Evidence of Collective Charge Behavior in the Insulating State of Ultrathin Films of Superconducting Metals

Abstract

Nonlinear I-V characteristics have been observed in insulating quench-condensed films which are locally superconducting. We suggest an interpretation in terms of the enhancement of conduction by the depinning of a Cooper pair charge density wave, Cooper pair crystal, or Cooper pair glass that may characterize the insulating regime of locally superconducting films. We propose that this is a more likely description than the Coulomb blockade or charge-anticharge unbinding phenomena.In the context of the Bose-Hubbard model, which is equivalent to the model of a Josephson junction array with charging, zero-temperature superconductorinsulator(SI) transitions in two dimensions (2D), tuned by disorder or magnetic field, are believed to be direct, with metallic behavior only at the quantum critical point [1]. Recent experiments have suggested the existence of a significant metallic phase between the superconductor and insulator. The Stanford group reported this for nominally superconducting MoGe films in moderate magnetic fields at low temperatures, and conjectured that it was due to dissipation [2]. They later found "true" superconductivity in low fields [3]. Long ago, metallic behavior was reported in quench-condensed granular films over a range of thicknesses intermediate between those for which films were insulating and superconducting [4], and it was found more recently in Josephson junction arrays [5]. Re-examination of the theory has involved the inclusion of aspects of percolation [6], elaboration of the Bose-Hubbard model [7,8], and consideration of dissipative Bose systems [9]. Das and Doniach [7] explained aspects of Ref. 4 by extending the Bose-Hubbard model to high filling and including nearest-neighbor as well as on-site Coulomb interactions. Their phase diagram contains the possibility of an intervening Bose metal phase, or a direct transition, depending upon the relative magnitudes of the various Coulomb and Josephson coupling energies. The Bose metal contains free vortices and antivortices, prevented from Bose condensing by dissipation. The insulator is a condensate of vortices, or in other language, a Cooper pair charge density wave (CDW). Phillips and Dalidovich [8], using the original form of the Bose-Hubbard model, also demonstrated that there was a Bose metallic phase. This followed from a subtle cancellation in the expression for the conductivity between an exponentially small population of bosonic quasiparticles and their associated exponentially long scattering time. The Bose insulator in this picture results from dissipative processes such as coupling to a heat bath, or from a high enough level of disorder. Ng and Lee [9], using a different approach to theory of dissipative Bose systems, suggest that a Bose metal does not exist at zero temperature, but note a crossover regime at finite temperature that could be identified as a metallic phase.In this letter we shift the focus to the study of the insulating regime of granular quench-condensed films. In the past the insulator has not been carefully...

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