Localized superconductors

Interplay of Cooper Pairs and Zero-Energy Quasiparticles in a Gapless Superconductor

The interplay between Cooper pairs and Bogoliubov-de Gennes (BdG) quasiparticles is a topic of considerable interest in the quantum properties of solids, but its important ingredient, the sufficient amount of low-energy quasiparticles to interact with Cooper pairs remains elusive in conventional superconductors. Here a gapless superconductor with coupled paramagnetic atomic layers is used to generate a significant amount of zero-energy quasiparticles that Anderson-localize and bifurcate into regions of high and low zero-energy quasiparticle density of states. The enriched zero-energy quasiparticles induce puddled superconductivity and Josephson vortices. This discovery not only advances the understanding of the mutual interaction of Cooper pairs and BdG quasiparticles but also opens a new avenue for exploring and controlling exotic quantum phenomena where superconductivity, disorder, and spin degrees of freedom are entangled.

Disorder-Broadened Phase Boundary with Enhanced Amorphous Superconductivity in Pressurized In2Te5

As an empirical tool in materials science and engineering, the iconic phase diagram owes its robustness and practicality to the topological characteristics rooted in the celebrated Gibbs phase law free variables (F) = components (C) - phases (P) + 2. When crossing the phase diagram boundary, the structure transition occurs abruptly, bringing about an instantaneous change in physical properties and limited controllability on the boundaries (F = 1). Here, the sharp phase boundary is expanded to an amorphous transition region (F = 2) by partially disrupting the long-range translational symmetry, leading to a sequential crystalline-amorphous-crystalline (CAC) transition in a pressurized In2Te5 single crystal. Through detailed in situ synchrotron diffraction, it is elucidated that the phase transition stems from the rotation of immobile blocks [In2Te2]2+, linked by hinge-like [Te3]2- trimers. Remarkably, within the amorphous region, the amorphous phase demonstrates a notable 25% increase of the superconducting transition temperature (Tc), while the carrier concentration remains relatively constant. Furthermore, a theoretical framework is proposed revealing that the unconventional boost in amorphous superconductivity might be attributed to an intensified electron correlation, triggered by a disorder-augmented multifractal behavior. These findings underscore the potential of disorder and prompt further exploration of unforeseen phenomena on the phase boundaries.

Quantum phase transitions in two-dimensional superconductors: a review on recent experimental progress

Superconductor-insulator/metal transition (SMT) as a paradigm of quantum phase transition has been a research highlight over the last three decades. Benefit from recent developments in the fabrication and measurements of two-dimensional (2D) superconducting films and nanodevices, unprecedented quantum phenomena have been revealed in the quantum phase transitions of 2D superconductors. In this review, we introduce the recent progress on quantum phase transitions in 2D superconductors, focusing on the quantum Griffiths singularity (QGS) and anomalous metal state. Characterized by a divergent critical exponent when approaching zero temperature, QGS of SMT is discovered in ultrathin crystalline Ga films and subsequently detected in various 2D superconductors. The universality of QGS indicates the profound influence of quenched disorder on quantum phase transitions. Besides, in a 2D superconducting system, whether a metallic ground state can exist is a long-sought mystery. Early experimental studies indicate an intermediate metallic state in the quantum phase transition of 2D superconductors. Recently, in high-temperature superconducting films with patterned nanopores, a robust anomalous metal state (i.e. quantum metal or Bose metal) has been detected, featured as the saturated resistance in the low temperature regime. Moreover, the charge-2equantum oscillations are observed in nanopatterned films, indicating the bosonic nature of the anomalous metal state and ending the debate on whether bosons can exist as a metal. The evidences of the anomalous metal states have also been reported in crystalline epitaxial thin films and exfoliated nanoflakes, as well as granular composite films. High quality filters are used in these works to exclude the influence of external high frequency noises in ultralow temperature measurements. The observations of QGS and metallic ground states in 2D superconductors not only reveal the prominent role of quantum fluctuations and dissipations but also provide new perspective to explore quantum phase transitions in superconducting systems.

Pressure-induced disorder and nanosizing inhibits superconductivity in In2Te3

The generation of disorder often gives rise to profound and irreversible physical phenomena. Here, we explore the influence of disorder on the superconducting properties of In2Te3through comprehensive high-pressure investigations. Building upon previous findings, we investigated the progressive suppression of superconductivity in In2Te3during the depressurization process: the increased disorder that ultimately leads to the complete disappearance of the superconducting state. Simultaneously, our high-pressure x-ray diffraction analysis reveals an irreversible structural phase transition. Furthermore, microstructure analysis using transmission electron microscopy clearly demonstrates both grain refinement and a substantial enhancement of disorder. These findings not only provide valuable insights into the mechanism by which disorder suppresses superconductivity, but also offer guidance for future advancements in the fabrication of atmospheric-pressure superconductors.

Evidence for isotropic s-wave superconductivity in high-entropy alloys

High-entropy alloys (HEA) form through the random arrangement of five or more chemical elements on a crystalline lattice. Despite the significant amount of resulting compositional disorder, a subset of HEAs enters a superconducting state below critical temperatures, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\text{c}}<10\,$$\end{document}Tc<10 K. The superconducting properties of the known HEAs seem to suffice a Bardeen–Cooper–Schrieffer (BCS) description, but little is known about their superconducting order parameter and the microscopic role of disorder. We report on magnetic susceptibility measurements on films of the superconducting HEA (TaNb)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1-x}$$\end{document}1-x(ZrHfTi)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{x}$$\end{document}x for characterizing the lower and upper critical fields \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\text{c,1}}(T)$$\end{document}Hc,1(T) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\text{c,2}}(T)$$\end{document}Hc,2(T), respectively as a function of temperature T. Our resulting analysis of the Ginzburg–Landau coherence length and penetration depth demonstrates that HEAs of this type are single-band isotropic s-wave superconductors in the dirty limit. Despite a significant difference in the elemental composition between the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0.35$$\end{document}x=0.35 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0.71$$\end{document}x=0.71 films, we find that the observed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\text{c}}$$\end{document}Tc variations cannot be explained by disorder effects.

Superfluid density in conventional superconductors: from clean to strongly disordered

The highly convergent form of superfluid density in disordered conventional superconductors available in the literature and independently obtained by us following the approach of an earlier paper (Mandal and Ramakrishnan 2020Phys. Rev.B102024514) has been reformulated to separate out the generally used so-called 'dirty-limit' term and an additional term. We use this new expression for making an extensive comparison with previously published experimental data and show that the former, generally used, term isnotsufficient for analyzing these results. We point out that consequently, there is a large regime (disordered superconductors with moderate to no disorder) where theoretical predictions need to be confronted with experiment.

Uniformly Frustrated XY Model: Strengthening of the Vortex Lattice by Intrinsic Disorder

In superconducting films, the role of intrinsic disorder is typically to compete with superconductivity by fragmenting the global phase coherence and lowering the superfluid density. Nonetheless, when a transverse magnetic field is applied to the system and an Abrikosov vortex lattice form, the presence of disorder can actually strengthen the superconducting state against thermal fluctuations. By means of Monte Carlo simulations on the uniformly frustrated XY model in two dimensions, we show that while for weak pinning the superconducting critical temperature Tc increases with the applied field H, for strong enough pinning, the experimental decreasing dependence between Tc and H is recovered with a resulting more robust vortex lattice.

Superconducting Phase Induced by a Local Structure Transition in Amorphous Sb_{2}Se_{3} under High Pressure

Superconductivity and Anderson localization represent two extreme cases of electronic behavior in solids. Surprisingly, these two competing scenarios can occur in the same quantum system, e.g., in an amorphous superconductor. Although the disorder-driven quantum phase transition has attracted much attention, its structural origins remain elusive. Here, we discovered an unambiguous correlation between superconductivity and density in amorphous Sb_{2}Se_{3} at high pressure. Superconductivity first emerges in the high-density amorphous (HDA) phase at about 24 GPa, where the density of glass unexpectedly exceeds its crystalline counterpart, and then shows an enhanced critical temperature when pressure induces crystallization at 51 GPa. Ab initio simulations reveal that the bcc-like local geometry motifs form in the HDA phase, arising from distinct "metavalent bonds." Our results demonstrate that HDA phase is critical for the incipient superconductive behavior.

