Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures
Ur Rehman Majeed1, 2, †, A Abid A1, 2
(color online) (a) The spectrum remains gapped when . The spectrum becomes gapless when (b) and (c) . The presence of exchange-field M removes the spin-degeneracy, i.e., the spin-up (spin-down ) bands move upward (downward). But still there is two-fold spin degeneracy at E = 0.