Spin connection and boundary states in a topological insulator

Abstract

We study the surface resistivity of a three-dimensional topological insulator when the boundaries exhibit a non trivial curvature. We obtain an analytical solution for a spherical topological insulator, and we show that a non trivial quantum spin connection emerges from the three dimensional band structure. We analyze the effect of the spin connection on the scattering by a bump on a flat surface. Quantum effects induced by the geometry lead to resonances when the electron wavelength is comparable to the size of the bump.

11 pages, 4 figures, submitted

References in corpus (19)

• The electronic properties of graphene
• Topological Insulators
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Topological invariants of time-reversal-invariant band structures
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Helical Metal Inside a Topological Band Insulator
• Effective continuous model for surface states and thin films of three dimensional topological insulators
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Charge inhomogeneities due to smooth ripples in graphene sheets
• Topological insulators in three dimensions from spontaneous symmetry breaking
• Majorana Fermions and Non-Abelian Statistics in Three Dimensions
• The surface states of topological insulators - Dirac fermion in curved two dimensional spaces
• Helical Luttinger liquid in topological insulator nanowires
• Quantum impurity on the surface of a topological insulator
• Anderson Impurity in Helical Metal
• Three Dimensional Gross-Neveu Model on Curved Spaces
• Geodesic scattering by surface deformations of a topological insulator
• Electronic interactions in fullerene spheres

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• Novel effects of strains in graphene and other two dimensional materials
• Random-matrix theory of Majorana fermions and topological superconductors
• Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space
• Spherical topological insulator
• Scattering of two-dimensional massless Dirac electrons by a circular potential barrier
• 2D and 3D topological insulators with isotropic and parity-breaking Landau levels
• Spherical topological-insulator nanoparticles: Quantum size effects and optical transitions
• Unified description of Dirac electrons on a curved surface of topological insulators
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Synthetic Landau levels and spinor vortex matter on Haldane spherical surface with magnetic monopole
• Time-reversal-symmetric topological magnetoelectric effect in three-dimensional topological insulators
• Geometric Model of Topological Insulators from the Maxwell Algebra
• Landau levels in curved space realized in strained graphene
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Finite-size effects in cylindrical topological insulators
• Curved domain-wall fermions
• Magnetic tilting and emergent Majorana spin connection in topological superconductors
• Effective Hamiltonian for surface states of topological insulator nanotubes
• Topological spinor vortex matter on spherical surface induced by non-Abelian spin-orbital-angular-momentum coupling
• Superconductive proximity in a Topological Insulator slab and excitations bound to an axial vortex
• Berry phases and zero-modes in toroidal topological insulator
• Signatures of surface Majorana modes in the magnetic response of topological superconductors
• Electronic confinement of surface states in a topological insulator nanowire
• Anomalous Currents on Closed Surfaces: Extended Proximity, Partial Quantization, and Qubits