Abstract
The magneto-oscillations in graphene bilayers are studied in the vicinity of the K and K' points of the Brillouin zone within the four-band continuum model based on the simplest tight-binding approximation involving only nearest-neighbor interactions. The model is employed to construct Landau plots for a variety of carrier concentrations and bias strengths between the graphene planes. The quantum-mechanical and quasiclassical approaches are compared. We have found that the quantum magneto-oscillations are only asymptotically periodic and reach the frequencies predicted quasiclassically for high indices of Landau levels. In unbiased bilayers, the phase of oscillations is equal to the phase of massive fermions. Anomalous behavior of oscillation phases was found in biased bilayers with broken inversion symmetry. The oscillation frequencies again tend to quasiclassically predicted ones, which are the same for K and K', but the quantum approach yields the gate-tunable corrections to oscillation phases, which differ in sign for K and K'. These valley-dependent phase corrections give rise to two series with the same frequency but shifted in phase, instead of a single quasiclassical series of oscillations.
Export citation and abstract BibTeX RIS
GENERAL SCIENTIFIC SUMMARY Introduction and background. Due to their unusual electronic properties, graphene and graphene bilayers are presently of central interest to solid state physicists and technologists. This paper presents a theoretical study of the magnetic-field-induced oscillations of the electron density of states (DOS) in graphene bilayers. Using the four-band continuum model based on the tight-binding approximation considering nearest-neighbour interactions, we construct analytically Landau plots (a standard tool used to determine the frequency and phase of magneto-oscillations) for unbiased and (gated) biased bilayers in the vicinity of K and K' points of the Brillouin zone.
Main results. Our theory shows that magneto-oscillation phases in biased graphene bilayers, with broken inversion symmetry and a finite gap between the valence and conduction bands, behave anomalously. Similarly to unbiased bilayers, magneto-oscillations are only asymptotically periodic and for low magnetic fields reach the frequencies predicted quasiclassically. The frequencies are the same for K and K', but the quantum approach yields the valley-dependent gate-tunable phase corrections which give rise to two series of magneto-oscillations with the same frequency but shifted in phase.
Wider implications. The reported phase anomalies for biased bilayer graphene have potential for experimental detection.
Figure. The DOS of the unbiased (a) and biased (b, c) graphene bilayers with the fixed quasiclassical frequency F1 = 70 T. In (b, c) 2u denotes the gate-induced energy difference between layers. The blue peaks show DOS calculated for the K valley, whereas the red ones are related to the K' valley.