Typically the disorder that alters the interference of particle waves to produce Anderson localization is potential scattering from randomly placed impurities. Here we show that disorder in the form of random gauge fields that act directly on particle phases can also drive localization. We present evidence of a superfluid bose glass to insulator transition at a critical level of this gauge field disorder in a nano-patterned array of amorphous Bi islands. This transition shows signs of metallic transport near the critical point characterized by a resistance , indicative of a quantum phase transition. The critical disorder depends on interisland coupling in agreement with recent Quantum Monte Carlo simulations. We discuss how this disorder tuned SIT differs from the common frustration tuned SIT that also occurs in magnetic fields. Its discovery enables new high fidelity comparisons between theoretical and experimental studies of disorder effects on quantum critical systems.
Typically the disorder that alters the interference of particle waves to produce Anderson localization is potential scattering from randomly placed impurities. Here we show that disorder in the form of random gauge fields that act directly on particle phases can also drive localization. We present evidence of a superfluid bose glass to insulator transition at a critical level of this gauge field disorder in a nano-patterned array of amorphous Bi islands. This transition shows signs of metallic transport near the critical point characterized by a resistance , indicative of a quantum phase transition. The critical disorder depends on interisland coupling in agreement with recent Quantum Monte Carlo simulations. We discuss how this disorder tuned SIT differs from the common frustration tuned SIT that also occurs in magnetic fields. Its discovery enables new high fidelity comparisons between theoretical and experimental studies of disorder effects on quantum critical systems.
It is well known that the metal-insulator transition in two dimensions for non-interacting fermions takes place at infinitesimal disorder. In contrast, the superconductor-to-insulator transition takes place at a finite critical disorder (on the order of Vc ~ 2t), where V is the typical width of the distribution of random site energies and t is the hopping scale. In this article we compare the localization/delocalization properties of one and two particles. Whereas the metal-insulator transition is a consequence of single-particle Anderson localization, the superconductor-insulator transition (SIT) is due to pair localization – or, alternatively, fluctuations of the phase conjugate to pair density. The central question we address is how superconductivity emerges from localized single-particle states. We address this question using inhomogeneous mean field theory and quantum Monte Carlo techniques and make several testable predictions for local spectroscopic probes across the SIT. We show that with increasing disorder, the system forms superconducting blobs on the scale of the coherence length embedded in an insulating matrix. In the superconducting state, the phases on the different blobs are coherent across the system whereas in the insulator long-range phase coherence is disrupted by quantum fluctuations. As a consequence of this emergent granularity, we show that the single-particle energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the SIT despite a robust single-particle gap.
We study numerically the superconductor-insulator transition in two-dimensional inhomogeneous superconductors with gauge disorder, described by four different quantum rotor models: a gauge glass, a flux glass, a binary phase glass, and a Gaussian phase glass. The first two models describe the combined effect of geometrical disorder in the array of local superconducting islands and a uniform external magnetic field, while the last two describe the effects of random negative Josephson-junction couplings or $\ensuremath{\pi}$ junctions. Monte Carlo simulations in the path-integral representation of the models are used to determine the critical exponents and the universal conductivity at the quantum phase transition. The gauge- and flux-glass models display the same critical behavior, within the estimated numerical uncertainties. Similar agreement is found for the binary and Gaussian phase-glass models. Despite the different symmetries and disorder correlations, we find that the universal conductivity of these models is approximately the same. In particular, the ratio of this value to that of the pure model agrees with recent experiments on nanohole thin-film superconductors in a magnetic field, in the large disorder limit.
We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above Tc and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.
Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important. The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder. The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
We show, using a Bogoliubov-de Gennes (BdG) mean field theory, that the local pairing amplitude Δ(r) becomes highly inhomogeneous with increasing disorder in an s-wave superconductor. The probability distribution P(Δ) is peaked about the BCS value at low disorder, but with increasing disorder, progressively develops into a broad distribution with significant build up of weight near Δ≈0. At high disorder, the system is found to form superconducting "islands" separated by a non-superconducting sea. Surprisingly, a finite energy gap persists into the highly disordered state in spite of many sites having negligible pairing amplitude and is understood in detail within the BdG framework. Once the pairing amplitude becomes inhomogeneous, the role of quantum phase fluctuations becomes crucial in driving a superconductor-insulator transition at a critical disorder. The insulator is unusual as it has a finite gap for all disorder strengths in marked contrast to the Anderson insulator in non-interacting systems. We treat the phase fluctuations within a self consistent harmonic approximation and obtain the superfluid stiffness as a function of disorder, which agrees well with our earlier quantum Monte Carlo studies.
We investigate the critical behavior and the dynamics of the amplitude (Higgs) mode close to the superfluid-insulator quantum phase transition in an amorphous system (i.e., a system subject to topological randomness). In particular, we map the two-dimensional Bose-Hubbard Hamiltonian defined on a random Voronoi-Delaunay lattice onto a (2+1)-dimensional layered classical XY model with correlated topological disorder. We study the resulting model by laying recourse to classical Monte Carlo simulations. We specifically focus on the scalar susceptibility of the order parameter to study the dynamics of the amplitude mode. To do so, we harness the maximum entropy method to perform the analytic continuation of the scalar susceptibility to real frequencies. Our analysis shows that the amplitude mode remains delocalized in the presence of such topological disorder, quite at odds with its behavior in generic disordered systems, where the randomness localizes the Higgs mode. Furthermore, we show that the critical behavior of the topologically disordered system is identical to that of its translationally invariant counterpart, consistent with a modified Harris criterion. This suggests that the localization of the collective excitations in the presence of disorder is tied to the critical behavior of the quantum phase transition rather than a simple Anderson-localization-type interference mechanism.