When subject to a pair-breaking perturbation, the pairing susceptibility of a disordered superconductor exhibits substantial long-ranged mesoscopic fluctuations. Focusing on a thin film subject to a parallel magnetic field, it is proposed that the quantum phase transition to the bulk superconducting condensate may be pre-empted by the formation of a glass-like phase with multi-fractal correlations of a complex order parameter. Although not universal, we argue that such behaviour may be a common feature of quantum critical phenomena in disordered environments.When subject to a pair-breaking perturbation, the pairing susceptibility of a disordered superconductor exhibits substantial long-ranged mesoscopic fluctuations. Focusing on a thin film subject to a parallel magnetic field, it is proposed that the quantum phase transition to the bulk superconducting condensate may be pre-empted by the formation of a glass-like phase with multi-fractal correlations of a complex order parameter. Although not universal, we argue that such behaviour may be a common feature of quantum critical phenomena in disordered environments.

arXiv:cond-mat/0406122Journal of Physics A Mathematical and GeneralAug 25, 20044 citations

SUPERCONDUCTOR-INSULATOR TRANSITIONS

Allen M. Goldman

Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.Superconductor-insulator transitions, especially in thin films, can provide the simplest examples of the continuous quantum phase transition paradigm. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In the example of the superconductor-insulator transition, this control parameter could be the parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements at nonzero temperature of physical behaviors influenced by the quantum fluctuations associated with the transition. This review will focus on experimental aspects of superconductor-insulator transition in disordered films that are effectively two-dimensional. In particular, the evidence for quantum critical behavior in the various types of transitions will be presented. The various theoretical scenarios for the transitions will also be discussed along with the extent to which they are supported by experiment. Open questions relating to the nature of the very puzzling insulating regime and whether there are many different types of superconductor-insulator transitions will be presented. Although this research area is more than 20 years old, rather central issues are not resolved.

International Journal of Modern Physics BAug 30, 2010137 citations

Theory of a Strange Metal in a Quantum Superconductor to Metal Transition

Jaewon Kim, Erez Berg, Ehud Altman

Recent experiments with nanopatterned thin films revealed an unusual quantum superconductor to metal phase transition (QSMT) with a linear in temperature resistivity. In contrast, most known examples of such transitions and standard theoretical considerations predict a temperature-independent sheet resistance of order $R_Q = \frac{\hbar}{e^2}$ . We propose an effective theory of a disordered superconductor which features a QSMT with robust $T$ linear resistivity at the critical point. The crucial ingredient in our model is spatial disorder in the pairing interaction. Such random pairing mirrors the emergent phase disorder seen in a recent mean field study of a microscopic $d$ -wave superconductor subject to potential disorder. We also make the prediction that in such systems the diamagnetic susceptibility diverges as $\log\fracΛ{T}$ , which starkly differs from the power law divergence in standard XY transitions.Recent experiments with nanopatterned thin films revealed an unusual quantum superconductor to metal phase transition (QSMT) with a linear in temperature resistivity. In contrast, most known examples of such transitions and standard theoretical considerations predict a temperature-independent sheet resistance of order $R_Q = \frac{\hbar}{e^2}$. We propose an effective theory of a disordered superconductor which features a QSMT with robust $T$ linear resistivity at the critical point. The crucial ingredient in our model is spatial disorder in the pairing interaction. Such random pairing mirrors the emergent phase disorder seen in a recent mean field study of a microscopic $d$-wave superconductor subject to potential disorder. We also make the prediction that in such systems the diamagnetic susceptibility diverges as $\log\fracΛ{T}$, which starkly differs from the power law divergence in standard XY transitions.

