Particle-hole asymmetry on Hall conductivity of a topological insulator

Abstract

The helical Dirac states on the surface of a topological insulator are protected by topology and display significant particle-hole asymmetry. This asymmetry arises from a subdominant Schrödinger type contribution to the Hamiltonian which provides a small perturbation to a dominant Dirac contribution. This changes the Landau levels energies in an external magnetic field ($B$) and provides modifications to the usual relativistic optical matrix elements. Nevertheless we find that the relativistic quantization of the Hall plateaux remains even when the ratio of the Schrödinger ($E_0$) to Dirac ($E_1$) magnetic energy scale increases either through an increase in $B$, a decrease in the Schrödinger mass or of the Dirac fermi velocity. First corrections to the optical matrix elements(OME) in the relativistic case drop out at least to order $(E_0/E_1{)}^3$. In the opposite limit $E_1$ small, the quantization remains classical but there is a split into two series. The first corrections to the OME in this case, cancel out at least to order $(E_1/E_0{)}^4$.

10 pages, 7 figures, to appear in Phys. Rev. B

References in corpus (7)

• Unconventional Integer Quantum Hall effect in graphene
• Magneto-optical conductivity in Graphene
• Phase analysis of quantum oscillations in graphite
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations II: transport properties
• Quantum oscillations and Berry's phase in topological insulator surface states with broken particle-hole symmetry
• Magnetic quantum oscillations of the topological insulator surface states
• Measuring the Chern number with quantum oscillations

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