreev reflection processes cause a rich subharmonic structure in the DC current-voltage curve at low temperatures and small voltages due to Doppler shifts of the spectral gap. In the current-biased case, the diode efficiency has maximal rectification efficiency $η_0\approx 0.4$ for this model. In the voltage-biased case, however, the rectification efficiency can reach the ideal value $η=1$. We also discuss charge transport for NS junctions between a normal metal and a helical superconductor and comment on related models with spin-orbit interactions and magnetic Zeeman fields.

Motivation & Objective

• To develop a microscopic scattering theory for charge transport in voltage-biased Josephson diodes with helical superconductors.
• To investigate how multiple Andreev reflection processes shape the current-voltage characteristics under non-equilibrium conditions.
• To determine the rectification efficiency η in the voltage-biased regime and compare it with the current-biased case.
• To explore the role of finite Cooper pair momentum and Doppler shifts in generating subharmonic features in the I-V curve.
• To extend the analysis to NS junctions and compare with models involving spin-orbit coupling and Zeeman fields.

Proposed method

• Formulates a scattering theory for voltage-biased Josephson junctions with helical superconductors, incorporating multiple Andreev reflection (MAR) processes.
• Uses the Nambu formalism to describe the Hamiltonian of superconducting leads with finite Cooper pair momentum 2q, including the spectral gap and Doppler shift effects.
• Derives the exact DC current-voltage (I-V) curve from scattering matrix elements, valid in the low-temperature and subgap regime (e|V| < 2Δ).
• Introduces a model with a single-channel weak link between two helical superconductors, assuming identical pairing gap Δ and momentum 2q on both sides.
• Applies the theory to NS junctions between a normal metal and a helical superconductor, and compares with alternative models involving spin-orbit coupling and Zeeman fields.
• Computes the rectification efficiency η(V) in the subgap regime, showing that η can reach η = 1 under voltage bias.

Experimental results

Research questions

• RQ1 How does multiple Andreev reflection influence the current-voltage characteristics in voltage-biased Josephson diodes with finite Cooper pair momentum?
• RQ2 What is the origin of the observed subharmonic structure in the DC I-V curve, and how is it related to Doppler shifts of the superconducting gap?
• RQ3 Can the rectification efficiency η in the voltage-biased regime exceed the maximum achievable in the current-biased regime, and if so, under what conditions?
• RQ4 How does the presence of finite Cooper pair momentum (2q ≠ 0) lead to nonreciprocal charge transport in the absence of external magnetic fields?
• RQ5 What is the role of resonant dot levels and junction transparency in maximizing the superconducting diode effect efficiency η₀ in related models with spin-orbit coupling and Zeeman fields?

Key findings

• The voltage-biased Josephson diode exhibits a rich subharmonic structure in the DC current-voltage curve due to multiple Andreev reflection and Doppler shifts of the spectral gap.
• In the voltage-biased case, the rectification efficiency can reach the ideal value η = 1, significantly exceeding the maximum η₀ ≈ 0.4 observed in the current-biased case.
• The subharmonic features in the I-V curve emerge specifically in the low-temperature and subgap regime (e|V| < 2Δ), where MAR dominates charge transport.
• For the Josephson diode model with finite Cooper pair momentum, the critical current is direction-dependent, confirming the superconducting diode effect in equilibrium.
• In models with spin-orbit coupling and Zeeman fields, large SDE efficiency η₀ ≈ 0.25 is achieved when a dot level is nearly resonant with the Fermi energy, indicating a strong correlation between resonance and high efficiency.
• The rectification efficiency η(V) remains large in the subgap regime for the spin-orbit/Zeeman model, indicating potential for high-performance nonreciprocal devices.