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arXiv:0804.2215 · Physical Review B

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

Thomas Ludwig, I. V. Gornyi, A. D. Mirlin, P. Wölfle

Published Jun 11, 2008• 8 citations
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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 $\ensuremath{\lambda}⪡{g}^{\ensuremath{-}1/2}$ to the gauge field ($g⪢1$ is the dimensionless conductance) and results in an antilocalizing conductivity correction $\ensuremath{\sim}{\ensuremath{\lambda}}^{2}g\text{ }{\text{ln}}^{2}\text{ }T$. In the case of strong coupling, an infinite summation of higher-order terms is necessary, which includes both the virtual (renormalization of the frequency) and real (dephasing) processes. At intermediate temperatures, ${T}_{0}⪡T⪡g{T}_{0}$, where ${T}_{0}\ensuremath{\sim}1/{g}^{2}\ensuremath{\tau}$ and $\ensuremath{\tau}$ is the elastic scattering time, the $T$ dependence of the conductivity is determined by the Hartree correction, $\ensuremath{\delta}{\ensuremath{\sigma}}^{H}(T)\ensuremath{-}\ensuremath{\delta}{\ensuremath{\sigma}}^{H}(g{T}_{0})\ensuremath{\propto}{g}^{1/2}\ensuremath{-}{(T/{T}_{0})}^{1/2}[1+\text{ln}{(g{T}_{0}/T)}^{1/2}]$, so that $\ensuremath{\sigma}(T)$ increases with lowering $T$. At low temperatures, $T⪡{T}_{0}$, the temperature-dependent part of the Hartree correction assumes a logarithmic form with a coefficient of order unity, $\ensuremath{\delta}{\ensuremath{\sigma}}^{H}\ensuremath{\propto}\text{ln}(1/T)$. As a result, the negative exchange contribution $\ensuremath{\delta}{\ensuremath{\sigma}}^{\text{ex}}\ensuremath{\propto}\ensuremath{-}\text{ln}\text{ }g\text{ }\text{ln}(1/T)$ becomes dominant, which yields localization in the limit of $T\ensuremath{\rightarrow}0$. 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, ${L}_{\ensuremath{\varphi}}⪡{L}_{T}$, where ${L}_{T}$ is the thermal length. For the case of composite fermions with long-range Coulomb interaction, the gauge-field propagator is less singular. The resulting Hartree correction has the usual sign and temperature dependence, $\ensuremath{\delta}{\ensuremath{\sigma}}^{H}\ensuremath{\propto}\text{ln}\text{ }g\text{ }\text{ln}(1/T)$, 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 ${L}_{\ensuremath{\varphi}}$ is of the order of ${L}_{T}$ for not too low temperatures and exceeds ${L}_{T}$ for $T\ensuremath{\lesssim}g{T}_{0}$.

DOI
10.1103/physrevb.77.235414

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