Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems

Abstract

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the non-linear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore 2D systems that would be Anderson insulators in the absence of interaction and 2D or 3D systems that undergo Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature $T_c$) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions -- especially, in the regime when $T_c$ is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approaches the SIT.

References in corpus (10)

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• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Phase fluctuations in a strongly disordered s-wave superconductor close to the metal-insulator transition
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• Fermionic scenario for the destruction of superconductivity in ultrathin MoC films evidenced by STM measurements
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• Berezinskii-Kosterlitz-Thouless transition in homogeneously disordered superconducting films
• Superconductor-insulator quantum phase transition
• Multifractality and electron-electron interaction at Anderson transitions

Cited by in corpus (18)

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• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way
• Multifractally-enhanced superconductivity in thin films
• Self-consistent-field ensembles of disordered Hamiltonians: Efficient solver and application to superconducting films
• Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling
• Tunneling probe of fluctuating superconductivity in disordered thin films
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Ultrasonic attenuation in a pseudogapped superconductor
• Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion
• Effect of Coulomb Interaction and Disorder on Density of States in Conventional Superconductors
• Magnetic disorder in superconductors: Enhancement by mesoscopic fluctuations
• Mesoscopic fluctuations of the local density of states in interacting electron systems
• Surface symmetry breaking and disorder effects on superconductivity in perovskite BaBi3 epitaxial films
• Anomalous mesoscopic kinetics in disordered superconductors
• The effect of superconducting fluctuations on the ac conductivity of a 2D electron system in the diffusive regime
• Multifractal correlations of the local density of states in dirty superconducting films
• Scanning tunneling spectroscopy of superconducting nitridized aluminum thin films