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We revisit the effect of local interactions on the quadratic band touching (QBT) of Bernal stacked bilayer graphene models using renormalization group (RG) arguments and quantum Monte Carlo simulations of the Hubbard model. We present an RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased quantum Monte Carlo simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite $U/t$, despite the $U=0$ hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with a dynamical critical exponent $z=1$ as expected for 2+1 d Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.
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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.
Graphene nanoribbons are widely regarded as promising building blocks for next-generation carbon-based devices. A critical issue to their prospective applications is whether and to what degree their electronic structure can be externally controlled. Here, we combine simple model Hamiltonians with extensive first-principles calculations to investigate the response of armchair graphene nanoribbons to transverse electric fields. Such fields can be achieved either upon laterally gating the nanoribbon or incorporating ambipolar chemical co-dopants along the edges. We reveal that the field induces a semiconductor-to-semimetal transition, with the semimetallic phase featuring zero-energy Dirac fermions that propagate along the armchair edges. The transition occurs at critical fields that scale inversely with the width of the nanoribbons. These findings are universal to group-IV honeycomb lattices, including silicene and germanene nanoribbons, irrespective of the type of edge termination. Overall, our results create new opportunities to electrically engineer Dirac fermions in otherwise semiconducting graphene-like nanoribbons.
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 ($n=pm2$).
Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is found that at the transition a repulsive interaction is marginally relevant and an attractive interaction is marginally irrelevant. We corroborate the results obtained from the RG calculation by studying a microscopic model whose ground state and Greens functions can be obtained exactly. We find that away from the transition, the system displays an instability towards forming and excitonic condensate.
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