We investigate the influence of inhomogeneity in the pairing coupling constant U͑r ជ͒ on dirty BCS superconductors, focusing on T c , the order parameter ⌬͑r ជ͒, and the energy gap E g ͑r ជ͒. Within mean-field theory, we find that when the length scale of the inhomogeneity is comparable to or larger than the coherence length, the ratio 2E g / T c is significantly reduced from that of a homogeneous superconductor, while in the opposite limit, this ratio stays unmodified. In two dimensions, when strong phase fluctuations are included, the KosterlitzThouless temperature T KT is also studied. We find that when the inhomogeneity length scale is much larger than the coherence length, 2E g / T KT can be larger than the usual BCS value. We use our results to qualitatively explain recent experimental observation of a surprisingly low value of 2E g / T c in thin films.

A bilayer system of two-dimensional electron gases in a perpendicular magnetic field exhibits rich phenomena. At total filling factor tot = 1, as one increases the layer separation, the bilayer system goes from an interlayer-coherent exciton condensed state to an incoherent phase of, most likely, two decoupled compositefermion Fermi liquids. Many questions still remain as to the nature of the transition between these two phases. Recent experiments have demonstrated that spin plays an important role in this transition. Assuming that there is a direct first-order transition between the spin-polarized interlayer-coherent quantum Hall state and spin partially polarized composite Fermi-liquid state, we calculate the phase boundary ͑d / l͒ c as a function of parallel magnetic field, NMR/heat pulse, temperature, and density imbalance, and compare with experimental results. Remarkably good agreement is found between theory and various experiments.

The magnetically driven superconductor-insulator transition in amorphous thin films ͑e.g., InO and Ta͒ exhibits several mysterious phenomena, such as a putative metallic phase and a huge magnetoresistance peak. Unfortunately, several conflicting categories of theories, particularly quantum-vortex condensation, and normal region percolation, explain key observations equally well. We present a experimental setup, an amorphous thin-film bilayer, where a drag resistance measurement would clarify the role quantum vortices play in the transition, and hence decisively point to the correct picture. We provide a thorough analysis of the device, which shows that the vortex paradigm gives rise to a drag with an opposite sign and orders of magnitude larger than the drag measured if competing paradigms apply. DOI: 10.1103/PhysRevB.80.180503 PACS number͑s͒: 74.78.Db, 73.43.Nq, 74.25.Fy, 74.78.Fk The superconducting state and the metallic Fermi-liquid form the very basis of our understanding of correlated electron systems. Nevertheless, the transition between these two phases in disordered films is shrouded in mystery. Experiments probing this transition in amorphous thin films such as Ta, MoGe, InO, and TiN used a perpendicular magnetic field and disorder ͑tuned through film thickness͒ to destroy superconductivity. But instead of a superconductor-metal transition, they observed in many cases a superconductor-insulator transition ͑SIT͒. 1 The "dirty boson" model 2 propounded the notion that the insulator is the mark of vortex condensation, and that the SIT occurs at a universal critical resistance, R ᮀ = h / 4e 2 . More recent experiments, however, showed the critical resistance to be nonuniversal. 3 Furthermore, in many field tuned experiments, a surprising metallic phase intervenes between the superconductor and insulator, 4-6 with a temperature-independent resistance below T ϳ 50 mK, and ͑at least in Ta films͒ a distinct nonlinear I-V characteristics. 7 Quite generically, 5,6,8 these films exhibit a peak in the magnetoresistance ͑MR͒ curve ͑particularly strong in InO and TiN͒ as in Fig. 1͑a͒.Two competing categories of theories may account for these phenomena. On one hand, within the quantum vortex pictures, 2,9,10 the insulating phase implies vortex condensation, the intervening metallic phase is described as uncondensed vortex liquid ͑e.g., vortex Fermi liquid͒, and the high field nonmonotonic MR indicates the appearance of a finite electronic density of states ͑DOS͒ at the Fermi level. On the other hand, the percolation paradigm 11,12 describes the films as consisting of superconducting ͑SC͒ and normal puddles; at the MR peak SC puddles exhibit a Coulomb blockade, and the percolating normal regions consist of narrow conduction channels. Yet a third theory tries to account for the low field SC-metal transition using a phase glass model 13 ͑see, however, Ref. 14 which argues against these results͒ but does not address the full MR curve. Qualitatively, both paradigms above are consistent with MR observations, and recent...

The magnetical field tuned superconductor-insulator transition in amorphous thin films, e.g., Ta and InO, exhibits a range of yet unexplained curious phenomena, such as a putative low-resistance metallic phase intervening the superconducting and the insulating phase, and a huge peak in the magnetoresistance at large magnetic field. Qualitatively, the phenomena can be explained equally well within several significantly different pictures, particularly the condensation of quantum vortex liquid, and the percolation of superconducting islands embedded in normal region. Recently, we proposed and analyzed a distinct measurement in Y. Zou, G. Refael, and J. Yoon, Phys. Rev. B 80, 180503 ͑2009͒ that should be able to decisively point to the correct picture: a drag resistance measurement in an amorphous thin-film bilayer setup. Neglecting interlayer tunneling, we found that the drag resistance within the vortex paradigm has opposite sign and is orders of magnitude larger than that in competing paradigms. For example, two identical films as in G. Sambandamurthy, L. W. Engel, A. Johansson, and D. Shahar, Phys. Rev. Lett. 92, 107005 ͑2004͒ with 25 nm layer separation at 0.07 K would produce a drag resistance ϳ10 −4 ⍀ according the vortex theory but only ϳ10 −12 ⍀ for the percolation theory. We provide details of our theoretical analysis of the drag resistance within both paradigms and report some results as well.

The random hopping models exhibit many fascinating features, such as diverging localization length and density of states as energy approaches the band center due to its particle-hole symmetry. Nevertheless, such models are yet to be realized experimentally because the particle-hole symmetry is easily destroyed by diagonal disorder. Here we propose that a pure random hopping model can be effectively realized in ultracold atoms by modulating a disordered onsite potential in particular frequency ranges. This idea is motivated by the recent development of the phenomena called "dynamical localization" or "coherent destruction of tunneling." Investigating the application of this idea in one dimension, we find that if the oscillation frequency of the disorder potential is gradually increased from zero to infinity, one can tune a noninteracting system from an Anderson insulator to a random hopping model with diverging localization length at the band center, and eventually to a uniform-hopping tight-binding model.