Finite-size energy gap in weak and strong topological insulators

@article{Imura2012FinitesizeEG,
  title={Finite-size energy gap in weak and strong topological insulators},
  author={Ken-Ichiro Imura and Mayuko Okamoto and Yukinori Yoshimura and Yositake Takane and Tomi Ohtsuki},
  journal={Physical Review B},
  year={2012},
  volume={86},
  pages={245436}
}
The non-trivialness of a topological insulator (TI) is characterized either by a bulk topological invariant or by the existence of a protected metallic surface state. Yet, in realistic samples of finite size this non-trivialness does not necessarily guarantee the gaplessness of the surface state. Depending on the geometry and on the topological indices, a finite-size energy gap of different nature can appear, and correspondingly, exhibits various scaling behaviors of the gap. The spin-to… 
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References

SHOWING 1-10 OF 41 REFERENCES
Strong side of weak topological insulators
Three-dimensional topological insulators are classified into "strong" (STI) and "weak" (WTI) according to the nature of their surface states. While the surface states of the STI are topologically…
Quantum transport and two-parameter scaling at the surface of a weak topological insulator.
TLDR
Through numerical simulations, it is shown that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface.
Weak topological insulator with protected gapless helical states
A workable model for describing dislocation lines introduced into a three-dimensional topological insulator is proposed. We show how fragile surface Dirac cones of a weak topological insulator evolve…
Spin Berry phase in anisotropic topological insulators
Three-dimensional topological insulators are characterized by the presence of protected gapless spin helical surface states. In realistic samples these surface states are extended from one surface to…
Finite size effects of the surface states in a lattice model of topological insulator
Aharonov-Bohm interference in topological insulator nanoribbons.
TLDR
Pronounced Aharonov-Bohm oscillations in the magnetoresistance clearly demonstrate the coherent propagation of two-dimensional electrons around the perimeter of the nanoribbon surface, as expected from the topological nature of the surface states.
One-dimensional topologically protected modes in topological insulators with lattice dislocations
Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems such as the B-phase of superfluid helium He3, where vortices are…
The Quantum Spin Hall Effect: Theory and Experiment
The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These…
Spherical topological insulator
The electronic spectrum on the spherical surface of a topological insulator reflects an active property of the helical surface state that stems from a constraint on its spin on a curved surface. The…
Topological insulators with inversion symmetry
Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$…
...
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4
5
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