Time-reversal symmetry breaking at Josephson tunnel junctions of purely d-wave superconductors

T. Löfwander; V. S. Shumeiko; G. Wendin

doi:10.1103/PhysRevB.62.R14653

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Time-reversal symmetry breaking at Josephson tunnel junctions of purely d-wave superconductors

T. Löfwander, V. S. Shumeiko, G. Wendin

DOI 10.1103/PhysRevB.62.R14653 · Physical Review B

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Abstract

We study spontaneous time-reversal symmetry breaking at Josephson tunnel junctions of d-wave superconductors in the absence of subdominant components of the order parameter. For tunnel junctions, when the orientation is close to 0/45 (for which a gap lobe points towards the junction on one side and a gap node on the other), the mechanism of the symmetry breaking is the splitting of midgap states (MGS) by spontaneous establishment of a phase difference φ=±π/2 across the junction. This occurs for transparencies D≫ξ0/λ and temperatures kBT≪DΔ0, where ξ0 is the coherence length, λ is the penetration depth, and Δ0 is the maximum energy gap. On the other hand, tunnel junctions with D≪ξ0/λ effectively behave as surfaces, for which the mechanism of symmetry breaking is self-induced Doppler shifts of MGS. For this instability, we calculate the phase-transition temperature kBTTRSB=(1/6)(ξ0/λ)Δ0 and show that the spatial shape of the gap is unimportant.