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Abstract: We study spatial symmetry in general ABA-stacked multilayer graphene toillustrate how electronic spectra at the two valleys are related in a magneticfield. 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-reversalsymmetry. A multilayer with an odd number of layers three or more lacksinversion symmetry, but there is another transformation imposing an approximatevalley degeneracy, which arises because the low-energy Hamiltonian consists ofseparate monolayerlike and bilayerlike parts. We show that an externalelectrostatic potential generally breaks valley degeneracy in a magnetic field,in a markedly different manner in odd and even multilayers.



Author: Mikito Koshino, Edward McCann

Source: https://arxiv.org/







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