Magnetization of the Metallic Surface States in Topological Insulators

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 ($\mu$) 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 $\mu$. 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.

arXiv commentTo be published in J. Phys.: Condens. Matter

References in corpus (31)

• Topological Insulators
• Topological insulators and superconductors
• Spintronics: Fundamentals and applications
• Quantum Spin Hall Effect in Graphene
• First observation of Spin-Momentum Helical Locking in Bi2Se3 and Bi2Te3, demonstration of Topological-Order at 300K and a realization of topological-transport-regime
• Topological Insulator Materials
• Model Hamiltonian for Topological Insulators
• Magneto-optical conductivity in Graphene
• Semiconductor Spintronics
• Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
• Observation of Dirac Holes and Electrons in a Topological Insulator
• Phase analysis of quantum oscillations in graphite
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations
• From dia- to paramagnetic orbital susceptibility of Dirac cones
• Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
• Berry phase of non-ideal Dirac fermions in topological insulators
• High-Field Shubnikov-de Haas Oscillations in the Topological Insulator Bi${}_2$Te${}_2$Se
• Quantum oscillations and Berry's phase in topological insulator surface states with broken particle-hole symmetry
• Surface state charge dynamics of a high-mobility three dimensional topological insulator
• Magneto-optical conductivity in a topological insulator
• Quantum oscillations in topological superconductor candidate Cu${}_{0.25}$Bi${}_2$Se${}_3$
• Surface Theory of a Family of Topological Kondo Insulators
• Hexagonal warping on optical conductivity of surface states in Topological Insulator Bi_{2}Te_{3}
• Magneto-optical conductivity in graphene including electron-phonon coupling
• The Berry phase and the phase of the Shubnikov-de Haas oscillations in three-dimensional topological insulators
• Band structure and magnetotransport of a two-dimensional electron gas in the presence of spin-orbit interaction
• Magnetic quantum oscillations of the topological insulator surface states
• Landau level mixing by full spin-orbit interactions
• Quantum oscillations of magnetization in the tight-binding electrons on honeycomb lattice
• Particle-hole asymmetry on Hall conductivity of a topological insulator
• Measuring the Chern number with quantum oscillations

Cited by in corpus (6)

• Magnetic Properties of Dirac Fermions in a Buckled Honeycomb Lattice
• Particle-Hole Asymmetry in Gapped Topological Insulator Surface States
• Ferromagnetism and glassiness on the surface of topological insulators
• Thermodynamic properties of the 2+1-dimensional Dirac fermions with broken time-reversal symmetry
• Anomalous Behaviour in the Magneto-Optics of a Gapped Topological Insulator
• Cyclotron Resonance in Topological Insulators: Non-Relativistic Effects