Magnetization of the Metallic Surface States in Topological Insulators
arXiv:1411.5973 · doi:10.1088/0953-8984/27/1/015008
Abstract
We calculate the magnetization of the helical metallic surface states of a topological insulator. We account for the presence of a small sub-dominant Schr{ö}dinger piece in the Hamiltonian in addition to the dominant Dirac contribution. This breaks particle-hole symmetry. The cross-section of the upper Dirac cone narrows while that of the lower cone broadens. The sawtooth pattern seen in the magnetization of the pure Dirac limit as a function of chemical potential () is shifted; but, the quantization of the Hall plateaus remains half integral. This is verified by taking the derivative of the magnetization with respect to . We compare our results with those when the non-relativistic piece dominates over the relativistic contribution and the quantization is integral. Analytic results for the magnetic oscillations are obtained where we include a first order correction in the ratio of non-relativistic to relativistic magnetic energy scales. Our fully quantum mechanical derivations confirm the expectation of semiclassical theory except for a small correction to the expected phase. There is a change in the overall amplitude of the magnetic oscillations. The Dingle and temperature factors are modified.
To be published in J. Phys.: Condens. Matter
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