We present electronic structure calculations of twisted double bilayer graphene (TDBG): A tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles calculations, we find that TDBG is semiconducting with a band gap that depends on the twist angle, that can be tuned by an external electric field. The gap is consistent with TDBG symmetry and its magnitude is related to surface effects, driving electron transfer from outer to inner layers. The surface effect competes with an energy upshift of localized states at inner layers, giving rise to the peculiar angle dependence of the band gap, which reduces at low angles. For these low twist angles, the TDBG develops flat bands, in which electrons in the inner layers are localized at the AA regions, as in twisted bilayer graphene. arXiv:1911.01347v1 [cond-mat.mes-hall]

We study the low energy spin excitations of zigzag graphene nanoribbons of varying width. We find their energy dispersion at small wave vector to be dominated by antiferromagnetic correlations between the ribbon's edges, in accrodance with previous calculations. We point out that spin wave lifetimes are very long due to the semi-conducting nature of the electrically neutral nanoribbons. However, application of very modest gate voltages cause a discontinuous transition to a regime of finite spin wave lifetime. By further increasing doping the ferromagnetic alignments along the edge become unstable against transverse spin fluctuations. This makes the experimental detection of ferromagnetism is this class of systems very delicate, and poses a difficult challenge to the possible uses of these nanoribbons as basis for spintronic devices.Graphene is being hailed as the big promise for nanoelectronics and spintronics. Its unique transport properties are expected to play a fundamental role in the develpment of new technologies [1][2][3]. New physics is also emerging from the interplay between low dimensionality, a bipartite lattice and electron-electron interaction. One of the most striking properties of graphene nanoribbons is the possibility of spontaneous magnetization [4][5][6]. This, combined with the long spin-coherence times of electrons propagating across graphene, indicates that this system is a strong candidate for future spintronics applications.The ground state properties of magnetic graphene nanoribbons have been extensively explored by a variety of methods. Recent works have investigated the properties of static excited states based on adiabatic approximations [7,8]. This approach has been employed to describe the lowest-lying excitations of magnetic metals with relative success. However, it is well known that it misses important features of the excited states, such as its finite lifetime. This arises due to the coupling between spin waves and Stoner excitations, a distinctive feature of itinerant magnets. Moreover, these recent investigations of excited states seem to have disregarded the antiferromagnetic coupling between the magnetizations on opposite edges of graphene nanoribbons. As we shall see, this leads to an incorrect prediction concerning the wave vector dependence of low energy spin excitations. This has already been demonstrated more than a decade ago in the seminal work by Wakabayashi et al. [9]. Those authors used an itinerant model to describe the π electrons in graphene nanoribbons of various widths. They showed clearly the presence of a linear term in the spin wave dispersion relation for small wave vector.One interesting feature of magnetic graphene nanoribbons is that the spins along each border are ferromagnetically coupled to each other, but there is an antiferromagnetic exchange coupling between the two opposite borders. This coupling is mediated by the conduction electrons, and decreases as the ribbon width is increased. Thus, it may appear, at first sight, that this antiferromagneti...

No abstract

The formation of a superstructure -with a related Moiré pattern -plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moiré angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moiré pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the nearinfrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the Moiré angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-Hänchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that sub-wavelength spin-orbit interactions of light provide a unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.At macroscopic scales geometric optics provides an adequate description of several photonic phenomena. However, in the sub-wavelength regime light's spatial and polarization degrees of freedom are not independent quantities, resulting in deviations from the traditional ray optics picture due to optical spin-orbit interactions 1-10 . The scattered electromagnetic field due to a linearly polarized finite width beam impinging on an interface develops a non-trivial spin texture arising from the shift of photons with contrary helicity to opposite edges of the beam cross section, a phenomenon known as the spin Hall effect of light (SHEL) 4,7-9 . The SHEL is ubiquitous to any interface and represents a remarkable failure of geometric optics at the nanoscale. Recent experimental demonstrations have shown that the SHEL is uniquely suited for applications in precision metrology, including nanoprobing 11 , thin films characterization 12,13 , mapping of absorption mechanisms in bulk semiconductors 14,15 , and multilayer graphene identification in the absence of interlayer coupling 16 . More recently, it has been proposed that the SHEL can be used to probe the quantum Hall effect in monolayer graphene 17,18 , topological phase transitions in the expanded graphene family 19 , and hyperbolic behavior in anisotropic 2D atomic crystals 20 .In recent years, another class of 2D materials has drawn a lot attention, namely van der Waals structures assembled together layer-by-layer with controllable sequence and orientation 21 . These structures exhibit unusual physical properties that cannot be found in either monolayers or in bulk. Twisted Bilayer Graphene (TBG) is one important example of these multilayer materials, where the twist produces a Moiré pattern and induces a static periodic potential from the coupling bet...