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Register a new userHigh-order nonlinear optical response of a twisted bilayer graphene
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Authors
Tatsuhiko N. Ikeda
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Focusing on the twist angle for the minimal commensurate structure, we perform nonperturbative calculations of electron dynamics in the twisted bilayer graphene (TBG) under intense laser fields. We show that the TBG exhibits enriched high-harmonic generation that cannot occur in monolayer or conventional bilayers. We elucidate the mechanism of these nonlinear responses by analyzing dynamical symmetries, momentum-resolved dynamics, and roles of interlayer coupling. Our results imply nonlinear optotwistronics, or controlling optical properties of layered materials by artificial twists.
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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.
Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of $pm 1$. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.
Flat electronic bands, characteristic of magic-angle twisted bilayer graphene (TBG), host a wealth of correlated phenomena. Early theoretical considerations suggested that, at the magic angle, the Dirac velocity vanishes and the entire width of the moire bands becomes extremely narrow. Yet, this scenario contradicts experimental studies that reveal a finite Dirac velocity as well as bandwidths significantly larger than predicted. Here we use spatially resolved spectroscopy in finite and zero magnetic fields to examine the electronic structure of moire bands and their intricate connection to correlated phases. By following the relative shifts of Landau levels in finite fields, we detect filling-dependent band flattening, that unexpectedly starts already at ~1.3 degrees, well above the magic angle and hence nominally in the weakly correlated regime. We further show that, as the twist angle is reduced, the moire bands become maximally flat at progressively lower doping levels. Surprisingly, when the twist angles reach values for which the maximal flattening occurs at approximate filling of $-2$, $+1$,$+2$,$+3$ electrons per moire unit cell, the corresponding zero-field correlated phases start to emerge. Our observations are corroborated by calculations that incorporate an interplay between the Coulomb charging energy and exchange interactions; together these effects produce band flattening and hence a significant density-of-states enhancement that facilitates the observed symmetry-breaking cascade transitions. Besides emerging phases pinned to integer fillings, we also experimentally identify a series of pronounced correlation-driven band deformations and soft gaps in a wider doping range around $pm 2$ filling where superconductivity is expected. Our results highlight the role of interaction-driven band-flattening in forming robust correlated phases in TBG.
We derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4)$times$U(4) symmetry, and we find that the exact ground states at integer filling $-4le ule 4$ relative to charge neutrality are Chern insulators of Chern numbers $ u_C=4-| u|,2-| u|,cdots,| u|-4$, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $ u=0,pm2$ has exact ground states of Chern number $0$, while $ u=pm1,pm3$ has perturbative ground states of Chern number $ u_C=pm1$, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ u_C=0$ ($0<| u_C|<4-| u|$) at integer fillings $ u$ are fully (partially) intervalley coherent, while the insulator states with Chern number $| u_C|=4-| u|$ are valley polarized. However, for $0<| u_C|le4-| u|$, the fully intervalley coherent states are highly competitive (0.005meV/electron higher). At nonzero magnetic field $|B|>0$, a first-order phase transition for $ u=pm1,pm2$ from Chern number $ u_C=text{sgn}( u B)(2-| u|)$ to $ u_C=text{sgn}( u B)(4-| u|)$ is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.
Flat band moire superlattices have recently emerged as unique platforms for investigating the interplay between strong electronic correlations, nontrivial band topology, and multiple isospin flavor symmetries. Twisted monolayer-bilayer graphene (tMBG) is an especially rich system owing to its low crystal symmetry and the tunability of its bandwidth and topology with an external electric field. Here, we find that orbital magnetism is abundant within the correlated phase diagram of tMBG, giving rise to the anomalous Hall effect (AHE) in correlated metallic states nearby most odd integer fillings of the flat conduction band, as well as correlated Chern insulator states stabilized in an external magnetic field. The behavior of the states at zero field appears to be inconsistent with simple spin and valley polarization for the specific range of twist angles we investigate, and instead may plausibly result from an intervalley coherent (IVC) state with an order parameter that breaks time reversal symmetry. The application of a magnetic field further tunes the competition between correlated states, in some cases driving first-order topological phase transitions. Our results underscore the rich interplay between closely competing correlated ground states in tMBG, with possible implications for probing exotic IVC ordering.
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