Abstract
We study the topological feature of gapless states in the fermionic Kitaev model on a square lattice. There are two types of gapless states which are topologically trivial and nontrivial. We show that the topological gapless phase lives in a wide two-dimensional parameter region and are characterized by two vertices of an auxiliary vector field de-fined in the two-dimensional momentum space, with opposite winding numbers. The isolated band touching points, as the topological defects of the field, move, emerge, and disappear as the parameters vary. The band gap starts to open only at the merg-ing points, associated with topologically trivial gapless states. The symmetry protect-ing the topological gapless phase and the robustness under perturbations are also discussed.
Highlights
In this paper we have studied the topological gapless state and edge modes of the Kitaev model on a square lattice
The advantage of studying the Kitaev model is that it is the minimal model in two dimensions where one can derive a number of analytical results for the topological gapless phase
It is shown that the topological gapless phase is characterized by two topological vortices with opposite chirality in the momentum plane
Summary
We study the topological feature of gapless states in the fermionic Kitaev model on a square lattice. We show that the topological gapless phase lives in a wide two-dimensional parameter region and are characterized by two vertices of an auxiliary vector field de-fined in the two-dimensional momentum space, with opposite winding numbers. System in the topological gapless phase exhibits band structures with band-touching points in the momentum space, where these kinds of nodal points appear as topological defects of an auxiliary vector field. These points are unremovable due to the symmetry protection, until a pair of them meets and annihilates together. In contrast to previous study, this symmetry does not involve any anti-unitary operation
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