Suppression of superfluidity by dissipation: An application to failed superconductors

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 ρ of Bose metal at zero temperature behaves as ρ∼ρn(B/Bc2) with ρn being the residual resistivity in the normal state and 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.

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