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arXiv:cond-mat/0007155 · Physical review. B, Condensed matter

Possibility of a metallic phase in granular superconducting films

Tai Kai Ng, Derek K. K. Lee

Published Mar 19, 2001• 14 citations
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Abstract

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.

DOI
10.1103/physrevb.63.144509

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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.
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.
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
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 $\ensuremath{\rho}$ 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 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.
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.
We discuss some problems related to quantum critical phenomena in superfluids and superconductors. In Ch. 1, we apply generalizations of hyperuniversality to quantum phase transitions at zero temperature. We find new universal amplitude combinations involving the superfluid density in Bose systems, as well as confirm and extend previous proposals for universal transport coefficients in two-dimensional superconducting films and magnetic-field-induced metal-insulator transitions. In Ch. 2, we apply the double-dimensionality expansion of Dorogovstev to derive renormalization-group recursion relations for a Bose fluid in a random external potential. We find a nontrivial fixed point. The onset of mean-field behavior for dimensions d > d[subscript]c = 4 is unconventional, yielding discontinuous exponents. Including positive temperatures, we give a clear picture of various crossover regimes. In Ch. 3, We give a detailed derivation of the critical thermodynamics of O(n) spin models, correct to O([epsilon] = 4 - d), using a generalization of the renormalization-group trajectory integral and noncritical matching technique introduced by Rudnick and Nelson. We especially emphasize the coexistence-curve behavior for spins with a continuous symmetry (n [...] 2), deriving detailed expressions for the renormalized spin-wave stiffness and longitudinal susceptibility.