Tunable ground states in helicalp-wave Josephson junctions

Abstract

We study new types of Josephson junctions composed of helical p-wave superconductors with and -pairing symmetries using quasi-classical Green’s functions with generalized Riccati parametrization. The junctions can host rich ground states: π phase, 0 + π phase, φ0 phase and φ 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 d-vectors and the magnetization, which not only reveals the interaction forms of spin-triplet superconductivity and ferromagnetism, but can also directly lead 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 novel Josephson phases and in the design of quantum circuits.

Symmetry analysis of transport properties in helical superconductor junctions

“…The current will become irrespective of the azimuthal angle φ m . For the SS|F|TS and TS|F|TS junctions, we will have 31) and (40). This relation can also be found in the Josephson junction formed along the edges of quantum spin-Hall insulators with a Zeeman field along the spin quantization [46].…”

“…The other parameters for the figures are taken as: T = 0.3T C , M EF = 0.9 and 2mV0 2 kF = 1. The current has been expressed by the resistance in the normal state [40].…”

“…The helical Josephson junctions can host rich ground states which can be classified into 0 phase, π phase, 0 + π phase, ϕ 0 phase and ϕ phase [40]. The phase transition can be tuned by rotating the magnetization in the ferromagnetic interface.…”

“…Both sin φ-type and cos φ-type of current in the SS|F|helical TS junctions always exists; the selection rules for the current can be given by the orientation of magnetization [39]. The purely helical Josephson junctions with different d-vectors can host more ground states such as π-phase, ϕ-phase and ϕ 0 -phase which can be tuned easily by the direction of magnetization [40]. Especially, the ϕ 0 -phase is recently receiving an increasing interest [25,41,42,43,44,45,46,47].…”

Spin-triplet superconductor$-$quantum anomalous Hall insulator$-$spin-triplet superconductor Josephson junctions: $0$-$π$ transition, $ϕ_{0}$ phase and switch effects

“…The behaviours of CPRs in Josephson junctions are closely related to Hamiltonians of junctions. 13,53,54 Now, we derive the symmetries of CPRs from the continuum model in Eq. (1).…”