Self-consistent solution for the magnetic exchange interaction mediated by a superconductor

We theoretically determine the magnetic exchange interaction between two ferromagnets coupled by a superconductor using a tight-binding lattice model. The main purpose of this study is to determine how the self-consistently determined superconducting state influences the exchange interaction and the preferred ground-state of the system, including the role of impurity scattering. We find that the superconducting state eliminates RKKY-like oscillations for a sufficiently large superconducting gap, making the anti-parallel orientation the ground state of the system. Interestingly, the superconducting gap is larger in the parallel configuration than in the anti-parallel configuration, giving a larger superconducting condensation energy, even when the preferred ground state is anti-parallel. We also show that increasing the impurity concentration in the superconductor causes the exchange interaction to decrease, likely due to an increasing localization of the mediating quasiparticles in the superconductor.

Enhancing Superconductivity of the Nonmagnetic Quasiskutterudites by Atomic Disorder

We investigated the effect of enhancement of superconducting transition temperature Tc by nonmagnetic atom disorder in the series of filled skutterudite-related compounds (La3M4Sn13, Ca3Rh4Sn13, Y5Rh6Sn18, Lu5Rh6Sn18; M= Co, Ru, Rh), where the atomic disorder is generated by various defects or doping. We have shown that the disorder on the coherence length scale ξ in these nonmagnetic quasiskutterudite superconductors additionally generates a non-homogeneous, high-temperature superconducting phase with Tc⋆>Tc (dilute disorder scenario), while the strong fluctuations of stoichiometry due to increasing doping can rapidly increase the superconducting transition temperature of the sample even to the value of Tc⋆∼2Tc (dense disorder leading to strong inhomogeneity). This phenomenon seems to be characteristic of high-temperature superconductors and superconducting heavy fermions, and recently have received renewed attention. We experimentally documented the stronger lattice stiffening of the inhomogeneous superconducting phase Tc⋆ in respect to the bulk Tc one and proposed a model that explains the Tc⋆>Tc behavior in the series of nonmagnetic skutterudite-related compounds.

Superfluids, Fluctuations and Disorder

We present a field-theory description of ultracold bosonic atoms in the presence of a disordered external potential. By means of functional integration techniques, we aim to investigate and review the interplay between disordered energy landscapes and fluctuations, both thermal and quantum ones. Within the broken-symmetry phase, up to the Gaussian level of approximation, the disorder contribution crucially modifies both the condensate depletion and the superfluid response. Remarkably, it is found that the ordered (i.e., superfluid) phase can be destroyed also in regimes where the random external potential is suitable for a perturbative analysis. We analyze the simplest case of quenched disorder and then we move to present the implementation of the replica trick for ultracold bosonic systems. In both cases, we discuss strengths and limitations of the reviewed approach, paying specific attention to possible extensions and the most recent experimental outputs.

The BKT Universality Class in the Presence of Correlated Disorder

The correct detection of the Berezinskii-Kosterlitz-Thouless (BKT) transition in quasi-two-dimensional superconductors still remains a controversial issue. Its main signatures, indeed, are often at odds with the theoretical expectations. In a recent work (Maccari, I.; Benfatto, L.; Castellani, C. Phys. Rev. B 2017, 96, 060508), we have shown that the presence of spatially correlated disorder plays a key role in this sense because it is the reason underlying the experimentally-observed smearing of the universal superfluid-density jump. In the present paper we closely investigate the effects of correlated disorder on the BKT transition, specifically addressing the issue of whether or not it changes the BKT universality class.

Microwave Properties of Superconductors Close to the Superconductor-Insulator Transition

Strongly disordered pseudogapped superconductors are expected to display arbitrarily high values of kinetic inductance close to the superconductor-insulator transition (SIT), which make them attractive for the implementation of large dissipationless inductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become a relevant source of dissipation and noise in the outer proximity of the SIT.

Dielectric and diamagnetic susceptibilities near percolative superconductor-insulator transitions

Coarse-grained superconductor-insulator composites exhibit a superconductor-insulator transition governed by classical percolation, which should be describable by networks of inductors and capacitors. We study several classes of random inductor-capacitor networks on square lattices. We present a unifying framework for defining electric and magnetic response functions, and we extend the Frank-Lobb bond-propagation algorithm to compute these quantities by network reduction. We confirm that the superfluid stiffness scales approximately as [Formula: see text] as the superconducting bond fraction p approaches the percolation threshold p _c . We find that the diamagnetic susceptibility scales as [Formula: see text] below percolation, and as [Formula: see text] above percolation. For models lacking self-capacitances, the electric susceptibility scales as [Formula: see text]. Including a self-capacitance on each node changes the critical behavior to approximately [Formula: see text].

