Two-dimensional (2D) atomic crystals can radically change their properties in response to external influences such as substrate orientation or strain, resulting in essentially new materials in terms of the electronic structure 1-5 . A striking example is the creation of flat-bands in bilayer-graphene for certain "magic" twist-angles between the orientations of the two layers 6 . The quenched kineticenergy in these flat-bands promotes electron-electron interactions and facilitates the emergence of strongly-correlated phases such as superconductivity and correlated-insulators. However, the exquisite fine-tuning required for finding the magic-angle where flat-bands appear in twisted-bilayer graphene, poses challenges to fabrication and scalability. Here we present an alternative route to creating flat-bands that does not involve fine tuning. Using scanning tunneling microscopy and spectroscopy, together with numerical simulations, we demonstrate that graphene monolayers placed on an atomically-flat substrate can be forced to undergo a buckling-transition 7-9 , resulting in a periodically modulated pseudo-magnetic field 10-14 , which in turn creates a post-graphene material with flat electronic bands. Bringing the Fermi-level into these flat-bands by electrostatic doping, we observe a pseudogap-like depletion in the density-of-states (DOS), which signals the emergence of a correlated-state 15-17 . The described approach of 2D crystal buckling offers a strategy for creating other superlattice systems and, in particular, for exploring interaction phenomena characteristic of flat-bands.

When two-dimensional atomic crystals are brought into close proximity to form a van der Waals heterostructure, neighbouring crystals can start influencing each other's electronic properties. Of particular interest is the situation when the periodicity of the two crystals closely match and a moiré pattern forms, which results in specific electron scattering, reconstruction of electronic and excitonic spectra, crystal reconstruction, and many other effects. Thus, formation of moiré patterns is a viable tool of controlling the electronic properties of 2D materials. At the same time, the difference in the interatomic distances for the two crystals combined, determines the range in which the electronic spectrum is reconstructed, and thus is a barrier to the low energy regime. Here we present a way which allows spectrum reconstruction at all energies. By using graphene which is aligned simultaneously to two hexagonal boron nitride layers, one can make electrons scatter in the differential moiré pattern, which can have arbitrarily small wavevector and, thus results in spectrum reconstruction at arbitrarily low energies. We demonstrate that the strength of such a potential relies crucially on the atomic reconstruction of graphene within the differential moiré super-cell. Such structures offer further opportunity in tuning the electronic spectra of two-dimensional materials.Introduction: Van der Waals heterostructures allow combining different two-dimensional (2D) materials into functional stacks(1, 2), which has already produced a range of interesting electronic(3, 4) and optoelectronic(5-8) devices and resulted in observation of exciting physical phenomena. The large variety of the heterostructures is mainly due to the large selection of 2D materials. However, the assembly of van der Waals heterostructures allow one extra degree of freedom: apart from the selection of the sequence of the 2D crystalsthe individual crystals can be differently oriented with respect to each other. Previously such control over the rotational alignment between crystals resulted in the observation of the resonant tunnelling(9-11), renormalisation of exciton binding energy(12) insulating(13) and superconducting(4) states. 01129a). J.Y. and A.M. acknowledge the support of EPSRC Early Career Fellowship EP/N007131/1.

Valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudomagnetic field created by the deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. We show that valley filtering is most effective with bumps of a certain height and width. Despite the fact that the highest contribution to the polarized current comes from electrons from the lowest sub-band, contributions of other sub-bands are not negligible and can significantly enhance the output current.PACS numbers: 02.60. Cb, 72.80.Vp, Conduction and valence band of graphene 1 touch in six points referred to as Dirac points. However, only two of them, labeled as K and K', are inequivalent and are related by time-reversal symmetry. This new degree of freedom opens the possibility to use these two valleys to encode information. However, the applicability of "valleytronics" relies on the assumption that the valley-polarized current can be easily generated and controlled. So far, there have been a number of propositions for such a device relying on the usage of ferromagnetic stripes 2-4 , nano-constrictions 5 , line defects 6-8 , specific substrates 9,10 , etc.On the other hand, it was previosuly shown that graphene can sustain a large amount of strain. Due to its strong covalent sp 2 −bonds, graphene can stretch up to 25% of its original size without breaking 11 . Mechanical deformations can lead to the generation of pseudomagnetic fields (PMFs) that exceed 12 300 T. Triaxial 13,14 strain and strain generated by bending 15,16 graphene give rise to a quasi-homogeneous PMF. Moreover, imperfections of the substrate can lead to the formation of bubbles and balloons that generate inhomogeneous PMFs 12,17 . In the case of suspended devices a scanning tunnelling microscopy (STM) probe tip can be used to locally deform graphene membranes 18 . It was shown that the PMF generated in this manner produces regions with opposite sign of the pseudo-magnetic field 14,18,19 .The generated PMF has the opposite direction for electrons originating from different valleys. This property can be used in order to separate electrons from the two valleys and obtain a valley-polarized current 20,21 -a prerequisite for valleytronics. Recently, CarrilloBastos et al. showed that by using a Gaussian fold one is able to spatially separate electrons from opposite valleys 22 . Cavalcante et al. proposed a particular straining of a graphene nanoribbon to realize a valley polarized current 23 . These proposals have the disadvantage that the valley polarization is difficult to tune and that actual a) Electronic mail: slavisa.milovanovic@uantwerpen.be b) Electronic mail: francois.peeters@uantwerpen.be devices are difficult to realize. In this Letter we show that straining graphene locally into a Gaussian bump by e.g. an AFM (atomic-force microscopy) tip, it is possible to obtain highly tunable polarized valley currents in two realistic de...

A periodic spatial modulation, as created by a moiré pattern, has been extensively studied with the view to engineer and tune the properties of graphene. Graphene encapsulated by hexagonal boron nitride (hBN) when slightly misaligned with the top and bottom hBN layers experiences two interfering moiré patterns, resulting in a so-called super-moiré (SM). This leads to a lattice and electronic spectrum reconstruction. A geometrical construction of the non-relaxed SM patterns allows us to indicate qualitatively the induced changes in the electronic properties and to locate the SM features in the density of states and in the conductivity. To emphasize the effect of lattice relaxation, we report band gaps at all Dirac-like points in the hole doped part of the reconstructed spectrum, which are expected to be enhanced when including interaction effects. Our result is able to distinguish effects due to lattice relaxation and due to the interfering SM and provides a clear picture on the origin of recently experimentally observed effects in such trilayer heterostuctures. arXiv:1910.00345v1 [cond-mat.mes-hall]

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