Using a structural search method in combination with first-principles calculations, we found lots of low energy 2D carbon allotropes and examined all possible Dirac points around their Fermi levels. Three amazing 2D Dirac carbon allotropes have been discovered, named as S-graphene, D-graphene and E-graphene. By analyzing the topology correlations among S-, T, net W graphene and graphene, we fou...

In this paper, we study the inverse problem for Dirac differential operators with  discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfun...

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Rec...

This paper aims at studying the characterization of Dirac-structure edges with wavelet transform, and selecting the suitable wavelet functions to detect them. Three significant characteristics of the local maximum modulus of the wavelet transform with respect to the Dirac-structure edges are presented: (1) slope invariant: the local maximum modulus of the wavelet transform of a Dirac-structure ...

We have investigated the effect of electronic topological transition on the electric field-induced band gap in sliding bilayer graphene by using the density functional theory calculations. The electric field-induced band gap was found to be extremely sensitive to the electronic topological transition. At the electronic topological transition induced by layer sliding, four Dirac cones in the Ber...

the degree of φ : S → SU(N), where S is the 3sphere “at infinity” in R. The topological charge has a fermionic description: by the Index Theorem, Q = index(%∂ ) where %∂ A is the Dirac operator coupled to A. The situation is similar for gauge fields on compact manifolds such as S, T , . . . Consider now a family A of SU(N) gauge fields on the 4-torus T 4 parameterized by y ∈ Y (a smooth paramet...

Abstract. This paper is companion to our earlier work [8] (see also announcement [7]). Let M be a closed manifold and Y be an embedded hypersurface, such that there is a decomposition of M = M1 ∪M2 into two manifolds with boundary M1 and M2 , with M1 ∩M2 = Y . In [8] we proved the decomposition formula for detζ∆ the ζ-determinant of a Dirac Laplacian ∆ on M . The contributions coming from M1 an...

We derive the vector-like four dimensional overlap Dirac operator starting from a five dimensional Dirac action in the presence of a delta-function space-time defect. The effective operator is obtained by first integrating out all the fermionic modes in the fixed gauge background, and then identifying the contribution from the localized modes as the determinant of an operator in one dimension l...

Dirac equation in (1+2) dimensions for quasi-particles in graphene and quantum field theory of their Coulomb interaction. Abstract There is evidence for existance of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's bril-luoin zone. Certain subtle points which are peculiar to od...