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 Tc) 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 Tc 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.

Tunneling probe of fluctuating superconductivity in disordered thin films

“…See also Ref. [52] for a microscopic model describing the effect of superconducting fluctuations close to the SIT and their effects on the DOS.…”

Response theory of the ergodic many-body delocalized phase: Keldysh Finkel’stein sigma models and the 10-fold way

“…In classes AII and CI, for simplicity we ignore the BCS interaction channel [27] in this work (see Refs. [57,58,59,60,61,62] where various effects stemming from the Cooper channel renormalizations were scrutinized).…”

“…62) from which one can infer the renormalized interaction strength γ R . In a disordered normal metal, this identity holds to all loop orders, meaning the charge compressibility κ defined in Eq.…”

Mesoscopic fluctuations of the local density of states in interacting electron systems

“…Within plain perturbation theory the average density of states near T c is strongly affected by Cooper channel attraction [64][65][66]. These classical results can be extended to incorporate the renormalization group flow near the non-interacting critical point [42].…”

“…It was found that in some range of parameters multifractality favours the superconducting instability which results in enhanced superconducting transition temperature T c in comparison with the clean case. Recently, the present authors have demonstrated that near the superconducting transition with enhanced T c one can expect enhanced mesoscopic fluctuations of the local density of states governed by the critical exponents for the non-interacting critical point [42].…”