Quantum Hall effect in a singly and doubly connected 3D topological insulator

Abstract

The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy spectrum is found for a singly and doubly connected geometry. This is in turn used to argue that the way to measure the quantized Hall conductivity is to perform the Laughlin's flux ramping experiment and measure the charge transferred from the inner to the outer surface, analogous to the experiment in Ref.[2]. Unlike the Hall bar setup used currently, this has the advantage of being free of the contamination from the delocalized continuum of the surface edge states. In the presence of the Zeeman coupling, and/or interaction driven Quantum Hall ferromagnetism, which translate into the Dirac mass term, the quantized charge Hall conductivity sigma_{xy}=n e^2/h, with n=0,\pm 1,\pm 3,\pm 5... Backgating of one of the surfaces leads to additional Landau level splitting and in this case n can be any integer.

10 pages 5 figures

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• Half-integer quantum Hall effect of disordered Dirac fermions at a topological insulator surface
• Edge states and integer quantum Hall effect in topological insulator thin films
• Robust Transport Signatures of Topological Superconductivity in Topological Insulator Nanowires
• Two-Dimensional Lattice Model for the Surface States of Topological Insulators
• Electronic States of Wires and Slabs of Topological Insulators: Quantum Hall Effects and Edge Transport
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• Solution to the hole-doping problem and tunable quantum Hall effect in Bi${}_2$Se${}_3$ thin films
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• Optical properties of magnetically doped ultra-thin topological insulator slabs
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• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
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• Surface Step Defect in 3D Topological Insulators: Electric Manipulation of Spin and Quantum Spin Hall Effect
• Theory of magnetotransport in shaped topological insulator nanowires
• Transport in Selectively Magnetically Doped Topological Insulator Wires
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• Anisotropic transport properties in prismatic topological insulator nanowires