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Register a new userUniversal classification of twisted, strained and sheared graphene moire superlattices
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Moire superlattices in graphene supported on various substrates have opened a new avenue to engineer graphenes electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting non-trivial nanopatterns for moire superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moire is presented to classify all reported structures.
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Twisted bilayers of van der Waals materials have recently attracted great attention due to their tunable strongly correlated phenomena. Here, we investigate the chirality-specific physics in 3D moire superlattices induced by Eshelby twist. Our direct DFT calculations reveal helical rotation leads to optical circular dichroism, and chirality-specific nonlinear Hall effect, even though there is no magnetization or magnetic field. Both these phenomena can be reversed by changing the structural chirality. This provides a way to constructing chirality-specific materials.
We present a systematic classification and analysis of possible pairing instabilities in graphene-based moire superlattices. Motivated by recent experiments on twisted double-bilayer graphene showing signs of triplet superconductivity, we analyze both singlet and triplet pairing separately, and describe how these two channels behave close to the limit where the system is invariant under separate spin rotations in the two valleys, realizing an SU(2)$_+$ $times$ SU(2)$_-$ symmetry. Further, we discuss the conditions under which singlet and triplet can mix via two nearly degenerate transitions, and how the different pairing states behave when an external magnetic field is applied. The consequences of the additional microscopic or emergent approximate symmetries relevant for superconductivity in twisted bilayer graphene and ABC trilayer graphene on hexagonal boron nitride are described in detail. We also analyze which of the pairing states can arise in mean-field theory and study the impact of corrections coming from ferromagnetic fluctuations. For instance, we show that, close to the parameters of mean-field theory, a nematic mixed singlet-triplet state emerges. Our study illustrates that graphene superlattices provide a rich platform for exotic superconducting states, and allow for the admixture of singlet and triplet pairing even in the absence of spin-orbit coupling.
Recently twisted bilayer graphene (t-BLG) emerges as a new strongly correlated physical platform near a magic twist angle, which hosts many exciting phenomena such as the Mott-like insulating phases, unconventional superconducting behavior and emergent ferromagnetism. Besides the apparent significance of band flatness, band topology may be another critical element in determining strongly correlated twistronics yet receives much less attention. Here we report compelling evidence for nontrivial noninteracting band topology of t-BLG moire Dirac bands through a systematic nonlocal transport study, in conjunction with an examination rooted in $K$-theory. The moire band topology of t-BLG manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. We further show that the nonlocal responses are robust to the interlayer electric field, twist angle, and edge termination, exhibiting a universal scaling law. While an unusual symmetry of t-BLG trivializes Berry curvature, we elucidate that two $Z_2$ invariants characterize the topology of the moire Dirac bands, validating the topological edge origin of the observed nonlocal responses. Our findings not only provide a new perspective for understanding the emerging strongly correlated phenomena in twisted van der Waals heterostructures, but also suggest a potential strategy to achieve topologically nontrivial metamaterials from topologically trivial quantum materials based on twist engineering.
A remarkable property of twisted bilayer graphene (TBG) with small twist angle is the presence of a well-defined and conserved low-energy valley degrees of freedom1, which can potentially bring about new types of valley-associated spontaneous-symmetry breaking phases. Electron-electron (e-e) interactions in the TBG near the magic angle 1.1 degree can lift the valley degeneracy, allowing for the realization of orbital magnetism and topological phases2-11. However, direct measurement of the orbital-based magnetism in the TBG is still lacking up to now. Here we report evidence for orbital magnetic moment generated by the moire-scale current loops in a TBG with a twist angle {theta} ~ 1.68 degree. The valley degeneracy of the 1.68 degree TBG is removed by e-e interactions when its low-energy van Hove singularity (VHS) is nearly half filled. A large and linear response of the valley splitting to magnetic fields is observed, attributing to coupling to the large orbital magnetic moment induced by chiral current loops circulating in the moire pattern. According to our experiment, the orbital magnetic moment is about 10.7 uB per moire supercell. Our result paves the way to explore magnetism that is purely orbital in slightly twisted graphene system.
Twisted moire superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moire twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topological edge and corner states, which can be understood via the Wannier centers of the acoustic Bloch bands below the band gap. We confirm experimentally the higher-order band topology by characterizing the edge and corner states using acoustic pump-probe measurements. With complementary theory and experiments, our study opens a pathway toward band topology in TMSs.
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