arXiv:2401.17353Jan 30, 20240 citations

Quantum Theory of Disordered Superconductors - A Replica Approach

Yat Fan Lau

Motivated by the experimental observations of the anomalous metal states in many superconducting thin films systems, this thesis studies the interplay of disorder and interactions in superconductivity. We first demonstrate that the Fermi glass ground state is unstable in first-order perturbation theory under weak, short-ranged interaction, provided all states are localized. This finding elucidates why methods like the Hartree-Fock approximation are adequate to explain local moment formation in repulsive interactions. We then revisit the problem of dirty superconductors using a replica-symmetric BCS (RS-BCS) theory. We apply RS-BCS theory to disordered superconducting grains within the localization length, assuming the macroscopic system consists of weakly coupled grains. Besides disordered potential, We also consider regions with opposite signs of interaction exist in the grains, with net attractive interaction between electrons. Using RS-BCS mean field theory, we compute the phase diagram, tunneling density of states, and superfluid density across disorder strengths. Our results qualitatively agree with prior numerical studies for purely attractive interactions, and suggest a possible Cooper-pair-glass state when interactions of opposite signs nearly cancel.Motivated by the experimental observations of the anomalous metal states in many superconducting thin films systems, this thesis studies the interplay of disorder and interactions in superconductivity. We first demonstrate that the Fermi glass ground state is unstable in first-order perturbation theory under weak, short-ranged interaction, provided all states are localized. This finding elucidates why methods like the Hartree-Fock approximation are adequate to explain local moment formation in repulsive interactions. We then revisit the problem of dirty superconductors using a replica-symmetric BCS (RS-BCS) theory. We apply RS-BCS theory to disordered superconducting grains within the localization length, assuming the macroscopic system consists of weakly coupled grains. Besides disordered potential, We also consider regions with opposite signs of interaction exist in the grains, with net attractive interaction between electrons. Using RS-BCS mean field theory, we compute the phase diagram, tunneling density of states, and superfluid density across disorder strengths. Our results qualitatively agree with prior numerical studies for purely attractive interactions, and suggest a possible Cooper-pair-glass state when interactions of opposite signs nearly cancel.

Jan 1, 20250 citations

Phase transitions with critical loop disorder

Hannes Meier, Mats Wallin

Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition.Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$ -transition in $^{4}$ He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario.For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$ .Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role.Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.Condensed matter systems undergoing phase transitions rarely allow exact solutions. The presence of disorder renders the situation even worse but collective Monte Carlo methods and parallel algorithms allow numerical descriptions. This thesis considers classical phase transitions in disordered spin systems in general and in effective models of superfluids with disorder and novel interactions in particular. Quantum phase transitions are considered via a quantum to classical mapping. Central questions are if the presence of defects changes universal properties and what qualitative implications follow for experiments. Common to the cases considered is that the disorder maps out correlated structures. All results are obtained using large-scale Monte Carlo simulations of effective models capturing the relevant degrees of freedom at the transition.Considering a model system for superflow aided by a defect network, we find that the onset properties are significantly altered compared to the $\lambda$-transition in $^{4}$He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario.For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent $z=1.8 \pm 0.05$ contradicting the long standing result $z=d$.Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role.Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.

Jan 1, 20151 citation

Phase transitions in systems with critical cluster defects

Hannes Meier, Mats Wallin

Jan 1, 20151 citation

R_Q = \frac{\hbar}{e^2}

. We propose an effective theory of a disordered superconductor which features a QSMT with robust

T

linear resistivity at the critical point. The crucial ingredient in our model is spatial disorder in the pairing interaction. Such random pairing mirrors the emergent phase disorder seen in a recent mean field study of a microscopic

d

-wave superconductor subject to potential disorder. We also make the prediction that in such systems the diamagnetic susceptibility diverges as

\log\fracΛ{T}

, which starkly differs from the power law divergence in standard XY transitions.

\lambda

-transition in

^{4}

He. This has qualitative implications on expected experimental signatures in a defect supersolid scenario.For the Bose glass to superfluid quantum phase transition in 2D we determine the quantum correlation time by an anisotropic finite size scaling approach. Without a priori assumptions on critical parameters, we find the critical exponent

z=1.8 \pm 0.05

contradicting the long standing result

z=d

.Using a 3D effective model for multi-band type-1.5 superconductors we find that these systems possibly feature a strong first order vortex-driven phase transition. Despite its short-range nature details of the interaction are shown to play an important role.Phase transitions in disordered spin models exposed to correlated defect structures obtained via rapid quenches of critical loop and spin models are investigated. On long length scales the correlations are shown to decay algebraically. The decay exponents are expressed through known critical exponents of the disorder generating models. For cases where the disorder correlations imply the existence of a new long-range-disorder fixed point we determine the critical exponents of the disordered systems via finite size scaling methods of Monte Carlo data and find good agreement with theoretical expectations.

\lambda

-transition in

^{4}

z=1.8 \pm 0.05

contradicting the long standing result

z=d