Parity and valley degeneracy in multilayer graphene

Koshino, Mikito and McCann, Edward (2010) Parity and valley degeneracy in multilayer graphene. Physical review B, 81 (11): 115315. ISSN 1550-235X

[thumbnail of koshinoABAPRB10.pdf]
koshinoABAPRB10.pdf - Published Version

Download (309kB)


We study spatial symmetry in general ABA-stacked multilayer graphene to illustrate how electronic spectra at the two valleys are related in a magnetic field. We show that the lattice of multilayers with an even number of layers as well as that of monolayer graphene satisfy spatial inversion symmetry, which rigorously guarantees valley degeneracy in the absence of time-reversal symmetry. A multilayer with an odd number of layers (three or more) lacks inversion symmetry, but there is another transformation imposing an approximate valley degeneracy, which arises because the low-energy Hamiltonian consists of separate monolayerlike and bilayerlike parts. We show that an external electrostatic potential generally breaks valley degeneracy in a magnetic field, in a markedly different manner in odd and even multilayers.

Item Type:
Journal Article
Journal or Publication Title:
Physical review B
Additional Information:
© 2010 The American Physical Society
Uncontrolled Keywords:
?? graphenephysicsqc physics ??
ID Code:
Deposited By:
Deposited On:
28 Aug 2012 13:54
Last Modified:
15 Jul 2024 13:11