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A substance that reaches superconductivity, a state in which magnetic fields cannot penetrate, and there is no electrical resistance, is referred to as a superconductor. In 1911, Heike Kamerlingh Onnes of Leiden University, a Dutch physicist, observed a relation between the temperature and the resistance of the element mercury. The mercury sample was then cooled in liquid helium to study the linear dependence of resistance on temperature. It was observed that, as the temperature decreased, the...
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Eigenfunction fractality and pseudogap state near the superconductor-insulator transition.

M V Feigel'man1, L B Ioffe, V E Kravtsov

  • 1L. D. Landau Institute for Theoretical Physics, Kosygin street 2, Moscow 119334, Russia.

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|March 16, 2007
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Summary

A theory explains the pseudogap state near the superconductor-insulator transition. This gap, caused by attractive interactions and fractal wave functions, persists even after superconductivity is lost.

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Area of Science:

  • Condensed Matter Physics
  • Disordered Systems
  • Superconductivity

Background:

  • Strongly disordered metals with attractive interactions exhibit complex electronic states.
  • The superconductor-insulator (SI) transition is a critical phenomenon in such systems.
  • Fractal nature of wave functions near the mobility edge influences electronic properties.

Purpose of the Study:

  • To develop a theoretical framework for the pseudogap state near the SI transition.
  • To investigate the role of attractive interactions and wave function geometry.
  • To understand the persistence of the pseudogap in the insulating phase.

Main Methods:

  • Theoretical modeling of disordered metals.
  • Analysis of single-particle wave functions and their localization.
  • Derivation of analytic expressions for the pseudogap.

Main Results:

  • An anomalously large single-particle gap (pseudogap) emerges near the SI transition.
  • The pseudogap is driven by attractive interactions and fractal wave functions.
  • The pseudogap persists and grows in the insulating state after superconductivity vanishes.

Conclusions:

  • The developed theory successfully explains the pseudogap state in disordered superconductors.
  • The interplay between attractive interactions and wave function localization is crucial.
  • The pseudogap offers insights into electronic behavior beyond the superconducting phase.