The bose metal: a commentary

Abstract

We review the concept of the Bose metal state which arises in 2D superconductors in the quantum limit where vortex loops can grow spontaneously in (2+1) dimensions and, as zero point motions become larger, eventually lead to an insulating state. A nonlocal Coulomb charging term in a Josephson array type model leads to an effective transverse gauge field which can suppress the condensate of vortices in the superinsulating state leading to an intermediate Bose liquid which is not superfluid at T=0, the Bose metal state. We comment on recent work on this state and on other non-superfluid Bose liquids. FormulationWe start from a 2D Josephson junction array model which can be expressed in terms of the Hamiltonian:where α denotes the nearest neighbor vector to site i, and δn i = (n i − n 0 ) with n i the number density operator which is conjugate to the phase φ i of the superconducting order paramter and n 0 the average density of Cooper pairs. The δn i satisfy the commutation relationsIn the case V 1 = 0, the physics of this model is equivalent to that of a (2+1) dimensional XY model and exhibits a second order phase transition at T = 0 from the superconducting state to the insulating state at a critical value of V 0 /J (Doniach 1981) 1 . In 1999, Das and Doniach (in a paper which we will refer to as DD1) 2 proposed that, as the nearest neighbor repulsion parameter V 1 is increased, a strong coupling phase transition occurs to a phase diagram in which a new Bose metal phase appears at T = 0 in between the superconductng state and the insulating state.Here we review the properties of this Bose metal state and discuss its relation to various investigations more recently carried out by other authors. Strong coupling transitionIn the insulating phase of the junction array model the long range phase coherence of the superconducting order parameter is destroyed by quantum zero point fluctuations and instead the Cooper pair density δn i acquires a non-zero ground state expectation value. In a path integral picture, these quantum fluctuation effects may be represented in terms of the infinite world lines for the Cooper pair bosons which occur in the superfluid state becoming finite loops (hence localized) in the insulator state.In a dual picture, the effects of quantum zero point motion on the superfluid state may be expressed in terms of the growth of vortex loops in (2+1) dimensions. The critical point is reached when the entropic contributions of the vortex loops to the ground state path integral overcome the energetic costs, and a "spaghetti" transition occurs in which the insulating state is filled with vortex loops of infinite extension.The physics in the dual picture may be expressed in terms a set of vortices at positions r i of charge q i = ±q and mass m v interacting via a transverse gauge field a( x) with Hamiltonian:(3) As we shall see below, the action for the gauge field depends on the strength of the near neighbor repulsion V 1 . For V 1 /V 0 sufficiently large (i.e. under strong coupling conditions) it will t...

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