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Temperature Dependence of the Spin-Hall Conductivity of a Two-Dimensional Impure Rashba Electron Gas in the Presence of Electron–Phonon and Electron–Electron Interactions

Authors
  • Yavari, H.1
  • Mokhtari, M.1
  • Bayervand, A.1
  • 1 University of Isfahan, Department of Physics, Isfahan, 81746, Iran , Isfahan (Iran)
Type
Published Article
Journal
Journal of Low Temperature Physics
Publisher
Springer US
Publication Date
Nov 18, 2014
Volume
178
Issue
5-6
Pages
331–344
Identifiers
DOI: 10.1007/s10909-014-1250-1
Source
Springer Nature
Keywords
License
Yellow

Abstract

Based on Kubo’s linear response formalism, temperature dependence of the spin-Hall conductivity of a two-dimensional impure (magnetic and nonmagnetic impurities) Rashba electron gas in the presence of electron–electron and electron–phonon interactions is analyzed theoretically. We will show that the temperature dependence of the spin-Hall conductivity is determined by the relaxation rates due to these interactions. At low temperature, the elastic lifetimes (τn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{n}$$\end{document} and τm)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{m} )$$\end{document} are determined by magnetic and nonmagnetic impurity concentrations which are independent of the temperature, while the inelastic lifetimes (τee\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{ee}$$\end{document} and τep)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau _\mathrm{ep} )$$\end{document} related to the electron–electron and electron–phonon interactions, decrease when the temperature increases. We will also show that since the spin-Hall conductivity is sensitive to temperature, we can distinguish the intrinsic and extrinsic contributions.

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