Reduction of Electron Repulsion and Enhancement of T_{c} in Small Diffusive Superconducting Grains

The superconducting properties of small metallic grains has been a topic of active research for half a century now. Early experiments demonstrated a remarkable rise in the critical temperature, T_{c}, with reducing grain size in a variety of materials. In two-dimensional diffusive superconductors, T_{c} is decreased due to enhanced Coulomb repulsion. We propose that in finite-size grains the diffusive enhancement of the Coulomb repulsion is weakened and leads ultimately to an increase in T_{c} in isolated, disordered two-dimensional grains. Our mechanism is superimposed on the possible enhancement in T_{c} due to the change in the density of states of finite-size systems.

Nanoscale Inhomogeneous Superconductivity in Fe(Te1-xSex) Probed by Nanostructure Transport

Among iron-based superconductors, the layered iron chalcogenide Fe(Te1-xSex) is structurally the simplest and has attracted considerable attention. It has been speculated from bulk studies that nanoscale inhomogeneous superconductivity may inherently exist in this system. However, this has not been directly observed from nanoscale transport measurements. In this work, through simple micromechanical exfoliation and high-precision low-energy ion milling thinning, we prepared Fe(Te0.5Se0.5) nanoflakes with various thicknesses and systematically studied the correlation between the thickness and superconducting phase transition. Our result revealed a systematic thickness-dependent evolution of superconducting transition. When the thickness of the Fe(Te0.5Se0.5) flake is reduced to less than the characteristic inhomogeneity length (around 12 nm), both the superconducting current path and the metallicity of the normal state in Fe(Te0.5Se0.5) atomic sheets are suppressed. This observation provides the first transport evidence for the nanoscale inhomogeneous nature of superconductivity in Fe(Te1-xSex).

Critical properties of the superfluid-bose-glass transition in two dimensions

We investigate the superfluid (SF) to Bose-glass (BG) quantum phase transition using extensive quantum Monte Carlo simulations of two-dimensional hard-core bosons in a random box potential. T=0 critical properties are studied by thorough finite-size scaling of condensate and SF densities, both vanishing at the same critical disorder Wc=4.80(5). Our results give the following estimates for the critical exponents: z=1.85(15), ν=1.20(12), η=-0.40(15). Furthermore, the probability distribution of the SF response P(lnρSF) displays striking differences across the transition: while it narrows with increasing system sizes L in the SF phase, it broadens in the BG regime, indicating an absence of self-averaging, and at the critical point P(lnρSF+zlnL) is scale invariant. Finally, high-precision measurements of the local density rule out a percolation picture for the SF-BG transition.

Amplitude fluctuations driven by the density of electron pairs within nanosize granular structures inside strongly disordered superconductors: evidence for a shell-like effect

Motivated by the recent observation of the shell effect in a nanoscale pure superconductor by Bose et al. [Nat. Mater. 9, 550 (2010)], we explore the possible shell-like effect in a strongly disordered superconductor as it is known to produce nanosize superconducting puddles (SPs). We find a remarkable change in the texture of the pairing amplitudes that is responsible for forming the SP, upon monotonic tuning of the average electron density, <n>, and keeping the disorder landscape unaltered. Both the spatially averaged pairing amplitude and the quasiparticle excitation gap oscillate with <n>. This oscillation is due to a rapid change in the low-lying quasiparticle energy spectra and thereby a change in the shapes and positions of the SPs. We establish a correlation between the formation of SPs and the shell-like effect. The experimental consequences of our theory are also discussed.

Bose-glass transition and spin-wave localization for 2D bosons in a random potential

A spin-wave approach of the zero temperature superfluid-insulator transition for two-dimensional hard-core bosons in a random potential μ=±W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations leads to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass phase emerges over a finite region until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the spin-wave excitation spectrum is found at a finite frequency Ω(c) decreasing with W, and presumably vanishing in the Bose-glass phase.

