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arXiv:cond-mat/0507218 · Physical Review Letters

Dissipative Dynamics of Planar d -Wave Josephson Junctions

Dmitri V. Khveshchenko

Published Jan 18, 2006• 5 citations
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Abstract

We study quantum dynamics of and phase transitions in a Josephson junction between two planar d-wave superconductors where the processes of both quasiparticle and Cooper pair tunneling give rise to nonlocal dissipative terms in the effective action. By combining a perturbative weak coupling analysis in the charge representation with a variational approach in the phase representation at strong coupling, we ascertain a layout of the junction's phase diagram and discuss the corresponding behaviors.

DOI
10.1103/physrevlett.96.027004

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We study quantum dynamics of and phase transitions in a Josephson junction between two planar d-wave superconductors where the processes of both quasiparticle and Cooper pair tunneling give rise to nonlocal dissipative terms in the effective action. By combining a perturbative weak coupling analysis in the charge representation with a variational approach in the phase representation at strong coupling, we ascertain a layout of the junction's phase diagram and discuss the corresponding behaviors.
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We investigate nonequilibrium transport through superconducting nanojunctions using a Liouville space approach. The formalism allows us to study finite-gap effects, and to account for both quasiparticle and Cooper-pair tunneling. With focus on the weak-tunneling limit, we study the stationary dc and ac current up to second order (cotunneling) in the hybridization energy. For the particular case of a strongly interacting quantum dot sandwiched between two superconductors, we identify the characteristic virtual processes that yield the Andreev and Josephson current and obtain the dependence on the gate and bias voltage for the dc current, the critical current, and the phase-dependent dissipative current. In particular, the critical current is characterized by regions in the stability diagram in which its sign changes from positive to negative, resulting in a multitude of $0\ensuremath{-}\ensuremath{\pi}$ transitions. The latter signal the interplay between strong interactions and tunneling at finite bias.
We study the Josephson junction between two d -wave superconductors, which is discussed as an implementation of a qubit. We propose an approach to calculate the decoherence time due to an intrinsic dissipative process: quantum tunneling between the two minima of the double-well potential excites nodal quasiparticles, which lead to incoherent damping of quantum oscillations. The decoherence is weakest in the mirror junction, where the contribution of nodal quasiparticles corresponds to the superohmic dissipation and becomes small at small tunnel splitting of the energy level in the double-well potential. For available experimental data, we estimate the quality factor.
We have theoretically investigated macroscopic quantum tunneling (MQT) and the influence of nodal quasiparticles and zero energy bound states (ZES) on MQT in s-wave/d-wave hybrid Josephson junctions. In contrast to d-wave/d-wave junctions, the low-energy quasiparticle dissipation resulting from nodal quasiparticles and ZES is suppressed due to a quasiparticle-tunneling blockade effect in an isotropic s-wave superconductor. Therefore, the inherent dissipation in these junctions is found to be weak. This result suggests high potential of s-wave/d-wave hybrid junctions for applications in quantum information devices.
The phase diagram of a system of interacting bosons (Cooper pairs) hoping on a one-dimensional (1D) lattice with onsite phase dissipation describing the Josephson tunneling to a nearby diffusive normal-metal electrode is studied. Starting from the system at commensurate lattice filling, it is shown by a combination of analytical techniques that the phase diagram contains two quantum phases: A dissipative Bose-Einstein condensate (D-BEC) or superconductor with long-range phase coherence, and a dissipative Mott insulator (D-Mott) or "metal" with exponentially decaying phase correlations in space and local imaginary-time correlations decaying as the local pairing correlations of the electrode. The D-Mott/metal phase can be described as a 1D array of dissipative boson puddles, weakly coupled by Josephson tunneling. The puddle size roughly corresponds to the length scale beyond which phase slips suppress phase coherence. The dissipative time-dependent Ginsburg-Landau theory phenomenologically used by Sachdev, Werner, and Troyer [Phys. Rev. Lett. {\bf 92} 237003 (2004)] for the superconductor-metal transition in quasi-1D wires is derived from this microscopic puddle picture. Thus, the criticality of the D-Mott/D-BEC transition is shown to belong to the Wilson-Fisher universality class with dynamical exponent z≈2z\approx 2z≈2. At small doping, the D-Mott/metal phase remains stable due to its finite compressibility, which is computed to leading order in a perturbation expansion of the dissipation strength and the inter-puddle Josephson coupling. At larger doping, using a mapping to a pseudospin chain combined with bosonization, the D-BEC/superconductor phase is the ground state for non-vanishing but arbitrarily small dissipation. Similarities and differences with deconfinement transition of an array 1D bosonic Mott insulators in anisotropic optical lattices are also discussed.