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arXiv:cond-mat/9509029 · Physical review. B, Condensed matter

Superconductor-insulator transition in a disordered electronic system

Nandini Trivedi, Richard T. Scalettar, Mohit Randeria

Published Aug 1, 1996• 125 citations
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Abstract

We study an electronic model of a two-dimensional $s$-wave superconductor in a random potential using quantum Monte Carlo simulations. The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder. We calculate the temperature-dependent resistivity ${\ensuremath{\rho}}_{\mathrm{dc}}(T)$ for a highly disordered interacting Fermi system. Using this we identify the nonsuperconducting state as an insulator.

DOI
10.1103/physrevb.54.r3756

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We study an electronic model of a two-dimensional sss-wave superconductor in a random potential using quantum Monte Carlo simulations. The superfluid density and the strength of the delta function in the optical conductivity are found to vanish beyond a critical disorder. We calculate the temperature-dependent resistivity \ensuremathρdc(T){\ensuremath{\rho}}_{\mathrm{dc}}(T)\ensuremathρdc​(T) for a highly disordered interacting Fermi system. Using this we identify the nonsuperconducting state as an insulator.
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We calculate the dynamical conductivity σðωÞ and the bosonic (pair) spectral function PðωÞ from quantum Monte Carlo simulations across clean and disorder-driven superconductor-insulator transitions (SITs).We identify characteristic energy scales in the superconducting and insulating phases that vanish at the transition due to enhanced quantum fluctuations, despite the persistence of a robust fermionic gap across the SIT.Disorder leads to enhanced absorption in σðωÞ at low frequencies compared to the SIT in a clean system.Disorder also expands the quantum critical region, due to a change in the universality class, with an underlying T ¼ 0 critical point with a universal low-frequency conductivity σ Ã ≃ 0.5ð4e 2 =hÞ.
We study the temperature-dependent conductivity $\ensuremath{\sigma}(T)$ and spin susceptibility $\ensuremath{\chi}(T)$ of the two-dimensional disordered Hubbard model. Calculations of the current-current correlation function using a quantum Monte Carlo method show that repulsion between electrons can significantly enhance the conductivity, and at low temperatures change the sign of $d\ensuremath{\sigma}/\mathrm{dT}$ from positive (insulating behavior) to negative (conducting behavior). This result suggests the possibility of a metallic phase, and consequently a metal-insulator transition, in a two-dimensional microscopic model containing both interactions and disorder. The metallic phase is a non-Fermi liquid with local moments as deduced from $\ensuremath{\chi}(T)$.
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 present results of path-integral Monte Carlo simulations of bosons on a two-dimensional square lattice in a random potential of average strength V and with on-site repulsion U. We find that the superfluid density ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$ is enhanced by increasing V and U in certain regions of parameter space. By combining the results of ${\mathrm{\ensuremath{\rho}}}_{\mathit{s}}$, with the behavior of the density-density correlation function on lattices of size up to 10\ifmmode\times\else\texttimes\fi{}10, we study the superfluid--to--Mott-insulator transition and the transition from a superfluid to a disorder-localized (``Bose glass'') phase.
Using exact quantum Monte Carlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.