Topological state transport in topological insulators under the influence of hexagonal warping and exchange coupling to in-plane magnetizations

Abstract

A hexagonal warping term has been proposed recently to explain the experimentally observed 2D equal energy contours of the surface states of the topological insulator Bi2Te3. Differing from the Dirac fermion Hamiltonian, the hexagonal warping term leads to the opening up of a band gap by an in-plane magnetization. We study the transmission between two Bi2Te3 segments subjected to different in-plane magnetizations and potentials. The opening up of a bandgap, and the accompanying displacement and distortion of the constant energy surfaces from their usual circular shapes by the in-plane magnetizations, modify the transverse momentum overlap between the two Bi2Te3 segments, and strongly modulate the transmission profile. The strong dependence of the TI surface state transport of Bi2Te3 on the magnetization orientation of an adjacent ferromagnetic layer may potentially be utilized in, e.g., a memory readout application.

Effective Hamiltonian for surface states of topological insulator thin films with hexagonal warping

“…In the latter, the hexagonal warping allows an in-plane magnetization opens up a bandgap. 5 In contrast, panel (a) shows that for a thin film there is no bandgap opening. Instead the coupling between the spin σ and surface τ degrees of freedom here leads causes the in-plane magnetization to generate a k space separation between the two initially overlapping Dirac cones centered at ⃗ k = 0.…”

“…The distortion in the presence of an in-plane magnetization due to hexagonal warping has also been reported in semi-infinite Bi 2 Te 3 slabs. 5 …”

“…(1) was experimentally discovered a year later. 4 We showed in an earlier work 5 that the additional hexagonal warping term in a semi-infinite Bi 2 Te 3 slab leads to the distortion of the Fermi surface and the opening of a bandgap by an in-plane magnetization, both of which would not have occurred in the absence of the hexagonal warping term.…”

Effective Hamiltonian for surface states of Bi2Te3nanocylinders with hexagonal warping

“…2a of Ref. [5] in which the bandgap in the flat +z terminated Bi 2 Te 3 slab subjected to an in-plane magnetization exhibits a similar 6 fold periodic variation with the in-plane magnetization angle.…”

“…We showed in an earlier work [5] that the additional hexagonal warping term in a flat Bi 2 Te 3 slab leads to the distortion of the Fermi surface and the opening of a bandgap by an in-plane magnetization, both of which would not have occured in the absence of the hexagonal warping term. These and the displacement of the Fermi surfaces by the in-plane magnetization lead to a complex profile of the transmission from an unmagnetized source segment to a magnetized drain segment, as a function of the magnetization direction and the electron energy.…”