Magnetotransport of Dirac Fermions on the surface of a topological insulator

TL;DR

This paper investigates the unique magnetotransport properties of Dirac fermions on topological insulator surfaces under crossed electric and magnetic fields, revealing tunable effects and potential for magnetic switching in various junction configurations.

Contribution

It provides exact solutions for Dirac fermions in crossed fields and explores novel control of transport properties in topological insulator junctions, highlighting phenomena absent in graphene or conventional materials.

Findings

Magnetic and electric fields allow tuning of Dirac fermion transport.

Critical exchange fields induce transitions in conductance behavior.

Magnetization controls zero-bias tunneling conductance peaks.

Abstract

We study the properties of Dirac fermions on the surface of a topological insulator in the presence of crossed electric and magnetic fields. We provide an exact solution to this problem and demonstrate that, in contrast to their counterparts in graphene, these Dirac fermions allow relative tuning of the orbital and Zeeman effects of an applied magnetic field by a crossed electric field along the surface. We also elaborate and extend our earlier results on normal metal-magnetic film-normal metal (NMN) and normal metal-barrier-magnetic film (NBM) junctions of topological insulators [Phys. Rev. Lett. {\bf 104}, 046403 (2010)]. For NMN junctions, we show that for Dirac fermions with Fermi velocity $v_F$, the transport can be controlled using the exchange field ${\mathcal J}$ of a ferromagnetic film over a region of width $d$. The conductance of such a junction changes from oscillatory to a monotonically decreasing function of $d$ beyond a critical ${\mathcal J}$ which leads to the possible realization of magnetic switches using these junctions. For NBM junctions with a potential barrier of width $d$ and potential $V_0$, we find that beyond a critical ${\mathcal J}$, the criteria of conductance maxima changes from $\chi= e V_0 d/\hbar v_F = n \pi$ to $\chi= (n+1/2)\pi$ for integer $n$. Finally, we compute the subgap tunneling conductance of a normal metal-magnetic film-superconductor (NMS) junctions on the surface of a topological insulator and show that the position of the peaks of the zero-bias tunneling conductance can be tuned using the magnetization of the ferromagnetic film. We point out that these phenomena have no analogs in either conventional two-dimensional materials or Dirac electrons in graphene and suggest experiments to test our theory.