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Engineering Dirac electrons emergent on the surface of a topological insulator

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ABSTRACT

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid 3He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.

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Typical energy spectrum of a rectangular, prism-shaped topological insulator nanowire. (a) As a consequence of the spin Berry phase, π, the spectrum of the surface state is gapped. (b) The same spectrum becomes gapless in the presence of an external flux, π, inserted along the axis of the prism to cancel the Berry phase.
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Figure 1: Typical energy spectrum of a rectangular, prism-shaped topological insulator nanowire. (a) As a consequence of the spin Berry phase, π, the spectrum of the surface state is gapped. (b) The same spectrum becomes gapless in the presence of an external flux, π, inserted along the axis of the prism to cancel the Berry phase.

Mentions: The orbital part of an electron state on the surface of a cylindrical topological insulator is represented as3where is the orbital angular momentum in the z-direction, along the axis of the cylinder. The Berry phase, π, modifies the boundary condition with respect to the polar angle, ϕ, from periodic to anti-periodic—that is,4This leads to the following quantization rule of the orbital angular momentum:5In this half-integral quantization, Lz = 0, and therefore is not allowed. On the other hand, the spectrum of the surface states takes the following Dirac form,6Combining equations (5) and (6), one is led to believe that the spectrum of the cylindrical topological insulator is generically gapped; see also a gapped spectrum shown in figure 1(a). The spectra shown in figure 1 are calculated using tight-binding implementation of the bulk 3D topological insulator of a rectangular prism shape [22].


Engineering Dirac electrons emergent on the surface of a topological insulator
Typical energy spectrum of a rectangular, prism-shaped topological insulator nanowire. (a) As a consequence of the spin Berry phase, π, the spectrum of the surface state is gapped. (b) The same spectrum becomes gapless in the presence of an external flux, π, inserted along the axis of the prism to cancel the Berry phase.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5036486&req=5

Figure 1: Typical energy spectrum of a rectangular, prism-shaped topological insulator nanowire. (a) As a consequence of the spin Berry phase, π, the spectrum of the surface state is gapped. (b) The same spectrum becomes gapless in the presence of an external flux, π, inserted along the axis of the prism to cancel the Berry phase.
Mentions: The orbital part of an electron state on the surface of a cylindrical topological insulator is represented as3where is the orbital angular momentum in the z-direction, along the axis of the cylinder. The Berry phase, π, modifies the boundary condition with respect to the polar angle, ϕ, from periodic to anti-periodic—that is,4This leads to the following quantization rule of the orbital angular momentum:5In this half-integral quantization, Lz = 0, and therefore is not allowed. On the other hand, the spectrum of the surface states takes the following Dirac form,6Combining equations (5) and (6), one is led to believe that the spectrum of the cylindrical topological insulator is generically gapped; see also a gapped spectrum shown in figure 1(a). The spectra shown in figure 1 are calculated using tight-binding implementation of the bulk 3D topological insulator of a rectangular prism shape [22].

View Article: PubMed Central - PubMed

ABSTRACT

The concept of the topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin–orbit coupled materials, some classes of nodal superconductors, superfluid 3He, etc. From a technological point of view, TIs are expected to serve as platforms for realizing dissipationless transport in a non-superconducting context. The TI exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context we contrast the cases of weak and strong TIs. We study the robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new research perspective in the field.

No MeSH data available.


Related in: MedlinePlus