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arXiv:1908.06590 · Physical review. B./Physical review. B

Suppression of superfluidity by dissipation: An application to failed superconductors

Kou Misaki, Naoto Nagaosa

Published Sep 30, 2020• 0 citations
arXivHTMLPDF

Abstract

The ground states of bosons have been classified into superfluids, bosonic quantum Hall states, Mott insulators, and Bose glass. Recent experiments in two-dimensional clean superconductors under an external magnetic field $B$ strongly suggest the existence of the fourth quantum state of Cooper pairs, i.e., Bose metal or quantum metal, where the resistivity remains constant at lowest temperature. However, its theoretical understanding remains unsettled. In this paper, we propose a model where the vortices behave as quantum bosons subject to dissipation at the normal core. We discuss that those bosons remain metallic even at zero temperature by generalizing the Feynman picture of superfluidity in the first quantization formulation and also by a perturbative calculation for a field theoretical model in the second quantization formalism. This result indicates that the resistivity $\ensuremath{\rho}$ of Bose metal at zero temperature behaves as $\ensuremath{\rho}\ensuremath{\sim}{\ensuremath{\rho}}_{n}(B/{B}_{c2})$ with ${\ensuremath{\rho}}_{n}$ being the residual resistivity in the normal state and ${B}_{c2}$ the second upper critical field. It also predicts that the Bose metal is missing in superclean superconductors and at the dirty limit or in granular superconductors.

