Parity and valley degeneracy in multilayer graphene

TL;DR

This paper investigates how spatial symmetry affects valley degeneracy in multilayer graphene, revealing differences between even and odd layers and the impact of external potentials.

Contribution

It provides a detailed analysis of symmetry-induced valley degeneracy in multilayer graphene with various layer counts, highlighting the role of inversion symmetry and low-energy Hamiltonian structure.

Findings

Even-layered multilayers and monolayer graphene have inversion symmetry, ensuring valley degeneracy.

Odd-layered multilayers lack inversion symmetry but still exhibit approximate valley degeneracy due to Hamiltonian structure.

External electrostatic potentials break valley degeneracy differently in odd and even multilayer graphene.

Abstract

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.