Degenerate Ground State in a MesoscopicYBa2Cu3O7−x

Abstract

We have measured the current-phase relationship I(ϕ) of symmetric 45 • YBa2Cu3O7−x grain boundary Josephson junctions. Substantial deviations of the Josephson current from conventional tunnel-junction behavior have been observed: (i) The critical current exhibits, as a function of temperature T , a local minimum at a temperature T * . (ii) At T ≈ T * , the first harmonic of I(ϕ) changes sign. (iii) For T < T * , the second harmonic of I(ϕ) is comparable to the first harmonic, and (iv) the ground state of the junction becomes degenerate. The results are in good agreement with a microscopic model of Josephson junctions between d-wave superconductors.The most important phenomenological difference between the high-T c cuprates and conventional superconductors regards the orbital symmetry of the superconducting order parameter. In the cuprates the pair potential changes sign depending on the direction in momentum space according to 1,2 ∆(ϑ) = ∆ 0 cos 2(ϑ − θ), where ϑ is the angle between the wave vector and the (laboratory) x-axis, while θ is the angle between the Cu-Cu bond direction of the superconductor and the x-axis. This unconventional d-wave symmetry was predicted 3 and experimentally confirmed 1,2 to be directly measurable in the Josephson effect between a high-T c and a conventional superconductor. Another consequence of the dwave symmetry is that mid-gap states (MGS) with energy ε = 0 should form on the free surface of a d-wave superconductor if ∆(ϑ) has opposite signs on incident and reflected electronic trajectories. 4 The MGS density must be maximal for (110)-like surfaces and this prediction has in fact been confirmed by STM microscopy on YBCO single crystals 5 which revealed the MGS contribution to the YBCO tunneling density of states. The presence of the MGS is expected to influence in a spectacular way also the Josephson effect in junctions between d-wave superconductors with different crystallographic orientations. Yet no clear manifestation of the MGS in the Josephson effect in such junctions has been observed so far, which is a challenge for the concept of d-wave superconductivity in the cuprates.Moreover, due to possible applications in quantum computing, 6,7 there is substantial interest in Josephson junctions and circuits with a doubly degenerate ground state. Such a state was predicted in an asymmetric 45 • junction (θ 1 = 0 • and θ 2 = 45 • , the angles θ 1,2 are defined in Fig. 1), since odd harmonics of the Josephson current I(ϕ) = n I n sin nϕ are suppressed by symmetry. 8,9The current-phase relation observed in Ref. 10 indeed showed a substantial contribution of the second harmonic I 2 . However, there is a finite supercurrent flowing along the interface in the ground state of asymmetric 45 • junctions. 9 Therefore they do not lead to completely quiet qubits in the sense of Ref. 6. Motivated by the search for both, the MGS in high-T c Josephson junctions and a quiet qubit, we have studied symmetric 45 • junctions (i.e. junctions with θ 1 = −θ 2 = 22.5 • ). In this paper we report the fir...

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