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Parity and valley degeneracy in multilayer graphene

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Parity and valley degeneracy in multilayer graphene. / Koshino, Mikito; McCann, Edward.
In: Physical review B, Vol. 81, No. 11, 115315, 12.03.2010.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Koshino, M & McCann, E 2010, 'Parity and valley degeneracy in multilayer graphene', Physical review B, vol. 81, no. 11, 115315. https://doi.org/10.1103/PhysRevB.81.115315

APA

Koshino, M., & McCann, E. (2010). Parity and valley degeneracy in multilayer graphene. Physical review B, 81(11), Article 115315. https://doi.org/10.1103/PhysRevB.81.115315

Vancouver

Koshino M, McCann E. Parity and valley degeneracy in multilayer graphene. Physical review B. 2010 Mar 12;81(11):115315. doi: 10.1103/PhysRevB.81.115315

Author

Koshino, Mikito ; McCann, Edward. / Parity and valley degeneracy in multilayer graphene. In: Physical review B. 2010 ; Vol. 81, No. 11.

Bibtex

@article{e74c803e68de474db3185b80743c0edf,
title = "Parity and valley degeneracy in 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.",
keywords = "graphene",
author = "Mikito Koshino and Edward McCann",
note = "{\textcopyright} 2010 The American Physical Society",
year = "2010",
month = mar,
day = "12",
doi = "10.1103/PhysRevB.81.115315",
language = "English",
volume = "81",
journal = "Physical review B",
issn = "1550-235X",
publisher = "AMER PHYSICAL SOC",
number = "11",

}

RIS

TY - JOUR

T1 - Parity and valley degeneracy in multilayer graphene

AU - Koshino, Mikito

AU - McCann, Edward

N1 - © 2010 The American Physical Society

PY - 2010/3/12

Y1 - 2010/3/12

N2 - 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.

AB - 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.

KW - graphene

U2 - 10.1103/PhysRevB.81.115315

DO - 10.1103/PhysRevB.81.115315

M3 - Journal article

VL - 81

JO - Physical review B

JF - Physical review B

SN - 1550-235X

IS - 11

M1 - 115315

ER -