Time-evolution patterns of electrons in twisted bilayer graphene

• Main Authors: Do, H. Nam, Le, H. Anh, Bercioux, D
• Format: Journal Article
• Language: English
• Published: 19-04-2019
• Subjects: Physics - Mesoscale and Nanoscale Physics
• DOI: 10.48550/arxiv.1901.02794

Phys. Rev. B 99, 165127 (2019) We characterise the dynamics of electrons in twisted bilayer graphene by
analysing the time-evolution of electron waves in the atomic lattice. We
perform simulations based on a kernel polynomial technique using Chebyshev
polynomial; this method does not requires any diagonalisation of the system
Hamiltonian. Our simulations reveal that the inter-layer electronic coupling
induces the exchange of waves between the two graphene layers. This wave
transfer manifests as oscillations of the layer-integrated probability
densities as a function of time. For the bilayer case, it also causes a
difference in the wavefront dynamics compared to monolayer graphene. The
intra-layer spreading of electron waves is irregular and progresses as a
two-stage process. The first one characterised by a well-defined wavefront
occurs in a short time | a wavefront forms instead during the second stage. The
wavefront takes a hexagon-like shape with the vertices developing faster than
the edges. Though the detail spreading form of waves depends on initial states,
we observe localisation of waves in specific regions of the moir\'e zone. To
characterise the electron dynamics, we also analyse the time auto-correlation
functions. We show that these quantities shall exhibit the beating modulation
when reducing the interlayer coupling.