DOI
10.1103/physrevb.102.104515

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The ground states of bosons have been classified into superfluids, bosonic quantum Hall states, Mott insulators, and Bose glass. Recent experiments in two-dimensional clean superconductors under an external magnetic field BBB strongly suggest the existence of the fourth quantum state of Cooper pairs, i.e., Bose metal or quantum metal, where the resistivity remains constant at lowest temperature. However, its theoretical understanding remains unsettled. In this paper, we propose a model where the vortices behave as quantum bosons subject to dissipation at the normal core. We discuss that those bosons remain metallic even at zero temperature by generalizing the Feynman picture of superfluidity in the first quantization formulation and also by a perturbative calculation for a field theoretical model in the second quantization formalism. This result indicates that the resistivity \ensuremathρ\ensuremath{\rho}\ensuremathρ of Bose metal at zero temperature behaves as \ensuremathρ\ensuremath∼\ensuremathρn(B/Bc2)\ensuremath{\rho}\ensuremath{\sim}{\ensuremath{\rho}}_{n}(B/{B}_{c2})\ensuremathρ\ensuremath∼\ensuremathρn​(B/Bc2​) with \ensuremathρn{\ensuremath{\rho}}_{n}\ensuremathρn​ being the residual resistivity in the normal state and Bc2{B}_{c2}Bc2​ the second upper critical field. It also predicts that the Bose metal is missing in superclean superconductors and at the dirty limit or in granular superconductors.
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.
Experiments in thin films whose thickness can be modified and by this way induce a superconductor to insulator transition, seem to suggest that in the quantum critical regime of this phase transition there might be a Bose metal, i.e., uncondensed bosonic carriers with a finite dissipation. This poses a fundamental problem as to our understanding of how such a state could be justified. On the basis of a simple Boson-Fermion model, where bosonic and fermionic degrees of freedom are strongly inter-related via a Boson-Fermion pair exchange coupling g, we illustrate how such a bosonic metal phase could possibly come about. We show that, as we approach the quantum critical point at some critical gc from the superfluid side, the superfluid phase locking is sustained only for longer and longer spatial scales. On a finite spatial scale, the boson have a quasi-free itinerant behavior with metallic features. At the quantum critical point the systems exhibits a phase separation which shows a ressemblance to that of a He 3– He 4 mixture. This could be the clue to the apparent dilemma of a Bose metal at zero temperature.
I argue that the system of interacting bosons at zero temperature and in random external potential possesses a simple critical point that describes the proliferation of disorder-induced defects in the superfluid ground state, and that is located at weak disorder close to and above one dimension. This makes it possible to address the critical behavior at the superfluid-Bose glass transition in dirty boson systems by expanding around the lower critical dimension of d=1.d=1.d=1. Within the formulated renormalization procedure near d=1,d=1,d=1, the dynamical critical exponent is obtained exactly and the correlation length critical exponent is calculated as a Laurent series in the parameter $\sqrt{\ensuremath{\epsilon}},$ with $\ensuremath{\epsilon}=d\ensuremath{-}1:$ z=d,z=d,z=d, $\ensuremath{\nu}=1/\sqrt{3\ensuremath{\epsilon}}+O(\sqrt{\ensuremath{\epsilon}})$ for the short-range, and z=1,z=1,z=1, $\ensuremath{\nu}=\sqrt{2/3\ensuremath{\epsilon}}+O(\sqrt{\ensuremath{\epsilon}}),$ for the long-range Coulomb interaction between bosons. The identified critical point should be stable against the residual perturbations in the effective action for the superfluid, at least in dimensions 1< d< 2,1<~d<~2,1< d< 2, for both short-range and Coulomb interactions. For the superfluid-Mott insulator transition in the system in a periodic potential and at a commensurate density of bosons, I find $\ensuremath{\nu}=(\frac{1}{2}\sqrt{\ensuremath{\epsilon}})+\frac{1}{4}+O(\sqrt{\ensuremath{\epsilon}}),$ which yields a result in reasonable agreement with the known XY\mathrm{XY}XY critical exponent in d=2.d=2.d=2. The critical behavior of the superfluid density, phonon velocity, and the compressibility in the system with short-range interactions is discussed.
We investigate the possibility of finding a zero-temperature metallic phase in granular superconducting films, modeled as a dissipative Bose system. We extend the conventional treatment of these systems to a formalism that can distinguish between insulator, metal, and superfluid phases. We do not find a metallic state at zero temperature. At finite temperatures, we find that the system exhibits a crossover between superfluid and metallic behavior. This has implications for the analysis of experimental results that makes use of a scaling hypothesis involving only a single parameter. We also investigate the effect of vortex dissipation in these systems.
We have observed a metallic-like state, which persists to the zerotemperature limit, in a 3D Bose-Hubbard system of ultra-cold atoms trapped in an optical lattice. The damping rate of atomic motion— the analog of electrical resistance in a solid—in the confining parabolic potential fits well to a model that includes finite damping at zero temperature. The low-temperature behavior is consistent with the theory of quantum tunneling of phase slips, while at higher temperatures a cross-over consistent with the transition between quantum tunneling and thermal activation of phase slips is evident. The existence of a metallic phase in a bosonic system may have implications for the unusual dissipative phases apparent in solid-state superconducting films. The ground state of a system of bosons is predicted to be either superconducting or insulating (1). However, experiments on superconducting films have shown that a dissipative phase can exist to the lowest temperatures attainable. For example, experiments on
Motivated by the recent experimental observation of an intermediate bosonic metallic state in the two-dimensional superconductor-insulator transition at T=0T=0T=0, we study an extended Bose-Hubbard model in the limit of a large number of particles per site. Using a representation of this in terms of two coupled XYXYXY models, we find, in addition to an insulating phase and a (2+1)D(2+1)\mathrm{D}(2+1)D superfluid phase, two other phases. One phase is a 2D superfluid phase where a crossover from (2+1)D(2+1)\mathrm{D}(2+1)D to 2D has taken place as a result of incipient charge ordering, signaled by $\ensuremath{\theta}$ disordering, and which is closely related to a supersolid phase. The other new phase is an edge metal state characterized by zero superfluid stiffness, zero charge ordering, and zero bulk compressibility. However, the edge compressibility of the system is nonzero. While we do not find any intermediate state with 2D metallic conductivity, we are able to connect these results to STM experiments on MoS2{\mathrm{MoS}}_{2}MoS2​ showing brims of finite density of states around the entire edge of 2D MoS2{\mathrm{MoS}}_{2}MoS2​ samples.