2010/10/31 by Jun Goryo
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.1143/jpsj.80.043704
published as J. Phys. Soc. Jpn., Vol.80, No.4, (2011) p.043704 · 5 pages, 1 figure, some comments are added/revised, accepted for publication in J. Phys. Soc. Jpn
arxiv created 2011/02/25 · openalex publication_date 2011/03/29 · arxiv updated 2011/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a two-dimensional bipartite lattice system. In such a system, the Bloch band spectrum can have some valley points, around which Dirac fermions appear as the low-energy excitations. Each valley point has a valley spin +1 or -1. In such a system, there are two topological numbers counting vortices and merons in the Brillouin zone, respectively. These numbers are equivalent, and this fact leads to a sum rule which states that the total sum of the valley spins is absent even in a system without time-reversal and parity symmetries. We can see some similarity between the valley spin and chirality in the Nielsen-Ninomiya no-go theorem in odd-spatial dimensions.