Gate Voltage Tuned Quantum Superconductor to Insulator Transition in an Ultrathin Bismuth Film Revisited

Abstract

We explore the implications of Berezinskii-Kosterlitz-Thouless (BKT) critical behavior and variablerange hopping on the two dimensional (2D) quantum superconductor-insulator (QSI) transition driven by tuning the gate voltage. To illustrate the potential and the implications of this scenario we analyze sheet resistance data of Parendo et al. taken on a gate voltage tuned ultrathin amorphous bismuth film. The finite size scaling analysis of the BKT-transition uncovers a limiting length L preventing the correlation length to diverge and to enter the critical regime deeply. Nevertheless the attained BKT critical regime reveals consistency with two parameter quantum scaling and an explicit quantum scaling function determined by the BKT correlation length. The two parameter scaling yields for the zero temperature critical exponents of the QSItransition the estimates zν ≃ 3/2, z ≃ 3 and ν ≃ 1/2, revealing that hyperscaling is violated and in contrast to finite temperature disorder is relevant at zero temperature. Furthermore, zν ≃ 3/2 is also consistent with the two variable quantum scaling form associated with a variable-range hopping controlled insulating ground state.

Suppression of the Berezinskii-Kosterlitz-Thouless and quantum phase transitions in two-dimensional superconductors by finite-size effects

“…As a consequence the occurrence of BKT transitions is suppressed and with that the occurrence of quantum phase transitions in the limit T c (d, V g , H) → 0 as well. Nevertheless, in agreement with previous studies, 9,29,30 the lines T c (d, V g , H) exhibit the characteristic quantum critical properties. Additional implications of finite size scaling adapted to the BKT transition include: the magnetic field induced finite size effect generates a flattening out of the sheet resistance in the T → 0 limit, while in zero field it exhibits a characteristic temperature dependence and vanishes at T = 0 only.…”

“…The finite size effects stemming from the limited extent of the homogeneous domains or the applied magnetic field have a profound influence on the observation of the BKT behavior and have been studied intensely in recent years. 9,24,25,29,30 On the other hand, over the years, consistency with BKT behavior has been reported in thin films, 17,[29][30][31][32][33][34][35] and in systems exhibiting interfacial superconductivity. [7][8][9]24 Here we extend previous work 9,24,29,30 and analyze the sheet resistance data of Bi-films 6 and the LaAlO 3 /SrTiO 3 interface 8,9 using the finite size scaling formulas appropriate for the BKT transition, which include multiplicative corrections when present.…”

“…9,24,25,29,30 On the other hand, over the years, consistency with BKT behavior has been reported in thin films, 17,[29][30][31][32][33][34][35] and in systems exhibiting interfacial superconductivity. [7][8][9]24 Here we extend previous work 9,24,29,30 and analyze the sheet resistance data of Bi-films 6 and the LaAlO 3 /SrTiO 3 interface 8,9 using the finite size scaling formulas appropriate for the BKT transition, which include multiplicative corrections when present. 24,25 These systems have been chosen because the data comprise the low temperature limit, namely T << T c where T c is the extrapolated BKT transition temperature attained in the limit of an infinite limiting length L.…”

“…It leads to a characteristic size dependence of the sheet resistance 9,24,25,29,30 Indeed, Eqs. ( 2) and (4) imply that for z = 2 at T * > T c the sheet resistance adopts the size dependence…”