Two-dimensional surface charge transport in topological insulators

Abstract

We construct a theory of charge transport by the surface states of topological insulators in three dimensions. The focus is on the experimentally relevant case when the electron doping is such that the Fermi energy ${\epsilon }_F$ and transport scattering time $\tau$ satisfy ${\epsilon }_F\tau /\hslash \gg 1$, but sufficiently low that ${\epsilon }_F$ lies below the bottom of the conduction band. Our theory is based on the spin density matrix and takes the quantum Liouville equation as its starting point. The scattering term is determined accurately to linear order in the impurity density. We consider scattering by charged impurities and short-range scatterers such as surface roughness. We calculate also the polarization function in topological insulators, emphasizing the differences from graphene. We find that the main contribution to the conductivity is $\propto n_i^{-1}$, where $n_i$ is the impurity density, and will have different carrier density dependencies for different forms of scattering. Two different contributions to this conductivity are traced to the scalar and spin-dependent terms in the Hamiltonian and their relative weight depends on the doping density. Our results contain all contributions to the conductivity to orders zero and one in the impurity density. We discuss also a way to determine the dominant scattering angles by studying the ratio of the transport relaxation time to the Bloch lifetime as a function of the Wigner-Seitz radius $r_s$. We also discuss the effect on the surface states of adding metallic contacts.

20 pages, 3 figures

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• Interface-Induced Phenomena in Magnetism
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• Observation of Dirac Holes and Electrons in a Topological Insulator
• First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials
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• Spin-Polarized Tunneling Study on Spin-Momentum Locking in the Topological Insulators
• Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures
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• Inter-band Coherence Response to Electric Fields in Crystals
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• Parallel magnetic field driven quantum phase transition in a thin topological insulator film
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• Linear magnetoresistance on the topological surface
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• Hybrid helical state and superconducting diode effect in S/F/TI heterostructures
• Thin topological insulator film in a perpendicular magnetic field
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• Benchmarking of spin-orbit torque switching efficiency in Pt alloys
• Magnetic-proximity-induced magnetoresistance on topological insulators
• Electrostatically Controlled Magnetization Rotation in Ferromagnet-Topological Insulator Planar Structures
• Observation of Volkov-Pankratov states in topological HgTe heterojunctions using high-frequency compressibility
• Fermi-Level Pinning, Charge Transfer, and Relaxation of Spin-Momentum Locking at Metal Contacts to Topological Insulators
• Unusual magnetoresistance in a topological insulator with a single ferromagnetic barrier
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• Collective excitations on a surface of topological insulator
• Many-body effects and possible superconductivity in the 2D metallic surface states of 3D topological insulators
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• Linear response theory of interacting topological insulators
• Two-dimensional electronic transport on the surface of 3D topological insulators
• Surface charge conductivity of topological insulator in a magnetic field: effect of hexagonal warping
• Theory of the random potential and conductivity at the surface of a topological insulator
• Enhanced transport length of spin-helical Dirac fermions in disordered 3D topological insulators
• Hybridization-induced interface states in a topological insulator-magnetic metal heterostructure
• Reading charge transport from spin dynamics on the surface of topological insulator
• Interpreting current-induced spin polarization in topological insulator surface states
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• Van der Waals heterostructures with spin-orbit coupling
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• Dirac electrons and domain walls: a realization in junctions of ferromagnets and topological insulators
• Magnetization reversal in S/F/S Josephson junctions on a 3D topological insulator
• Hot-carrier transport and spin relaxation on the surface of topological insulator
• Anisotropic surface transport in topological insulators in proximity to a helical spin density wave
• Bulk-impurity induced noise in large-area epitaxial thin films of topological insulators
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• Electrically controllable spin filtering based on superconducting helical states
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• Non-orthogonal Spin-Momentum Locking
• Dynamical charge and pseudospin currents in graphene and possible Cooper pair formation
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