ABSTRACT

The central idea is the topological equivalence between objects that have the same genus and can be mapped to each other by continuous deformation with the genus kept invariant. There is the homotopy group, which contains all the topologically equivalent objects of a certain class. The first demonstration of 2D massless Dirac fermions in condensed matter was addressed on the 2D honeycomb lattice, where spinless condition or spin degeneracy was assumed while the two sublattices come into play as a pseudospin. It is remarkable that the chiral zero-mode LL can serve as a mark of 2D massless Dirac fermions existing in a noninteracting fermionic lattice with sublattice symmetry and the resulting continuous chiral symmetry. The present concern is about the topological characteristics of 2D massless Dirac fermions that are hosted in the vicinity of nodes in 3D layered systems.