Edge States in Silicene Nanodisks

Abstract

Silicene is a honeycomb-structure silicon atoms, which shares many intriguing properties with graphene. Silicene is expected to be a quantum spin-Hall insulator due to its spin-orbit interactions. We investigate the electronic properties of silicene nanodisks, which are silicene derivatives with closed edge. In case of the simplest model of graphene nanodisks, the number of the zero-energy modes is given by the lower bound of the Lieb theorem. They are standing wave states.When the spin-orbit interaction is introduced and the system becomes a topological insulator, they begin to propagate around a nanodisk. Helical edge currents flow around the edge of a nanodisk though the crystal momentum is ill-defined. We have newly found the counting rule of the zero-energy states, and constructed the low-energy theory of zigzag triangular silicene. We also show the validity of the bulk-edge correspondence in nanodisks with rough edge by calculating the local probability amplitude and current. Finally, the signatures of the topological phase transition in silicene nanodisks under an external electric field are revealed.Our results will be observable by means of STM experiments.

5 pages, 6 figures

References in corpus (10)

• Half-Metallic Graphene Nanoribbons
• Electronic States of Graphene Nanoribbons
• Emergence of magnetism in graphene materials and nanostructures
• Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene
• Magnetism in graphene nano-islands
• Peculiar Width Dependence of the Electronic Property of Carbon Nanoribbons
• Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene
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• Metallic Graphene Nanodisks
• In-gap impurity states as the hallmark of the Quantum Spin Hall phase

Cited by in corpus (14)

• Colloquium: Topological Band Theory
• Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers
• Direct Evidence of Interaction-Induced Dirac Cones in Monolayer Silicene/Ag(111) System
• Classical and Quantum Plasmonics in Graphene Nanodisks: the Role of Edge States
• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• Electrostatic quantum dots in silicene
• Transport through graphene-like flakes with intrinsic spin orbit interactions
• Topological insulator ring with magnetic impurities
• Spin and valley manipulation in single and double electrostatic silicene quantum dots
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• Protected edge states in silicene antidots and dots in magnetic field
• Helical edge states in silicene and germanene nanorings in perpendicular magnetic field
• Electrical control of a confined electron spin in a silicene quantum dot
• Variable Coupling Strength of Silicene on Ag(111)