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Parity and valley degeneracy in multilayer graphene

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Article number115315
<mark>Journal publication date</mark>12/03/2010
<mark>Journal</mark>Physical Review B
Issue number11
Number of pages6
<mark>Original language</mark>English


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.

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© 2010 The American Physical Society