Emergence of nanoscale inhomogeneity in the superconducting state of a homogeneously disordered conventional superconductor

The notion of spontaneous formation of an inhomogeneous superconducting state is at the heart of most theories attempting to understand the superconducting state in the presence of strong disorder. Using scanning tunneling spectroscopy and high resolution scanning transmission electron microscopy, we experimentally demonstrate that under the competing effects of strong homogeneous disorder and superconducting correlations, the superconducting state of a conventional superconductor, NbN, spontaneously segregates into domains. Tracking these domains as a function of temperature we observe that the superconducting domains persist across the bulk superconducting transition, T_c, and disappear close to the pseudogap temperature, T*, where signatures of superconducting correlations disappear from the tunneling spectrum and the superfluid response of the system.

Superconductivity in an Inhomogeneous Bundle of Metallic and Semiconducting Nanotubes

Using Bogoliubov-de Gennes formalism for inhomogeneous systems, we have studied superconducting properties of a bundle of packed carbon nanotubes, making a triangular lattice in the bundle's transverse cross-section. The bundle consists of a mixture of metallic and doped semiconducting nanotubes, which have different critical transition temperatures. We investigate how a spatially averaged superconducting order parameter and the critical transition temperature depend on the fraction of the doped semiconducting carbon nanotubes in the bundle. Our simulations suggest that the superconductivity in the bundle will be suppressed when the fraction of the doped semiconducting carbon nanotubes will be less than 0.5, which is the percolation threshold for a two-dimensional triangular lattice.

Superconductor-insulator transition in long MoGe nanowires

The properties of one-dimensional superconducting wires depend on physical processes with different characteristic lengths. To identify the process dominant in the critical regime we have studied the transport properties of very narrow (9-20 nm) MoGe wires fabricated by advanced electron-beam lithography in a wide range of lengths, 1-25  μm. We observed that the wires undergo a superconductor-insulator transition (SIT) that is controlled by cross sectional area of a wire and possibly also by the width-to-thickness ratio. The mean-field critical temperature decreases exponentially with the inverse of the wire cross section. We observed that a qualitatively similar superconductor-insulator transition can be induced by an external magnetic field. Our results are not consistent with any currently known theory of the SIT. Some long superconducting MoGe nanowires can be identified as localized superconductors; namely, in these wires the one-electron localization length is much smaller than the length of a wire.

Superconductor-insulator transition on annealed complex networks

Cuprates show multiphase and multiscale complexity that has hindered physicists search for the mechanism of high T{c} for many years. Recently the interest has been addressed to a possible optimum inhomogeneity of dopants, defects, and interstitials, and the structural scale invariance of dopants detected by scanning micro-x-ray diffraction has been reported to promote the critical temperature. In order to shed light on critical phenomena on granular materials, here we propose a stylized model capturing the essential characteristics of the superconducting-insulator transition of a highly dynamical, heterogeneous granular material: the random transverse Ising model (RTIM) on annealed complex network. We show that when the networks encode for high heterogeneity of the expected degrees described by a power-law distribution, the critical temperature for the onset of the superconducting phase diverges to infinity as the power-law exponent γ of the expected degree distribution is less than 3, i.e., γ<3. Moreover we investigate the case in which the critical state of the electronic background is triggered by an external parameter g that determines an exponential cutoff in the power-law expected degree distribution characterized by an exponent γ. We find that for g=g{c} the critical temperature for the superconducting-insulator transition has a maximum if γ>3 and diverges if γ<3.

Superfluid density and phase relaxation in superconductors with strong disorder

We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov-de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.

Enhancement of the critical temperature of superconductors by Anderson localization

The influence of disorder on the temperature of superconducting transition (T{c}) is studied within the σ-model renormalization-group framework. Electron-electron interaction in particle-hole and Cooper channels is taken into account and assumed to be short range. Two-dimensional systems in the weak localization and antilocalization regime, as well as systems near mobility edge are considered. It is shown that in all these regimes Anderson localization leads to strong enhancement of T{c} related to the multifractality of wave functions. Screening of the long-range Coulomb interaction thus opens a promising direction for searching novel materials for high-T{c} superconductivity.

Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal-insulator transition

We explore the role of phase fluctuations in a three-dimensional s-wave superconductor, NbN, as we approach the critical disorder for destruction of the superconducting state. Close to critical disorder, we observe a finite gap in the electronic spectrum which persists at temperatures well above T(c). The superfluid density is strongly suppressed at low temperatures and evolves towards a linear-T variation at higher temperatures. These observations provide strong evidence that phase fluctuations play a central role in the formation of a pseudogap state in a disordered s-wave superconductor.

Disorder-driven quantum phase transitions in superconductors and magnets

We develop an analytical theory, based on the quantum cavity method, describing the quantum phase transitions in low-temperature, strongly disordered ferromagnets and superconductors. At variance with the usual quantum critical points, we find a phase diagram with two critical points separating three phases. When the disorder increases, the systems goes from the ordered phase to an intermediate disordered phase characterized by activated transport and then to a second disordered phase where no transport is possible. Both the ordered and disordered phases exhibit strong inhomogeneity of their basic properties typical of glassy physics.

Influence of disorder on electron-hole pair condensation in graphene bilayers

Graphene bilayers can condense into a state with spontaneous interlayer phase coherence that supports dissipationless counterflow supercurrents. Here, we address the influence of disorder on the graphene bilayer mean field and Kosterlitz-Thouless critical temperatures and report on a simple criteria for the survival of pair condensation.

Disorder-induced inhomogeneities of the superconducting state close to the superconductor-insulator transition

Scanning tunneling spectroscopy at very low temperatures on homogeneously disordered superconducting titanium nitride thin films reveals strong spatial inhomogeneities of the superconducting gap Delta in the density of states. Upon increasing disorder, we observe suppression of the superconducting critical temperature Tc towards zero, enhancement of spatial fluctuations in Delta, and growth of the Delta/Tc ratio. These findings suggest that local superconductivity survives across the disorder-driven superconductor-insulator transition.

Eigenfunction fractality and pseudogap state near the superconductor-insulator transition

We develop a theory of a pseudogap state appearing near the superconductor-insulator (SI) transition in strongly disordered metals with an attractive interaction. We show that such an interaction combined with the fractal nature of the single-particle wave functions near the mobility edge leads to an anomalously large single-particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.

Doping controlled superconductor-insulator transition in Bi2Sr2-xLaxCaCu2O8+delta

We show that the doping-controlled superconductor-insulator transition (SIT) in a high critical temperature cuprate system (Bi(2)Sr(2-x)La(x)CaCu(2)O(8+delta)) exhibits a fundamentally different behavior than is expected from conventional SIT. At the critical doping, the sheet resistance seems to diverge in the zero-temperature limit. Above the critical doping, the transport is universally scaled by a two-component conductance model. Below, it continuously evolves from weakly to strongly insulating behavior. The two-component conductance model suggests that a collective electronic phase-separation mechanism may be responsible for this unconventional SIT behavior.

Superfluid-insulator transition in commensurate disordered bosonic systems: large-scale worm algorithm simulations

We report results of large-scale Monte Carlo simulations of superfluid-insulator transitions in disordered commensurate 2D bosonic systems. In the off-diagonal disorder case, we find that the transition is to a gapless incompressible insulator, and its dynamical critical exponent is z=1.5(2). In the diagonal-disorder case, we prove the conjecture that rare statistical fluctuations are inseparable from critical fluctuations on the largest scales and ultimately result in crossover to the generic universality class (apparently with z=2). However, even at strong disorder, the universal behavior sets in only at very large space-time distances. This explains why previous studies of smaller clusters mimicked a direct superfluid-Mott-insulator transition.

The Elusive Bose Metal

The conventional theory of metals is in crisis. In the past 15 years, there has been an unexpected sprouting of metallic states in low-dimensional systems, directly contradicting conventional wisdom. For example, bosons are thought to exist in one of two ground states: condensed in a superconductor or localized in an insulator. However, several experiments on thin metal-alloy films have observed that a metallic phase disrupts the direct transition between the superconductor and the insulator. We analyze the experiments on the insulator-superconductor transition and argue that the intervening metallic phase is bosonic. All relevant theoretical proposals for the Bose metal are discussed, particularly the recent idea that the metallic phase is glassy. The implications for the putative vortex-glass state in the copper oxide superconductors are examined.