# 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…

## Figures and Tables from this paper

## 22 Citations

Topological phase transition in a topological crystalline insulator induced by finite-size effects

- Physics
- 2014

We study electronic states and topological invariants of (001)-films of topological crystalline insulator (TCI) Pb_{x}Sn_{1-x}Te. Gapless surface Dirac cones on bulk TCIs become gapped in thin films…

Engineering Dirac electrons emergent on the surface of a topological insulator

- PhysicsScience and technology of advanced materials
- 2015

This work reviews peculiar finite-size effects applicable to such surface states in TI nanostructures and highlights the specific electronic properties of TI nanowires and nanoparticles, contrasting the cases of weak and strong TIs.

Landau Levels on a Surface of Weak Topological Insulators

- Physics
- 2015

A three-dimensional weak topological insulator (WTI), being equivalent to stacked layers of two-dimensional quantum spin-Hall insulators, accommodates massless Dirac electrons on its side surface. A…

Manipulating quantum channels in weak topological insulator nanoarchitectures

- Physics
- 2015

In strong topological insulators protected surface states are always manifest, while in weak topological insulators (WTIs) the corresponding metallic surface states are either manifest or hidden,…

Finite-Size Scaling Analysis of the Conductivity of Dirac Electrons on a Surface of Disordered Topological Insulators

- Physics
- 2016

Two-dimensional (2D) massless Dirac electrons appear on a surface of three-dimensional topological insulators. The conductivity of such a 2D Dirac electron system is studied for strong topological…

Delocalization of Surface Dirac Electrons in Disordered Weak Topological Insulators

- Physics
- 2014

The spectrum of massless Dirac electrons on the side surface of a three-dimensional weak topological insulator is significantly affected by whether the number of unit atomic layers constituting the…

Weak Topological Insulators with Step Edges: Subband Engineering and Its Effect on Electron Transport

- Physics
- 2016

A three-dimensional weak topological insulator (WTI) can be regarded as stacked layers of two-dimensional quantum spin-Hall insulators, each of which accommodates a one-dimensional helical edge mode.…

Manipulating topological-insulator properties using quantum confinement

- Physics
- 2017

Recent discoveries have spurred the theoretical prediction and experimental realization of novel materials that have topological properties arising from band inversion. Such topological insulators…

Anisotropic Quantum Confinement Effect and Electric Control of Surface States in Dirac Semimetal Nanostructures

- PhysicsScientific reports
- 2015

It is demonstrated that the topological surface states could be controlled by lateral electrostatic gating and it is possible to generate Rashba-like spin splitting for the surface states and to shift them relative to the confinement-induced bulk gap.

Nonunique connection between bulk topological invariants and surface physics

- PhysicsPhysical Review B
- 2019

At the heart of the study of topological insulators lies a fundamental dichotomy: Topological invariants are defined in infinite systems but surface states as their main footprint only exist in…

## References

SHOWING 1-10 OF 41 REFERENCES

Strong side of weak topological insulators

- Physics
- 2012

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.

- PhysicsPhysical review letters
- 2012

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

- Physics
- 2011

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

- Physics
- 2011

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…

Aharonov-Bohm interference in topological insulator nanoribbons.

- PhysicsNature materials
- 2010

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

- Physics
- 2009

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

- Physics
- 2008

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

- Physics
- 2012

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

- Physics
- 2007

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 ${Z}_{2}$…