Electron-electron interaction with decreasing conductance

Abstract

The contribution of the electron-electron interaction to conductivity is analyzed step by step starting from the high conductivity in gated GaAs/In x Ga 1Ϫx As/GaAs heterostructures with different starting disorders. We demonstrate that the diffusion theory works down to k F lӍ1.5Ϫ2, where k F is the Fermi quasimomentum and l is the mean free path. It is shown that the e-e interaction gives smaller contribution to the conductivity than the interference independent of the starting disorder, and its role rapidly decreases with decreasing k F l.Quantum corrections to the conductivity in disordered metals and doped semiconductors have been intensively studied since 1980. 1 Two mechanisms led to these corrections: ͑i͒ the interference of the electron waves propagating in opposite directions along closed paths; ͑ii͒ electronelectron (e-e) interaction. The interference decreases the conductivity and its role increases with decreasing temperature. Behavior of the e-e contribution to the conductivity strongly depends on value of k B T/ប, where is transport relaxation time, and Fermi liquid interaction parameter F 0 . 2,3 It dramatically changes at crossover from the diffusion regime (k B T/បӶ1) to the ballistic one (k B T/បտ1) and can lead to inversion of sign of the temperature dependence of the conductivity. In addition, in the ballistic regime the e-e contribution depends on scale of scattering potential. The interaction correction for pointlike scattering potential was considered in Refs. 2 and 3 and for the long-range potential was studied theoretically in Ref. 4 and experimentally in Ref. 5. In this paper we track the evolution of the interaction correction as the conductivity decreases. Because the absolute value of both interference and interaction corrections increases with decreasing temperature, they determine in large part the low-temperature transport in two-dimensional ͑2D͒ systems in this case. The interference or weaklocalization ͑WL͒ correction ␦ WL is proportional to Ϫln( /), where is the phase relaxation time, ϰT Ϫp , pӍ1 in dirty limit. The correction due to the e-e interaction ␦ ee is proportional to Ϫln͓ប/(k B T)͔ in the diffusion regime. 1 It immediately follows that at increasing disorder, i.e., at decreasing , both corrections have to be enhanced in absolute value and can become comparable with the Drude conductivity. In this case the low-temperature conductivity will be significantly less than the Drude conductivity, and the strong temperature dependence of the conductivity has to appear. On further increase of disorder the transition to the hopping conductivity has to occur.All theories of quantum corrections for both diffusive 1 and ballistic 2-4 regimes were developed for the case k F l ӷ1, where k F and l are the Fermi quasimomentum and the classical mean free path, respectively. Under this condition the quantum corrections to the conductivity are small in magnitude compared with the Drude conductivity 0 ϭk F lG 0 with G 0 ϭe 2 /(2 2 ប) at any accessible temperature. With decreasing k F l ...

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Conductivity of a two-dimensional electron gas in a Si/SiGe heterostructure near the metal-insulator transition: Role of the short- and long-range scattering potential

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