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

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.