Josephson diode effect: a phenomenological perspective

TL;DR

This paper presents a phenomenological model for the Josephson diode effect, classifies its types based on symmetry breaking, and discusses how external currents and noise influence the diode behavior, aiding in superconducting circuit design.

Contribution

It introduces a generalized RCSJ model for the Josephson diode effect, classifies different types based on symmetry considerations, and explains how external stimuli affect the diode characteristics.

Findings

Both inversion and time-reversal symmetries must be broken for the ideal diode effect.

The pseudo diode effect can occur without time-reversal symmetry breaking, driven by noise.

Shapiro steps under RF current can distinguish different diode effect types.

Abstract

As a novel quantum phenomenon with nonreciprocal supercurrent, the Josephson diode effect was intensively studied in recent years. Here, we construct a generalized resistively capacitance shunted junction (RCSJ) model as a low-energy effective/phenomenological theory for a general Josephson junction. For the ideal diode effect defined by unequal critical currents $|I_{c+}|\ne|I_{c-}|$, both inversion $\mathcal{I}$ and time-reversal $\mathcal{T}$ symmetries are required to be broken. It can be further divided into two classes: intrinsic ($\mathcal{T}$-breaking for the junction itself) and extrinsic ($\mathcal{T}$-breaking under external current reversion). In addition, a pseudo diode effect ($\mathcal{T}$-breaking not necessary) can be defined by $|I_{c+}|=|I_{c-}|$ but unequal retrapping currents $|I_{r+}|\ne|I_{r-}|$, for which noise current is further shown to produce the diode feature effectively. Finally, when radio-frequency AC external current exists, the Shapiro steps appear and can be used to distinguish the above three types of the diode effect. Our work provides a unified framework for studying the Josephson diode effect and can be applied to design workable superconducting circuits incorporating the Josephson diode as a fundamental circuit element.