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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • Quantum transport in disordered systems is crucial for understanding material properties.
  • Long-range hopping introduces unique quantum phenomena not seen in short-range models.
  • Disorder effects can lead to metal-insulator transitions.

Purpose of the Study:

  • To investigate the impact of disorder and shielding on quantum transport in 2D systems with all-to-all long-range hopping.
  • To analyze the emergence of conducting channels and the nature of wave function localization.
  • To characterize the phase transitions and transport properties under varying disorder strengths.

Main Methods:

  • Theoretical investigation of a two-dimensional system with all-to-all long-range hopping.
  • Analysis of quantum transport phenomena under varying degrees of disorder.
  • Examination of wave function properties, including localization centers and fractal dimensions.
  • Study of size scaling and conductance behavior to identify phase transitions.

Main Results:

  • Weak disorder leads to perfect conducting channels, masking long-range hopping effects.
  • Increased disorder breaks shielding, enhancing conductance fluctuations and enabling long-range hopping.
  • Wave functions exhibit hybrid localization-delocalization, with multiple centers and fractal dimensions between 0 and 2.
  • A marginal phase is identified, characterized by saturated conductance and a scaling function between metallic and insulating behaviors.
  • An isolated, disorder-robust extended state emerges due to all-to-all coupling, showing efficient transport via quantum short-circuiting.

Conclusions:

  • Disorder and shielding interplay significantly in 2D systems with long-range hopping.
  • A novel marginal phase of quantum transport exists, distinct from typical metallic or insulating states.
  • The unique properties of long-range hopping can lead to robust quantum transport phenomena, even in the presence of disorder.