Spherical topological insulator

Abstract

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 induced effective vector potential (spin connection) can be interpreted as an effective vector potential associated with a fictitious magnetic monopole induced at the center of the sphere. The strength of the induced magnetic monopole is found to be g=2pi, -2pi, being the smallest finite (absolute) value compatible with the Dirac quantization condition. We have established an explicit correspondence between the bulk Hamiltonian and the effective Dirac operator on the curved spherical surface. An explicit construction of the surface spinor wave functions implies a rich spin texture possibly realized on the surface of topological insulator nanoparticles. The electronic spectrum inferred by the obtained effective surface Dirac theory, confirmed also by the bulk tight-binding calculation, suggests a specific photo absorption/emission spectrum of such nanoparticles.

13 pages, 2 figures

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The Quantum Spin Hall Effect: Theory and Experiment
• Helical Metal Inside a Topological Band Insulator
• Aharonov-Bohm oscillations in disordered topological insulator nanowires
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Spin connection and boundary states in a topological insulator
• A Z${}_2$ index of Dirac operator with time reversal symmetry

Cited by in corpus (8)

• Finite-size energy gap in weak and strong topological insulators
• Interacting surface states of three-dimensional topological insulators
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Disorder effect on chiral edge modes and anomalous Hall conductance in Weyl semimetals
• Theory of magnetotransport in shaped topological insulator nanowires
• Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Equatorial magnetoplasma waves