Rashba-type Valley Splitting In Graphene
Yen-Chun Chen1*, Ning-Yuan Lue2, Miao-Ling Lin2, George Yu-Shu Wu1,2
1Departments of Physics, National Tsing-Hua Universsity, Hsin-Chu, Taiwan
2Departments of Electrical Engineering, National Tsing-Hua University, Hsin-Chu, Taiwan
* presenting author:陳彥君, email:ycc22537@gmail.com
Graphene [1] is considered as a promising candidate material for valleytronics [2]. In this discussion, we present the electronic band structure of gapped graphene in an in-plane electric field, which has an important implication for electrically driven valleytronic devices. Due to the coupling between the valley pseudospin and the orbital degree of freedom (i.e., valley-orbit coupling) [3], the band structure exhibits the Rashba-type valley splitting [4]. Specifically, we examine the splitting in both monolayer and bilayer graphene. In the case of monolayer graphene, we will show that a specific condition is required apart from the presence of an in-plane field, in order for the splitting to occur. On the other hand, in the case of bilayer graphene, owing to the existence of both intralayer and interlayer interatomic hopping, the Rashba-type splitting exhibits more complicated features. We discuss all these findings analytically, in terms of the Dirac theory [1] and the Schrodinger theory [3], and also numerically by performing the calculation of band structures.

[1] K. S. Novoselov et al. Science 306,666(2004); A. H. Casto Neto et al. Rev. Mod. Phys. 81, 109 (2009).
[2] A. Rycerz et al. Nature Phys. 3, 172-175 (2007).
[3] G. Y. Wu et al. Phys. Rev. B 84,195463 (2011).
[4] M. K. Lee Phys. Rev. B 86, 165411 (2011); G. Y. Wu et al. PRB 88, 125422 (2013).

Keywords: graphene, valleytronics (valley pseudospin)