Abstract
We propose the Josephson junctions linked by a normal metal between a d + id superconductor and another d + id superconductor, a d-wave superconductor, or a s-wave superconductor for identifying the chiral d + id superconductivity. The time-reversal breaking in the chiral d-wave superconducting state is shown to result in a Josephson φ0-junction state where the current-phase relation is shifted by a phase φ0 from the sinusoidal relation, other than 0 and π. The ground-state phase difference φ0 and the critical current can be used to definitely confirm and read the information about the d + id superconductivity. A smooth evolution from conventional 0-π transitions to tunable φ0-states can be observed by changing the relative magnitude of two types of d-wave components in the d + id pairing. On the other hand, the Josephson junction involving the d + id superconductor is also the simplest model to realize a φ0- junction, which is useful in superconducting electronics and superconducting quantum computation.
Highlights
As flux- or phase-based quantum bits[30]
We investigate the Josephson junctions linked by a normal metal between a d +id superconductor and another d +id superconductor, a d-wave superconductor, or a s-wave superconductor
Anomalous Josephson effect appears as a result of the broken time-reversal symmetry in the d +id superconductor
Summary
We begin with the BdG Hamiltonian of a two-dimensional d + id superconductor with parabolic spectrum in the normal state. The particular form of the spectrum may not take much effect in the ground-state phase difference of the Josephson junction, but the phase of the pair potential does. For a Josephson junction between two d +id superconductors, the pair potential can be approximately described by two step functions Δ(x) =[ΔLΘ(−x)eiφ/2 +ΔRΘ(x −L)e−iφ/2] where L is the length of the normal layer and φ is the macroscopic phase difference between two superconductors. Similar to Eq (delta), the left (right) pair potential ΔL(ΔR) reads ∆λ (θ) = ∆λ1 cos [2(θ − γλ)] + i∆λ2 sin [2(θ − γλ)] = ∆λ (θ) eiδλ(θ) with λ =L or R denoting the left or right superconductor respectively. Each interface gives a scattering matrix, from which the reflection matrix of the right-going (left-going) incident particles R1 (R2) can be abstracted in the normal layer.
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