Gate-induced magneto-oscillation phase anomalies in graphene bilayers

TL;DR

This paper investigates magneto-oscillations in graphene bilayers near the K and K' points, revealing gate-tunable phase anomalies and valley-dependent effects that differ from classical predictions.

Contribution

It introduces a quantum-mechanical analysis of magneto-oscillations in biased graphene bilayers, highlighting gate-tunable phase corrections and valley-dependent phase shifts.

Findings

Quantum oscillations are asymptotically periodic at high Landau levels.

Bias-induced inversion symmetry breaking causes phase anomalies in oscillations.

Valley-dependent phase shifts lead to two distinct oscillation series with the same frequency.

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 ased on the simplest tight-binding approximation involving only the 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 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, instead of a single quasiclassical series of oscillations, to two series with the same frequency but shifted in phase.