The superconductor-insulator transition of ultrathin films of bismuth, grown on liquid-helium-cooled substrates, has been studied. The transition was tuned by changing both film thickness and perpendicular magnetic field. Assuming that the transition is controlled by a Tϭ0 critical point, a finite-size scaling analysis was carried out to determine the correlation length exponent and the dynamical critical exponent z. The phase diagram and the critical resistance have been studied as a function of film thickness and magnetic field. The results are discussed in terms of bosonic models of the superconductor-insulator transition, as well as the percolation models which predict finite dissipation at Tϭ0.

The superconductor-insulator transition in ultrathin films of amorphous Bi has been tuned by changing both film thickness and magnetic field on the same set of films. A thickness -magnetic field phase diagram has been mapped in the T 0 limit. A finite size scaling analysis has been carried out to determine the critical exponent product nz, which was found to be 1.2 6 0.2 and 1.4 6 0.2 for the thickness-tuned transitions in zero and finite magnetic fields, respectively. These are different from the exponent found for the magnetic-field-tuned transition in the same system, 0.7 6 0.2.[S0031-9007(98)07907-1] PACS numbers: 74.76.Db, 72.15.Rn, 74.25.Dw, 74.40. + k Superconductor-insulator (SI) transitions in ultrathin films of metals are believed to be continuous quantum phase transitions [1] which can be traversed by tuning disorder, film thickness, carrier concentration or applied magnetic field [2,3]. A scaling theory and a phase diagram for a two-dimensional system as a function of disorder and magnetic field were postulated by Fisher et al. [3,4], based on the assumption that this transition can be fully described in terms of a model of interacting bosons, moving in the presence of disorder. Scaling arguments [1] give a lower bound on the correlation length exponent n $ 1, and predict the value of the dynamical critical exponent to be z 1 [3,4]. The dirty boson problem has been extensively studied by quantum Monte Carlo simulations [5-8], real-space renormalization group calculations [9,10], strong coupling expansion [11], and in other ways [12][13][14], but disagreement remains as to the universality class of the transition. Conflicting experimental evidence suggests that the bosonic model might be relevant [15], but does not give the full picture [16]. An alternative model of interacting electrons has also been proposed [17]. Experimentally, the SI transition has been studied in the context of the scaling theory on amorphous Bi (a-Bi) films in zero magnetic field [18], and on thin films of InO x [19] and MoGe [20] with magnetic field as the tuning parameter. In the present work, for the first time, the SI transition was tuned by systematically changing both film thickness and magnetic field on the same set of films. This allows a mapping of a thickness-magnetic field phase diagram as a function of thickness and magnetic field in the T 0 limit and a direct comparison of the critical exponents which characterize each type of the transition. The results suggest that the thickness-driven transition in a fixed magnetic field is similar to that in zero magnetic field, but its exponents are different from those of the magnetic-field-tuned transition studied on the same set of films.Ultrathin a-Bi films were grown on top of a 10 Å thick layer of amorphous Ge, which was previously deposited onto a 0.75 mm thick single crystal of SrTiO 3 ͑100͒. All films were grown in situ under UHV conditions (ϳ10 210 Torr) with substrate temperatures kept below 20 K. Successive depositions were carried out without contamination to in...

A field effect conductance modulation experiment has been performed on a series of nominally homogeneous ultrathin films of metals. The thicknesses of the films were varied over a range such that their properties traversed the insulator-to-superconductor transition. At low gate voltages V G the conductance G͑V G ͒ increased with either polarity for films on the insulating side of the transition and decreased at temperatures in the transition region for films which were just thick enough to be superconducting. A qualitative interpretation of these results suggests the consideration of Cooper pairing even for insulating films. [S0031-9007(97)02374-0] PACS numbers: 74.40.+ k, 73.40.Rw, The superconductor-insulator (S-I) transition in ultrathin films of metals, either as a consequence of disorder [1] or applied magnetic field [2], has been described by the boson Hubbard model and its variants which highlight the role of order parameter phase fluctuations [3]. In this approach, the superconducting state is considered to be a Cooper pair condensate with localized vortices, and the insulating state is a vortex condensate with localized Cooper pairs. The issue of the relevance of this theory to experiment has been challenged by tunneling investigations which have been interpreted as evidence that S-I transitions are dominated by order parameter amplitude fluctuations. Because the boson Hubbard model implies that there are Cooper pairs even on the insulating side of the transition, it is of interest to study the insulating state and the S-I transition in other ways, going beyond conductance and tunneling measurements, to determine whether there is evidence of behavior different from the usual picture of a strongly localized disordered system. This has been done through investigations of the thickness and temperature dependence of the field effect modulation of the conductance [5] of incrementally quench-deposited films of metal above and below the S-I transition. In this Letter we describe our findings which suggest the existence of a symmetry between the insulating and superconducting states implying that insulating films may be other than Coulomb glasses [6] of interacting localized electrons.Investigations were carried out on ultrathin films of Bi or Pb ranging in thickness from 3 to 20 Å, formed on a 10 Å thick predeposited layer of a-Ge, with all films being grown in situ under UHV conditions ͑ϳ10 210 to 10 29 Torr͒ onto single-crystal SrTiO 3 (100) substrates which were 0.75 mm thick. Substrate temperatures during all depositions were held at 9 K, and UHV conditions were sustained over an extended period so that sequential depositions to increase the film thickness could be carried out without contamination. It has been found that films prepared in such a manner become continuous at an average metal thickness on the order of one monolayer and, because of this, are generally considered to be homogeneous [7]. The quartz crystal monitor used to determine nominal film thickness was calibrated using Rutherford backscatte...

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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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The magnetoresistance of ultrathin insulating films of Bi has been studied with magnetic fields applied parallel and perpendicular to the plane of the sample. Deep in the strongly localized regime, the magnetoresistance is negative and independent of field orientation. As film thicknesses increase, the magnetoresistance becomes positive, and a difference between values measured in perpendicular and parallel fields appears, which is a linear function of the magnetic field and is positive. This is not consistent with the quantum interference picture. We suggest that it is due to vortices present on the insulating side of the superconductor-insulator transition.

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