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Register a new userElectron interactions in strain-induced zero-energy flat band in twisted bilayer graphene near the magic angle
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In the vicinity of the magic angle in twisted bilayer graphene (TBG), the two low-energy van Hove singularities (VHSs) become exceedingly narrow1-10 and many exotic correlated states, such as superconductivity, ferromagnetism, and topological phases, are observed11-16. Heterostrain, which is almost unavoidable in the TBG, can modify its single-particle band structure and lead to novel properties of the TBG that have never been considered so far. Here, we show that heterostrain in a TBG near the magic angle generates a new zero-energy flat band between the two VHSs. Doping the TBG to partially fill the zero-energy flat band, we observe a correlation-induced gap of about 10 meV that splits the flat band. By applying perpendicular magnetic fields, a large and linear response of the gap to magnetic fields is observed, attributing to the emergence of large orbital magnetic moments in the TBG when valley degeneracy of the flat band is lifted by electron-electron interactions. The orbital magnetic moment per moire supercell is measured as about 15 uB in the TBG.
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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.
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $thetasim1.05^circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also be applied only to the flat conduction or valence bands, if the substrate induces a single-particle gap at charge neutrality. Also in this case, the corresponding density matrix turns out to be irreducible, leading to ferromagnetism at half filling ($n=pm2$).
We present a systematic study of the low-energy collective modes for different insulating states at integer fillings in twisted bilayer graphene. In particular, we provide a simple counting rule for the total number of soft modes, and analyze their energies and symmetry quantum numbers in detail. To study the soft mode spectra, we employ time dependent Hartree-Fock whose results are reproduced analytically via an effective sigma model description. We find two different types of low-energy modes - (i) approximate Goldstone modes associated with breaking an enlarged U(4)$times$U(4) symmetry and, surprisingly, a set of (ii) nematic modes with non-zero angular momentum under three-fold rotation. The modes of type (i) include true gapless Goldstone modes associated with exact symmetries in addition to gapped pseudo-Goldstone modes associated with approximate symmetries. While the modes of type (ii) are always gapped, we show that their gap decreases as the Berry curvature grows more concentrated. For realistic parameter values, the gapped soft modes of both types have comparable gaps of only a few meV, and lie completely inside the mean-field bandgap. The entire set of soft modes emerge as Goldstone modes of a different idealized model in which Berry flux is limited to a solenoid, which enjoys an enlarged U(8) symmetry. Furthermore, we discuss the number of Goldstone modes for each symmetry-broken state, distinguishing the linearly vs quadratically dispersing modes. Finally, we present a general symmetry analysis of the soft modes for all possible insulating Slater determinant states at integer fillings that preserve translation symmetry, independent of the energetic details. The resulting soft mode degeneracies and symmetry quantum numbers provide a fingerprint of the different insulting states enabling their experimental identification from a measurement of their soft modes.
Magic angle twisted bilayer graphene has emerged as a powerful platform for studying strongly correlated electron physics, owing to its almost dispersionless low-energy bands and the ability to tune the band filling by electrostatic gating. Techniques to control the twist angle between graphene layers have led to rapid experimental progress but improving sample quality is essential for separating the delicate correlated-electron physics from disorder effects. Owing to the 2D nature of the system and the relatively low carrier density, the samples are highly susceptible to small doping inhomogeneity which can drastically modify the local potential landscape. This potential disorder is distinct from the twist-angle variation which has been studied elsewhere. Here, by using low temperature scanning tunneling spectroscopy and planar tunneling junction measurements, we demonstrate that flat bands in twisted bilayer graphene can amplify small doping inhomogeneity that surprisingly leads to carrier confinement, which in graphene could previously only be realized in the presence of a strong magnetic field.
The electronic properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, in particular when the two layers are rotated relative to each other by a small angle. TBG has recently attracted a great deal of interest, sparked by the discovery of correlated insulating and superconducting states, for twist angle $theta$ close to a so-called magic angle $approx 1.1{deg}$. In this work, we unveil, via near-field optical microscopy, a collective plasmon mode in charge-neutral TBG near the magic angle, which is dramatically different from the ordinary single-layer graphene intraband plasmon. In selected regions of our samples, we find a gapped collective mode with linear dispersion, akin to the bulk magnetoplasmons of a two-dimensional (2D) electron gas. We interpret these as interband plasmons and associate those with the optical transitions between quasi-localized states originating from the moire superlattice. Surprisingly, we find a higher plasmon group velocity than expected, which implies an enhanced strength of the corresponding optical transition. This points to a weaker interlayer coupling in the AA regions. These intriguing optical properties offer new insights, complementary to other techniques, on the carrier dynamics in this novel quantum electron system.
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