Effect of gauge-field interaction on fermion transport in 2D: Hartree conductivity correction and dephasing

TL;DR

This paper investigates how gauge-field interactions influence fermion transport in two dimensions, revealing complex temperature-dependent quantum corrections to conductivity, including localization effects and dephasing behavior, especially in strong coupling regimes.

Contribution

It provides a detailed analysis of Hartree corrections to conductivity under gauge interactions, including the effects of strong coupling and dephasing, extending understanding beyond weak coupling approximations.

Findings

Hartree correction causes antilocalization at weak coupling.

At strong coupling, higher-order terms lead to localization at low temperatures.

Dephasing rates are proportional to temperature, but dephasing length is anomalously short.

Abstract

We consider the quantum corrections to the conductivity of fermions interacting via a Chern-Simons gauge field, and concentrate on the Hartree-type contributions. The first-order Hartree approximation is only valid in the limit of weak coupling \lambda to the gauge field, and results in an antilocalizing conductivity correction, \sim \lambda^2 g \ln^2 T (g is the conductance). In the case of strong coupling, an infinite summation of higher-order terms is necessary, including both the virtual (renormalization) and real (dephasing) processes. At intermediate temperatures 1/g^2\tau<<T<<1/g\tau (\tau is the transport time), the T-dependence of the conductivity is determined by the Hartree correction. At low temperatures T<<1/g^2\tau, the Hartree correction assumes a logarithmic form with a coefficient of order unity. As a result, the negative exchange contribution becomes dominant, yielding localization in the limit of zero T. We further discuss dephasing at strong coupling and show that the dephasing rates are of the order of T, owing to the interplay of inelastic scattering and renormalization. On the other hand, the dephasing length is anomalously short, L_\phi<<L_T. For the case of composite fermions with long-range Coulomb interaction, the Hartree correction has the usual T-dependence, and for realistic g is overcompensated by the negative exchange contribution due to the gauge-boson and scalar parts of the interaction. In this case, the dephasing length L_\phi is of the order of L_T for not too low T and exceeds L_T for T<1/g\tau.