Massive Dirac fermions and spin physics in an ultrathin film of topological insulator

Abstract

We study transport and optical properties of the surface states which lie in the bulk energy gap of a thin-film topological insulator. When the film thickness is comparable with the surface state decay length into the bulk, the tunneling between the top and bottom surfaces opens an energy gap and form two degenerate massive Dirac hyperbolas. Spin dependent physics emerges in the surface bands which are vastly different from the bulk behavior. These include the surface spin Hall effects, spin dependent orbital magnetic moment, and spin dependent optical transition selection rule which allows optical spin injection. We show a topological quantum phase transition where the Chern number of the surface bands changes when varying the thickness of the thin film.

Observation of quantum-tunnelling-modulated spin texture in ultrathin topological insulator Bi2Se3 films

“…As long as the thickness of the film is comparable to the decay length of the surface states into the bulk, there is a spatial overlap between the top and bottom surface states resulting in an energy gap at the time-reversal invariant point (G point). As expected theoretically 26,27 , the energy gap decreases and eventually vanishes for sufficiently thick films, corresponding to the transition from a two-dimensional (2D) gapped system (insulator) to a 3D gapless system (metal) 10,11 . In particular, the gapless dispersion relation observed in the 7QL film from ARPES measurement indicates that this thickness is above the quantum tunnelling limit.…”

“…3d). The decrease can be understood as the presence of a tunnelling gap in the ultrathin limit that effectively prevents the partner-switching behaviour expected in the gapless topological surface states' system 27 . The tunnelling gap for ultrathin films can be seen in the data (Fig.…”

“…In addition, scattering from the extrinsic bulk states leads to the reduction of spin polarization of the surface states. One promising route to minimize bulk conductance and thus improve effective spin polarization is to work with ultrathin films where the surface-tovolume ratio is significantly enhanced 26,27 and surface current can potentially dominate. On the other hand, in this limit the desired spin polarization of the surface states is kinematically reduced near the metal-to-insulator transition in the ultrathin films where the spin behaviour is not known to this date 10,11,15,18,19 .…”

Model Hamiltonian for topological insulators

“…[31] Zhang et al [1] derived a model Hamiltonian for the 3D TI Bi 2 Se 3 , Bi 2 T e 3 and Sb 2 T e 3 , and obtained topological surface states consisting of a single Dirac cone. Interestingly, in the thin film limit, the 3D TI model reduces exactly to the 2D TI model by BHZ [32][33][34]. In this paper, we give the full microscopic derivation of our model Hamiltonian, first by constraining its form by symmetry principles and a careful analysis of the relevant atomic orbitals.…”

Charge-spin duality in nonequilibrium transport of helical liquids

“…These 1D systems have been coined helical liquids or helical Tomonaga Luttinger liquids (hTLLs). Transport properties of hTLLs have been predicted and observed at the edge of HgTe quantum wells 4,5 and proposed to also exist in InAs/GaSb quantum wells 6 as well as Bi 2 Se 3 or Bi 2 Te 3 thin films 7,8 . An important feature of the hTLL is that spin and momentum are locked to each other.…”