Effect of Electron-electron Interaction on Surface Transport in Three-Dimensional Topological Insulators

Abstract

We study the effect of electron-electron interaction on the surface resistivity of three-dimensional (3D) topological insulators. In the absence of umklapp scattering, the existence of the Fermi-liquid ($T^2$) term in resistivity of a two-dimensional (2D) metal depends on the Fermi surface geometry, in particular, on whether it is convex or concave. On doping, the Fermi surface of 2D metallic surface states in 3D topological insulators of the Bi${}_2$Te${}_3$ family changes its shape from convex to concave due to hexagonal warping, while still being too small to allow for umklapp scattering. We show that the $T^2$ term in the resistivity is present only in the concave regime and demonstrate that the resistivity obeys a universal scaling form valid for an arbitrary 2D Fermi surface near a convex/concave transition.

4 pages, 3 figures

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• Resistivity of non-Galilean-invariant Fermi- and non-Fermi liquids
• Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping
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• Bulk and surface spin conductivity in topological insulators with hexagonal warping
• Optical conductivity of a two-dimensional metal near a quantum-critical point: the status of the "extended Drude formula"
• Excitonic and Nematic Instabilities on the Surface of Topological Kondo Insulators
• Low temperature Hall effect in bismuth chalcogenides thin films
• Screening, Friedel oscillations and low-temperature conductivity in topological insulator thin films
• Electron beam splitting at topological insulator surface states and a proposal for electronic Goos-Hanchen shift measurement
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• Taking a critical look at holographic critical matter
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• Phase diagram and phonon-induced backscattering in topological insulator nanowires
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• Transport of Dirac electrons in a random magnetic field in topological heterostructures
• Two-particle scattering and resistivity of Rashba electron gas
• Magnetic interactions of 4$f$ electrons in the topological insulator chalcogenide Bi${}_2$Se${}_3$
• Optical conductivity of a Dirac-Fermi liquid
• Anomalous quasiparticle lifetime in geometric quantum critical metals