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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 moire 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.
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Quasi-periodic moir{e} patterns and their effect on electronic properties of twisted bilayer graphene (TBG) have been intensely studied. At small twist angle $theta$, due to atomic reconstruction, the moire superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride (hBN), which we use as a TBG substrate, is optically hyperbolic. Our results illustrate new capabilities of nano-photocurrent technique for probing nanoscale electronic inhomogeneities in two-dimensional materials.
Twisted van der Waals (vdW) heterostructures have recently emerged as an attractive platform to study tunable correlated electron systems. However, the quantum mechanical nature of vdW heterostructures makes their theoretical and experimental exploration laborious and expensive. Here we present a simple platform to mimic the behavior of twisted vdW heterostructures using acoustic metamaterials comprising of interconnected air cavities in a steel plate. Our classical analog of twisted bilayer graphene shows much of the same behavior as its quantum counterpart, including mode localization at a magic angle of about 1.1 degrees. By tuning the thickness of the interlayer membrane, we reach a regime of strong interactions more than three times higher than the feasible range of twisted bilayer graphene under pressure. In this regime, we find the magic angle as high as 6.01 degrees, corresponding to a far denser array of localized modes in real space and further increasing their interaction strength. Our results broaden the capabilities for cross-talk between quantum mechanics and acoustics, as vdW metamaterials can be used both as simplified models for exploring quantum systems and as a means for translating interesting quantum effects into acoustics.
Flatbands with extremely narrow bandwidths on the order of a few mili-electron volts can appear in twisted multilayer graphene systems for appropriate system parameters. Here we investigate the electronic structure of a twisted bi-bilayer graphene, or twisted double bilayer graphene, to find the parameter space where isolated flatbands can emerge as a function of twist angle, vertical pressure, and interlayer potential differences. We find that in twisted bi-bilayer graphene the bandwidth is generally flatter than in twisted bilayer graphene by roughly up to a factor of two in the same parameter space of twist angle $theta$ and interlayer coupling $omega$, making it in principle simpler to tailor narrow bandwidth flatbands. Application of vertical pressure can enhance the first magic angle in minimal models at $theta sim 1.05^{circ}$ to larger values of up to $theta sim 1.5^{circ}$ when $ P sim 2.5$~GPa, where $theta propto omega/ upsilon_{F}$. Narrow bandwidths are expected in bi-bilayers for a continuous range of small twist angles, i.e. without magic angles, when intrinsic bilayer gaps open by electric fields, or due to remote hopping terms. We find that moderate vertical electric fields can contribute in lifting the degeneracy of the low energy flatbands by enhancing the primary gap near the Dirac point and the secondary gap with the higher energy bands. Distinct valley Chern bands are expected near $0^{circ}$ or $180^{circ}$ alignments.
We present transport measurements of bilayer graphene with 1.38{deg} interlayer twist and apparent additional alignment to its hexagonal boron nitride cladding. As with other devices with twist angles substantially larger than the magic angle of 1.1{deg}, we do not observe correlated insulating states or band reorganization. However, we do observe several highly unusual behaviors in magnetotransport. For a large range of densities around half filling of the moire bands, magnetoresistance is large and quadratic. Over these same densities, the magnetoresistance minima corresponding to gaps between Landau levels split and bend as a function of density and field. We reproduce the same splitting and bending behavior in a simple tight-binding model of Hofstadters butterfly on a square lattice with anisotropic hopping terms. These features appear to be a generic class of experimental manifestations of Hofstadters butterfly and may provide insight into the emergent states of twisted bilayer graphene.
The effects of the long range electrostatic interaction in twisted bilayer graphene are described using the Hartree-Fock approximation. The results show a significant dependence of the band widths and shapes on electron filling, and the existence of broken symmetry phases at many densities, either valley/spin polarized, with broken sublattice symmetry, or both.
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