Emergence of quasimetallic state in a disordered two-dimensional electron gas

due to strong interactions

The question of mutual influence of long-range Coulombinteractions and disorder in two-dimensional electron gas (2DEG) attracted a great attention after an unexpected discovery of metallic state and clear metal-insulator transition by Kravchenko and co-workers.^1,2 The very existence of a metallic state with finite conductivity at zero temperature is in conflict with the weak-localization theory,³ which predicts that in 2D even negligible amount of disorder localizes elec-trons at sufficiently low temperature. The theory however was firmly established at weak coupling or for short-range interactions only, while the metallic state exists and the transition was found for rather strong coupling r_s 5 E_ee /E_F ; 10, where E_ee is the average interaction energy per elec-tron and E_F is the Fermi energy. Therefore Coulomb inter-actions dominate the kinetic energy and cannot be considered ‘‘small.’’ In addition to an obvious difficulty to treat quanti-tatively or even qualitatively the strong coupling, it is not clear which one, disorder or Coulomb interactions, should be considered as a most important cause of the transition to an insulating state (the corresponding insulating state in these cases is of ‘‘Anderson’’ or ‘‘Mott’’ type⁴). Most probably it results from a nontrivial combination of these interactions.

The standard approach starts with a commonly accepted argument that a long-range Coulomb interaction after ‘‘bubble resummation’’ of the random-phase-approximation (RPA) type⁵ becomes effectively short range. Therefore one can start the treatment of disorder after this resummation was performed. Disorder is treated within a similar approach in which ‘‘rainbow’’ diagrams⁶ ‘‘ladders and crossed ladders resummation’’⁷ (or, more systematically, the ‘‘steepest de-scent’’ approximations⁸ in the path-integral language⁹) with interaction being already short ranged. In this way two kinds of massless modes determining the properties of the disordered electron gas are identified: diffusons (describing diffusive nature of the electron motion due to impurities) And Cooperons in the particle-particle channel.

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