Unified description of Dirac electrons on a curved surface of topological insulators

Abstract

Existence of a protected surface state described by a massless Dirac equation is a defining property of the topological insulator. Though this statement can be explicitly verified on an idealized flat surface, it remains to be addressed to what extent it could be general. On a curved surface, the surface Dirac equation is modified by the spin connection terms. Here, in the light of the differential geometry, we give a general framework for constructing the surface Dirac equation starting from the Hamiltonian for bulk topological insulators. The obtained unified description clarifies the physical meaning of the spin connection.

9 pages, 1 figure

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• Transport study of the wormhole effect in three-dimensional topological insulators
• Effective Hamiltonian for surface states of topological insulator nanotubes
• Theory of magnetotransport in shaped topological insulator nanowires
• Vacuum currents in curved tubes
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Berry phases and zero-modes in toroidal topological insulator
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Sphere on a plane: Two-dimensional scattering from a finite curved region
• Electronic confinement of surface states in a topological insulator nanowire
• Local Density of States in a Helical Tomonaga-Luttinger Liquid of Loop and Josephson Junction Geometries