Confining electrons on a topological insulator surface using potentials and a magnetic field

Abstract

We study the effects of extended and localized potentials and a magnetic field on the Dirac electrons residing at the surface of a three-dimensional topological insulator. We use a lattice model to numerically study the various states; we show how the potentials can be chosen in a way which effectively avoids the problem of fermion doubling on a lattice. We show that extended potentials of different shapes can give rise to states which propagate freely along the potential but decay exponentially away from it. For an infinitely long potential barrier, the dispersion and spin structure of these states are unusual and these can be varied continuously by changing the barrier strength. In the presence of a magnetic field applied perpendicular to the surface, these states become separated from the gapless surface states by a gap, thereby giving rise to a quasi-one-dimensional system. Similarly, a magnetic field along with a localized potential can give rise to exponentially localized states which are separated from the surface states by a gap and thereby form a zero-dimensional system. Finally, we show that a long barrier and an impurity potential can produce bound states which are localized at the impurity, and an "L"-shaped potential can have both bound states at the corner of the "L" and extended states which travel along the arms of the potential.

11 pages, 11 figures

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Cited by in corpus (6)

• Helical bound states in the continuum of the edge states in two dimensional topological insulators
• Experimental search for one-dimensional edge states at surface steps of the topological insulator Bi${}_2$Se${}_3$: Distinguishing between effects and artifacts
• Connection topology of step edge state bands at the surface of a three dimensional topological insulator
• Influence of Helical Spin Structure on the Magnetoresistance of an Ideal Topological Insulator
• Electron dynamics in graphene with spin-orbit couplings and periodic potentials
• Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi${}_2$Se${}_3$