Tunable ground states in helical $p$-wave Josephson junctions

TL;DR

This paper explores tunable ground states in helical p-wave Josephson junctions, revealing rich phase diagrams and phase transitions controlled by magnetization orientation, with implications for quantum circuit design.

Contribution

It introduces a comprehensive analysis of ground states in helical p-wave Josephson junctions, including phase diagrams and free energy models, advancing understanding of spin-triplet superconductivity and ferromagnetism interactions.

Findings

Identification of multiple ground states: $ ext{0}$, $ ext{$ ext{0}+ ext{ extpi}$}$, $ ext{$ ext{ extpi}$}$, and $ ext{$ ext{ extpi}$}+ ext{ extpi}$ phases.

Phase transitions controlled by magnetization rotation and interfacial potentials.

Construction of a Ginzburg-Landau free energy model elucidating spin-triplet and ferromagnetic interactions.

Abstract

We study new types of Josephson junctions composed of helical $p$-wave superconductors with $k_{x}\hat{x}\pm k_{y}\hat{y}$ and $k_{y}\hat{x}\pm k_{x}\hat{y}$-pairing symmetries using quasiclassical Green's functions with the generalized Riccati parametrization. The junctions can host rich ground states: $\pi$ phase, $0+\pi$ phase, $\varphi_{0}$ phase and $\varphi$ phase. The phase transition can be tuned by rotating the magnetization in the ferromagnetic interface. We present the phase diagrams in the parameter space formed by the orientation of the magnetization or by the magnitude of the interfacial potentials. The selection rules for the lowest order current which are responsible for the formation of the rich phases are summarized from the current-phase relations based on the numerical calculation. We construct a Ginzburg-Landau type of free energy for the junctions with ${\bf{d}}$-vectors and the magnetization, which not only reveals the interaction forms of spin-triplet superconductivity and ferromagnetism but also can directly leads to the selection rules. In addition, the energies of the Andreev bound states and the novel symmetries in the current-phase relations are also investigated. Our results are helpful both in the prediction of the novel Josephson phases and in the design of the quantum circuits.