Huang D, Iurov A, Gumbs G, Zhemchuzhna L. Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential.
JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019;
31:125503. [PMID:
30625422 DOI:
10.1088/1361-648x/aafd01]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected [Formula: see text] effective Hamiltonian including interlayer effective mass, interlayer coupling and asymmetrical on-site energies due to a vertically-applied electric field. For bilayer graphene, we find two important characteristics, i.e. mixing and interference of intervalley scatterings in the presence of a scatter array, as well as a perpendicular-field induced site-energy asymmetry which deforms severely or even destroys completely the Hofstadter-type band structures due to the dependence of Bloch-wave expansion coefficients on the applied electric field.
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