Abstract
Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom -- charge, spin, and valley -- gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted hopping interaction that emerges due to the non-trivial topological properties of TBG. Such a non-local interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interaction. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.
Highlights
Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the Twisted bilayer graphene (TBG) experiments
The recent discovery of correlated insulating and superconducting phases in twisted bilayer graphene (TBG) [1,2,3] and other moiresystems [4,5,6,7] sparked a flurry of activity to
This important aspect of the TBG was not taken into consideration in the previous quantum Monte Carlo (QMC) simulations. We make this important step forward by studying the impact of the assisted-hopping interaction on the ground state of TBG at charge neutrality via signproblem-free QMC simulations. We find that such a term qualitatively changes the phase diagram, as compared to the case where only the cluster Hubbard interaction is included
Summary
The recent discovery of correlated insulating and superconducting phases in twisted bilayer graphene (TBG) [1,2,3] and other moiresystems [4,5,6,7] sparked a flurry of activity to. As the interaction strength increases, a different type of insulating phase arises, displaying intervalley coherence (IVC) order This on-site IVC order breaks the spin-valley SU(4) symmetry of the interacting part of the model, resembling recently proposed ferromagnetic-like SU(4) states proposed to emerge in TBG at charge neutrality and other integer fillings [37,48]. In the same Appendix, we extend the HF calculations to include longer-range hopping terms in H0 and find that the results are similar This result supports our aforementioned expectation that the nontrivial structure of the projected interactions, arising from the fragile topology of TBG, dominates the ground-state properties of the system, at least at charge neutrality. We note that in the limit of vanishing bandwidth, our analyses in Appendixes A and D reveal that in this verystrong-coupling limit, the ground state of the system is in the IVC phase for the range of α considered here
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