• 文献标题:   Edge states in proximitized graphene ribbons and Hakes in a perpendicular magnetic field: Emergence of lone pseudohelical pairs and pure spin-current states
  • 文献类型:   Article
  • 作  者:   ZHUMAGULOV Y, FRANK T, FABIAN J
  • 作者关键词:  
  • 出版物名称:   PHYSICAL REVIEW B
  • ISSN:   2469-9950 EI 2469-9969
  • 通讯作者地址:  
  • 被引频次:   0
  • DOI:   10.1103/PhysRevB.105.205134
  • 出版年:   2022

▎ 摘  要

We investigate the formation of edge states in graphene ribbons and flakes with proximity-induced valleyZeeman and Rashba spin-orbit couplings in the presence of a perpendicular magnetic field B. Two types of edge states appear in the spin-orbit gap at the Fermi level at zero field: strongly localized pseudohelical (intervalley) states and weakly localized intravalley states. We show that if the magnetic field is stronger than a crossover field Bc, which is a few milliteslas for realistic systems such as graphene/WSe2, only the pseudohelical edge states remain in zigzag graphene ribbons; the intravalley states disappear. The crossover is directly related to the closing and reopening of the bulk gap formed between nonzero Landau levels. Remarkably, in finite flakes the pseudohelical states undergo perfect reflection at the armchair edges if B > Bc, forming standing waves at the zigzag edges. These standing waves comprise two counterpropagating pseudohelical states; so while they carry no charge current, they do carry (pure) spin current.