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Journal of Physics Condensed Matter

Dissipative phase transition in two-dimensional d-wave Josephson junctions

Dmitri V. Khveshchenko

Published Feb 10, 2006• 3 citations
Publisher

Abstract

Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY -model, where both quasiparticle and Cooper pair tunnelling terms appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find compelling evidence of a dissipative phase transition. The corresponding critical behaviour is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.

DOI
10.1088/0953-8984/18/8/010

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Quantum dynamics of in-plane Josephson junctions between two d-wave superconducting films is described by the anisotropic XY -model, where both quasiparticle and Cooper pair tunnelling terms appear to be equally non-local. Applying a combination of the weak and strong coupling analyses to this model, we find compelling evidence of a dissipative phase transition. The corresponding critical behaviour is studied and contrasted with that found previously in the conventional (s-wave) Josephson junctions.
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.
This thesis presents seven research papers on topics in condensed-matter theory. Five of the papers report on Monte Carlo studies of quantum phase transitions in various (d+1)-dimensional statistical mechanics models featuring Caldeira-Leggettlike dissipation. The principal motivation for these studies was to investigate a particular bond-dissipative (2+1)-dimensional XY model of circulating currents in cuprate high-temperature superconductors. It has been proposed that quantum critical fluctuations associated with a local quantum critical point described by this model can explain the marginal-Fermi-liquid behaviour of the normal state of these compounds. We present simulation results for this model for both compact and noncompact phase variables and show unambiguously that the quantum critical point in the compact case is not local. If the phases are taken to be noncompact variables, the model is also a model of resistively shunted Josephson junction arrays. The results in this case reveal a more complicated phase diagram, but we have not been able to establish critical behaviour consistent with the scenario of local quantum criticality.\n\nThe study of extended quantum dissipative models is also motivated by the general effect on condensed-matter systems of the coupling to environmental degrees of freedom. Their influence on quantum critical phenomena is characterized by the dynamical critical exponent z, a measure of spatiotemporal anisotropy, the value of which can be estimated by naive scaling arguments. We confirm by numerical means that such scaling estimates give correct results to a good approximations (with a few reservations), irrespective of system dimensionality, order parameter symmetry, or whether the variables are compact or noncompact. Corrections to the naive scaling estimates have to be invoked for strongly super-Ohmic dissipation for d = 1 due to relatively large values of the anomalous scaling dimension η.\n\nThe two last research papers are concerned with the superconducting pairing state of the recently discovered class of iron-based high-temperature superconductors. Here, we calculate possible signatures of the proposed s±-wave pairing state in conductance-spectroscopy and Josephson-effect experiments.
We investigate nonequilibrium dynamics of a triad of fermionic superfluids connected via Josephson junctions, following sudden switch-on of two-body loss in one of the three superfluids. By formulating the dissipative BCS theory for the Lindblad equation, we find that the superfluid order parameter exhibits a phase rotation, thereby giving rise to three types of dc Josephson currents corresponding to different junctions. We demonstrate that, when the tunneling amplitude V31V_{31}V31​ between superfluids without two-body loss is weak, a two-step nonequilibrium phase transition characterized by the vanishing dc Josephson currents occurs: dissipation first induces the nonequilibrium phase transition by making one dc Josephson current finite, while further increasing dissipation makes this remaining dc Josephson current vanish. By contrast, when V31V_{31}V31​ is strong, dissipation induces the nonequilibrium phase transition in which all dc Josephson currents simultaneously vanish. An analytical study based on a simplified model further supports this observation.
The study of entanglement in quantum systems is an area of much recent experimental and theoretical work and is of central importance in the implementation of various protocols in quantum information science. The dynamical properties of entanglement are examined in the context of the XY spin 1/2 chain model with a staggered magnetic field. The quality of entangled state transfer is found to be comparable to the uniform field XY spin 1/2 chain in the strong field regime. The effects of anisotropy on state transfer is also considered, as well as the interaction between entanglement waves and the possibility of transmission of multiple bits of quantum information. As an additional system where these quantum entanglement dynamics might play out, a large array of mesoscopic junctions made out of gapless unconventional superconductors is also studied. In this model, the tunneling processes of both particle-hole and Cooper pairs give rise to a strongly retarded effective action which, contrary to the case of conventional superconductors, cannot be readily characterized in terms of a local Josephson energy. This is an action that describes, for example, grain boundary and c-axis junctions in layered high-Tc superconductors. The emergent collective phenomena in this system are obtained, along with the phase diagram and the electrical conductivity of the model.
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.