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 ${T}_{c}$ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.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 ${T}_{c}$ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.

arXiv:cond-mat/9807008Physical review. B, Condensed matterFeb 1, 199951 citations

Disorder Effects on the Topological Superconductor with Hubbard Interactions

Yiting Deng, Yan He

Jan 1, 20240 citations

Site-disorder driven superconductor–insulator transition: a dynamical mean field study

Naushad Ahmad Kamar, N S Vidhyadhiraja

We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.

arXiv:1309.7224Journal of Physics Condensed MatterFeb 13, 20142 citations

Universal conductivity of two-dimensional films at the superconductor-insulator transition

Min-Chul Cha, Matthew P. A. Fisher, S. M. Girvin +2 more

The zero-temperature universal conductivity of two-dimensional (2D) films at the supeconductor-insulator transition is studied. The existence of a finite conductivity at T=0 and the universality class for this transition is discussed. Neglecting disorder as a first approximation, so the transition is from a commensurate Mott-Hubbard insulator to a superconductor, we calculate analytically the universal conductivity for the 2D pure boson Hubbard model up to the first order in a large-N expansion and numerically by Monte Carlo simulation of the (2+1)-D XY model. From the Monte Carlo results we find the universal conductivity to be ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$=(0.285\ifmmode\pm\else\textpm\fi{}0.02)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}^{\mathrm{\ensuremath{-}}1}$== ${\mathit{R}}_{\mathit{Q}}$ ==h/(2e ${)}^{2}$ \ensuremath{\approxeq}6.45 k\ensuremath{\Omega}. An analysis in 1D suggests that in the presence of disorder, the universal conductivity in films might be somewhat smaller than this value. The possible existence of universal dissipation in $^{4}\mathrm{He}$ films is also discussed briefly.The zero-temperature universal conductivity of two-dimensional (2D) films at the supeconductor-insulator transition is studied. The existence of a finite conductivity at T=0 and the universality class for this transition is discussed. Neglecting disorder as a first approximation, so the transition is from a commensurate Mott-Hubbard insulator to a superconductor, we calculate analytically the universal conductivity for the 2D pure boson Hubbard model up to the first order in a large-N expansion and numerically by Monte Carlo simulation of the (2+1)-D XY model. From the Monte Carlo results we find the universal conductivity to be ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$=(0.285\ifmmode\pm\else\textpm\fi{}0.02)${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}^{\mathrm{\ensuremath{-}}1}$==${\mathit{R}}_{\mathit{Q}}$==h/(2e${)}^{2}$\ensuremath{\approxeq}6.45 k\ensuremath{\Omega}. An analysis in 1D suggests that in the presence of disorder, the universal conductivity in films might be somewhat smaller than this value. The possible existence of universal dissipation in $^{4}\mathrm{He}$ films is also discussed briefly.

Physical review. B, Condensed matterOct 1, 1991355 citations

Disorder effects on the topological superconductor with Hubbard interactions

Yiting Deng, Yan He

Physics Letters AApr 2, 20241 citation

{T}_{c}

and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.

{\mathit{R}}_{\mathit{Q}}

==h/(2e

{)}^{2}

\ensuremath{\approxeq}6.45 k\ensuremath{\Omega}. An analysis in 1D suggests that in the presence of disorder, the universal conductivity in films might be somewhat smaller than this value. The possible existence of universal dissipation in

^{4}\mathrm{He}

films is also discussed briefly.