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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.

No MeSH data available.


Topological insulator nanoparticle as an ‘artificial atom’. The antiperiodic version of the low-lying (a) s-type, and (b) p-type orbitals are shown. To highlight their characters, the orbitals are painted in red (in blue) when the real part of the wave function is positive (negative).
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Figure 2: Topological insulator nanoparticle as an ‘artificial atom’. The antiperiodic version of the low-lying (a) s-type, and (b) p-type orbitals are shown. To highlight their characters, the orbitals are painted in red (in blue) when the real part of the wave function is positive (negative).

Mentions: The spherical topological insulator naturally models a topological insulator nanoparticle. Taking it, therefore, as an artificial atom, let us focus on its low-lying electronic levels. The angular part of the wave function is described by an anti-periodic analogue of the spherical harmonics. A few examples are shown in figure 2, where represents the angular dependence of a surface eigenfunction, specified by quantum numbers n, m. An analogue of the s-orbital is12as seen in figure 2(a), while13can be regarded as an anti-periodic version of the p-orbital, as seen in figure 2(b). Further details on such ‘monopole harmonics’ [28] and the spectrum of the artificial atom are given in [27].


Engineering Dirac electrons emergent on the surface of a topological insulator
Topological insulator nanoparticle as an ‘artificial atom’. The antiperiodic version of the low-lying (a) s-type, and (b) p-type orbitals are shown. To highlight their characters, the orbitals are painted in red (in blue) when the real part of the wave function is positive (negative).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Topological insulator nanoparticle as an ‘artificial atom’. The antiperiodic version of the low-lying (a) s-type, and (b) p-type orbitals are shown. To highlight their characters, the orbitals are painted in red (in blue) when the real part of the wave function is positive (negative).
Mentions: The spherical topological insulator naturally models a topological insulator nanoparticle. Taking it, therefore, as an artificial atom, let us focus on its low-lying electronic levels. The angular part of the wave function is described by an anti-periodic analogue of the spherical harmonics. A few examples are shown in figure 2, where represents the angular dependence of a surface eigenfunction, specified by quantum numbers n, m. An analogue of the s-orbital is12as seen in figure 2(a), while13can be regarded as an anti-periodic version of the p-orbital, as seen in figure 2(b). Further details on such ‘monopole harmonics’ [28] and the spectrum of the artificial atom are given in [27].

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.