A Dirac fermion model associated with second order topological insulator

Abstract

We study topological aspects of a Dirac fermion coupled with a Higgs field associated with the lattice model introduced by Benalcazar et al. which shows the topological quadrupole phase. Using the index theorem, we show that the index of the Hamiltonian is just given by the winding number of the Higgs field, implying that a corner state of the lattice model belongs to the same class of the Jackiw-Rossi states localized at a vortex. We also calculate the current density of the Dirac fermion with a symmetry breaking term dependent on time, which is associated with the dipole pump proposed by Benalcazar et al. We argue that it is indeed a topological current, and the total pumped charge is given by an integer related with the index.

12 pages, 5 figures. Text revised. Figures and appendix added

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• First and Second Order Topological Phases on Ferromagnetic Breathing Kagome Lattice
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Second-order topological modes in two-dimensional continuous media
• Higher order topological matter and fractional chiral states
• Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators
• From orthosymplectic structure to super topological matter
• Signature of edge states in resonant wave scattering
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators