Intrinsic Josephson Effect and Violation of the Josephson Relation in Layered Superconductors

TL;DR

This paper derives equations for layered superconductors, revealing that at higher voltages, the Josephson relation is violated due to current nonuniformity and branch imbalance, challenging traditional Josephson junction models.

Contribution

It introduces a theoretical framework for the resistive state of layered superconductors, highlighting conditions where the Josephson relation breaks down.

Findings

Differential conductivity becomes negative at high voltages.

Nonuniform current distribution causes Josephson relation violation.

Layered superconductors can be modeled as stacked Josephson junctions at low voltages.

Abstract

Equations describing the resistive state of a layered superconductor with anisotropic pairing are derived. The similarity with a stack of Josephson junctions is found at small voltages only, when current density in the direction perpendicular to the layers can be interpreted as a sum of the Josephson superconducting, the Ohmic dissipative and the interference currents. In the spatially uniform state differential conductivity at higher voltages becomes negative. Nonuniformity of the current distribution generates the branch imbalance and violates the Josephson relation between frequency and voltage.