Critical behavior of transport and magnetotransport in a 2D electron system in Si near the metal-insulator transition

Abstract

We report on studies of the magnetoresistance in strongly correlated 2D electron system in Si in the critical regime, in the close vicinity of the 2D metal-insulator transition. We performed self-consistent comparison of our data with solutions of two equation of the cross-over renormalization group (CRG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ(T, B ) data and the RG theory in a wide range of the in-plane fields, 0-2.1 T. This agreement supports the interpretation of the observed 2D MIT as the true quantum phase transition. PACS: 73.40, 73.43 Low-temperature transport in many high mobility 2D electron systems was found to manifest a critical behavior [1][2][3][4]. This phenomenon takes place at low carrier densities, therefore the electron-electron correlations play a crucial role. In transport studies, as temperature decreases, the overall picture of the temperature dependence of resistivity ρ shows clearly distinct behavior in two different domains on the density scale. At low densities, n < n c , resistivity exponentially increases with cooling, whereas at high densities, n > n c , resistivity significantly decreases (here n c is a sampledependent critical density, ∼ 10 11 cm −2 for high mobility Si samples). In the former domain, transport is consistent with a conventional picture of hopping conduction, that is typical for an insulator [5]. In the latter domain, far from the critical density (and at ρ ≪ h/e 2 ), temperature dependence of conductivity was experimentally shown [6] to be explained by the Fermi-liquid effects that were calculated within the framework both of the quantum interaction corrections [7], and temperature dependent screening [8]. It was so far unclear whether the metallic type transport persists to T = 0 and whether the cross-over from the metallic to the insulating behavior (that is observed at low though finite temperatures) signifies a true quantum phase transition.The successful comparison with the theory of interaction corrections in the high density regime, n ≫ n c , encouraged us to extend the comparison to the critical regime of lower densities n ≈ n c and higher resistivities ρ ∼ h/e 2 . The method that now commonly in use for this regime and in the diffusive interaction limit T τ ≪ 1 is a generalization of the nonlinear σ-model theory, which has been developed by Finkelstein [9]. The RG equations [9,10] describe length scale (temperature) evolutions of the resistivity and interaction parameters for 2D electron system in the first order in ρ/(πh/e 2 ) and in all orders in interaction.Earlier [11], only experimental ρ(T )-data [12] in zero field has been compared with one of the RG-equations, while temperature dependence of the interaction parameter γ 2 (T ) [9] was not tested. In this paper we have extracted, for the first time, γ 2 (T ) from the lowfield magnetoresistance measurements, using cross-over RG (CRG) equations, proposed in Ref.[13] for in-plane mag...

Chapter 3 Transport in a Two-Dimensional Disordered Electron Liquid with Isospin Degrees of Freedom

“…It is in agreement with experimental data on magnetoresistance in Si-MOSFET. 74,77 However, if valley splitting ∆ v < T (II) max then the maximum in ρ(T ) remains even in the presence of parallel magnetic field.…”

Interaction effects in conductivity of a two-valley electron system in high-mobility Si inversion layers

“…and in all orders in interaction) have been compared with the conductivity of Si MOSFETs at low electron densities 29,31,32,33 .…”

Renormalization group study of a two-valley system with spin splitting

“…Electron-electron (e-e) interactions between the different spin-bands gives rise to a finite magnetoconductance, σ(B , T ), and hence measurement of σ(B , T ) provides a simple and accurate way of determining the effective spin-related interaction strength 1,2 . In a disordered two-dimensional electron gas (2DEG), the transport properties at low temperatures, k B T /τ , are governed by singular diffusive particle-hole propagators 3 , D(q, ω) = 1/(D 0 q 2 + ω).…”