Mechanisms of spontaneous current generation in an inhomogeneousd-wave superconductor

Abstract

A boundary between two d-wave superconductors or an s-wave and a d -wave superconductor generally breaks time-reversal symmetry and can generate spontaneous currents due to proximity effect. On the other hand, surfaces and interfaces in d-wave superconductors can produce localized current-carrying states by supporting the T -breaking combination of dominant and subdominant order parameters. We investigate spontaneous currents in the presence of both mechanisms and show that at low temperature, counter-intuitively, the subdominant coupling decreases the amplitude of the spontaneous current due to proximity effect. Superscreening of spontaneous currents is demonstrated to be present in any d-d (but not s-d) junction and surface with d + id ′ order parameter symmetry. We show that this supercreening is the result of contributions from the local magnetic moment of the condensate to the spontaneous current.(May 29, 2018)The time-reversal symmetry (T ) breaking on surfaces and interfaces of superconductors with d-wave orbital pairing has been intensively investigated in the last years both in theory and experiment [1][2][3][4][5][6][7][8]. Several mechanisms of T -breaking have been proposed, which fall in two categories: appearance of subdominant order parameter and proximity effect [2,3].In the first case the surface or interface suppresses the dominant order parameter (d x 2 −y 2 in YBCO [4]). If the pairing interaction in other channels is nonzero, the subdominant order parameter will be formed below the corresponding, smaller critical temperature T c2 [9]. The combination of the two order parameters with complex coefficients breaks the T -symmetry [1] and leads to spontaneous surface currents and magnetic fluxes. Usually d x 2 −y 2 ± is or d x 2 −y 2 ± id xy combinations are predicted. Recent observations of zero bias peak splitting in surface tunneling experiments [5] and spontaneous fractional flux (0.1-0.2 Φ 0 ) near the "green phase" inclusions in YBCO films [6] agree with this picture.The other possibility arises in a junction between two d-wave superconductors with different orientations of the order parameter [7]. In this case the two order parameters necessary to form a T -breaking state, d 1,2 , are supplied by the bulk superconductors. The equilibrium phase difference across the boundary, φ 0 , is generally neither 0 nor π, and therefore the states with d 1 +e ±iφ0 d 2 orderings are degenerate and may support spontaneous currents. The same mechanism applies in case of a boundary between an s-and a d-wave superconductor [8].In order to investigate the interplay of both mechanisms, in this letter we consider d-d and s-d interfaces as well as (110)-surface of a d-wave superconductor. We will see that generally the spontaneous currents due to proximity effect are suppressed by the existence of subdominant order parameter. There is also an important distinction between the d-d and s-d cases: In the former case the superconductor may have local orbital and magnetic moments, contributing to the non-dissipative...

Quasiparticle Decoherence ind-Wave Superconducting Qubits

“…In high T c superconductors, the relatively large T c /E F (E F is the Fermi energy), makes the quasiclassical approximation only marginally applicable. It nevertheless has proven successful in calculating equilibrium properties of d-wave superconductors [11,12,13] which are functions of the Fermi velocity v F , quasiparticle energy ǫ, position r, and time t. Here f †R (v F , ǫ; r, t) ≡ f R (−v F , −ǫ; r, t) * , etc. In equilibrium, the retarded and advanced Green's functions can be written in terms of Riccati amplitudes [12] a α 0 and b α 0 in a way very similar to the conventional method for the Matsubara Green's functions [12,13]:…”

“…It nevertheless has proven successful in calculating equilibrium properties of d-wave superconductors [11,12,13] …”

“…In high T c superconductors, the relatively large T c /E F (E F is the Fermi energy), makes the quasiclassical approximation only marginally applicable. It nevertheless has proven successful in calculating equilibrium properties of d-wave superconductors [11,12,13]. Here, we employ the theory of Ref.…”

“…In equilibrium, the retarded and advanced Green's functions can be written in terms of Riccati amplitudes [12] a α 0 and b α 0 in a way very similar to the conventional method for the Matsubara Green's functions [12,13]:…”

Josephson effect in point contacts between “f-wave” superconductors

“…17. Later this theory was generalized for a pinhole model in 3 He [18,19] and for point contacts between «d-wave» high-T c superconductors [20,21]. It was shown that current-phase relations for the Josephson current in such systems are quite different from those of conventional superconductors, and states with a spontaneous phase difference become possible.…”