Premium
Magnetisation oscillations, boundary conditions and the Hofstadter butterfly in graphene flakes
Author(s) -
Liu Yang,
Brada Matej,
Mele Eugene J.,
Kusmartsev Feodor V.
Publication year - 2014
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.201400143
Subject(s) - superlattice , physics , graphene , condensed matter physics , landau quantization , boundary value problem , magnetization , magnetic field , lattice (music) , quantum , periodic boundary conditions , energy spectrum , quantum oscillations , quantum mechanics , fermi surface , superconductivity , acoustics
New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov‐Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight‐binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moiré and graphene anti‐dot superlattices are discussed.