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I S Burmistrov1, I V Gornyi, A D Mirlin

  • 1L.D. Landau Institute for Theoretical Physics, Kosygina Street 2, 119334 Moscow, Russia.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Disordered systems

Background:

  • Disordered electronic systems exhibit localization phenomena.
  • Mesoscopic fluctuations and correlations in the local density of states (LDOS) are crucial for understanding electronic transport.
  • The role of electron-electron interactions on these properties near the localization transition is not fully understood.

Purpose of the Study:

  • To investigate the impact of Coulomb interaction on the multifractality of LDOS near the localization transition.
  • To calculate the spectrum of multifractal dimensions in the presence of interactions.
  • To propose experimental methods for observing these phenomena.

Main Methods:

  • Theoretical analysis of disordered interacting electronic systems.
  • Calculation of multifractal dimensions in 2+ϵ spatial dimensions.
  • Focus on mesoscopic fluctuations and correlations of LDOS.

Main Results:

  • The multifractality of LDOS persists even with Coulomb interaction.
  • The spectrum of multifractal dimensions is altered by electron interactions compared to non-interacting systems.
  • The study provides a theoretical framework for understanding these effects.

Conclusions:

  • Coulomb interactions do not destroy LDOS multifractality near the localization transition.
  • The interaction-dependent multifractal spectrum offers new insights into electronic behavior in disordered systems.
  • Scanning tunneling microscopy is a viable experimental technique to probe these multifractal properties in 2D and 3D disordered structures.