2008/04/14 by Thomas Ludwig, T. Ludwig, I. V. Gornyi +3
Physics and Astronomy · #Atomic and Subatomic Physics Research #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.77.235414
published as Phys. Rev. B 77, 235414 (2008) · 36 pages, 16 figures
arxiv created 2008/04/14 · openalex publication_date 2008/06/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 \ensuremathλ⪡g^\ensuremath-1/2 to the gauge field (g⪢1 is the dimensionless conductance) and results in an antilocalizing conductivity correction \ensuremath∼\ensuremathλ2g ln2 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, T0⪡T⪡gT0, where T0\ensuremath∼1/g2\ensuremathτ and \ensuremathτ is the elastic scattering time, the T dependence of the conductivity is determined by the Hartree correction, \ensuremathδ\ensuremathσH(T)\ensuremath-\ensuremathδ\ensuremathσH(gT0)\ensuremath∝g1/2\ensuremath-(T/T0)1/2[1+ln(gT0/T)1/2], so that \ensuremathσ(T) increases with lowering T. At low temperatures, T⪡T0, the temperature-dependent part of the Hartree correction assumes a logarithmic form with a coefficient of order unity, \ensuremathδ\ensuremathσH\ensuremath∝ln(1/T). As a result, the negative exchange contribution \ensuremathδ\ensuremathσex\ensuremath∝\ensuremath-ln g ln(1/T) becomes dominant, which yields localization in the limit of T\ensuremath→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_\ensuremathφ⪡LT, where LT 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, \ensuremathδ\ensuremathσH\ensuremath∝ln g 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_\ensuremathφ is of the order of LT for not too low temperatures and exceeds LT for T\ensuremath\lesssimgT0.