Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators

Abstract

By numerically solving the effective continuous model of a topological insulator with parameters corresponding to the band structure of the topological insulator Bi2Se3 , we analyze possible appearance of one-dimensional states in various geometries. Massless Dirac fermions are found at the edges of thin ribbons with surface oriented not only along the van der Waals gap but also in the perpendicular direction. Thick rods and slabs with surface steps host massive modes localized on surface faces. We argue that the modes are massive and their origin is due to the difference in the Dirac point energy of adjacent faces. The absence of one-dimensional states near edges of a large rectangular rod and surface steps is demonstrated.

arXiv comment9 pages, 10 figures; revised version, additional references, extended introduction and method description, enhanced figures

References in corpus (36)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Evidence for Helical Edge Modes in Inverted InAs/GaSb Quantum Wells
• Realization of Quantum Spin Hall State in Monolayer 1T'-WTe2
• Aharonov-Bohm interference in topological insulator nanoribbons
• Edge conduction in monolayer WTe2
• Oscillatory crossover from two dimensional to three dimensional topological insulators
• Monolayer Topological Insulators: Silicene, Germanene and Stanene
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Anomalous Finite Size Effects on Surface States in the Topological Insulator Bi${}_2$Se${}_3$
• Topological Insulator Nanowires and Nanoribbons
• Aharonov-Bohm oscillations in disordered topological insulator nanowires
• Robust topological edge states at the perfect surface step edge of topological insulator ZrTe${}_5$
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Quantized chiral edge conduction on reconfigurable domain walls of a magnetic topological insulator
• Sub-nm wide electron channels protected by topology
• One-dimensional helical transport in topological insulator nanowire interferometers
• Robust spin-polarized midgap states at step edges of topological crystalline insulators
• Scanning Tunneling Microscopy of Defect States in the Semiconductor Bi${}_2$Se${}_3$
• Helical Luttinger liquid in topological insulator nanowires
• Two-dimensional universal conductance fluctuations and the electron-phonon interaction of topological surface states in Bi2Te2Se nanoribbons
• New interpretation of the origin of 2DEG states at the surface of layered topological insulators
• Spin and Charge Structure of the Surface States in Topological Insulators
• Stationary phase approximation approach to the quasiparticle interference on the surface of a strong topological insulator
• Low-velocity anisotropic Dirac fermions on the side surface of topological insulators
• Junction between surfaces of two topological insulators
• Scattering from Surface Step Edges in Strong Topological Insulators
• Electronic States of Wires and Slabs of Topological Insulators: Quantum Hall Effects and Edge Transport
• STM imaging of a bound state along a step on the surface of the topological insulator Bi${}_2$Te${}_3$
• Surface states scattering from a step defect in topological insulator Bi_{2}Te_{3}
• Impact of Step Defects on Surface States of Topological Insulators
• Ab-initio transport across Bismuth Selenide surface barriers
• Experimental search for one-dimensional edge states at surface steps of the topological insulator Bi${}_2$Se${}_3$: Distinguishing between effects and artifacts
• Electronic properties of one-dimensional nanostructures of the Bi${}_2$Se${}_3$ topological insulator
• Energy gap in tunneling spectroscopy: effect of the chemical potential shift

Cited by in corpus (3)

• Electron-Hole Asymmetry of Surface States in Topological Insulator Sb2Te3 Thin Films Revealed by Magneto-Infrared Spectroscopy
• Experimental Observation of Bound States of 2D Dirac Electrons at Surface Steps of the Topological Insulator Bi${}_2$Se${}_3$
• Particle-hole asymmetry and quantum confinement effects on the magneto-optical response of topological insulator thin-films