Low-temperature insulating phases of uniformly disordered two-dimensional superconductors

Abstract

Temperature-and magnetic-field-dependent measurements of the longitudinal Rxx and transverse Rxy resistance of amorphous indium oxide thin-film superconductors reveal the presence of distinct insulating phases for sufficiently high disorder and/or magnetic field. For field-swept transitions at fixed disorder and low temperatures there is a critical field where Rxx diverges and the superconductor is transformed into a Bose-glass insulator with localized Cooper pairs. At higher fields there is a second critical field where Rxy appears to diverge, the pairs unbind, and localized single electrons characterizing a Fermiglass insulator dominate. PACS numbers: 74.65.+n, 73.60.Hy, 74.70.Mq, 74.75.+t Numerous studies, both theoretical and experimental, have been concerned with the competition between disorder and superconductivity [1]. Disorder induces localized eigenstates and enhanced Coulomb repulsions which jointly act to reduce the transition temperature and ultimately quench all remnants of superconductivity. This competition between disorder and superconductivity is particularly interesting in two dimensions (2D) where the delicate and marginally attractive pairing interaction is derived from electronic states which are localized for arbitrary weak disorder. Experimentally, systematics of the destruction of superconductivity with increasing disorder in thin films is studied by varying the thickness [2-7], composition [3,8], or resistivity for fixed thickness [9]. Convergence between experimental results and theoretical description has been somewhat hampered by the wide variation in microstructural and compositional properties of these thin-film systems. Recent scaling theories [10-12] of the superconducting-insulating (S-I) transition have avoided these details by taking a broad view and formulating a description which is conveniently insensitive to microscopic material properties. In this description the paired electrons and vortices are treated as quantum-mechanical objects which obey Bose statistics and hence can be treated within a purely "bosonic" formulation. There is experimental evidence for the predicted S-I transitions, driven either by increasing disorder in zero magnetic field [6,7,9] or by increasing field for fixed disorder [13,14]. In these experiments the putative S-I transition takes place at r=0 sheet resistances which vary within a factor of 2 of the predicted universal value, /z/4e^=6450 n/D. Measurements of the field-tuned S-I transition of InO;c films [13], however, confirm detailed predictions [11] of the theory such as the unity value of the dynamical exponent and the scaling collapse of the temperature-and field-dependent resistance data onto a single curve.An implicit assumption of the scaling treatment is that Cooper pairs exist and are finite in extent at the S-I transition. Thus the magnitude ^o of the order parameter is finite on both sides of the S-I transition and the true superconducting phase transition, where long-range order is established and the dc resistance is zero, is dom...

Experimental Evidence for a Collective Insulating State in Two-Dimensional Superconductors

“…Recent experiments provided evidence that at least some of the superconducting correlations remain in the insulating state of amorphous Indium-Oxide films [8,9,13,14]. The insulating behaviour showed a non-monotonic dependence on applied B, resulting in a resistance peak with a typical activation energy [9] that is close to the superconducting transition temperature of the film at B = 0.…”

Magnetic-Field-Tuned Quantum Phase Transition in the Insulating Regime of Ultrathin Amorphous Bi Films

“…In this picture the insulator consists of Bosecondensed, field-induced vortices and localized Cooper pairs [2]. An early experiment by Paalanen, Hebard and Ruel reported a peak in the magnetoresistance of InO x films on the insulating side of the SI transition [3]. The behavior of the Hall resistance at fields close to the peak field led these authors to suggest that there was a crossover from the state proposed by Fisher in which there are localized Cooper pairs, to one in which transport is dominated by single-particle excitations.…”

“…The behavior of the Hall resistance at fields close to the peak field led these authors to suggest that there was a crossover from the state proposed by Fisher in which there are localized Cooper pairs, to one in which transport is dominated by single-particle excitations. They referred to this as crossover between Bose and Fermi insulators [3]. This peak in R(B) in the insulating regime of the field-tuned SI transition has been the subject of numerous investigations in recent years.…”

Self-duality and a Hall-insulator phase near the superconductor-to-insulator transition in indium-oxide films

“…Previous studies have examined evidence for duality (18,19) from resistivity measurements, but have not examined the full conductivity tensor across the transition. In this paper we provide insights concerning the nature of the H-SIT in highly disordered films, using new measurements of the full resistivity tensor across the quantum transition.…”