Fermionic Monte Carlo Study of a Realistic Model of Twisted Bilayer Graphene

Abstract

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight-binding models, and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here, we present unbiased Monte Carlo simulations of realistic models of magic-angle TBG at charge neutrality. We establish the absence of a sign problem for this model in a momentum-space approach and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers intervalley coherent ground state in competition with a correlated semimetal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions that reveal a “pseudogap” regime, in which gap features are established at a higher temperature than the onset of order, and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic-angle graphene through exact simulations of over a hundred electrons across a wide temperature range.

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Plain Language Summary

Twisted bilayer graphene, where one sheet of graphene is laid atop another and rotated at a slight angle, exhibits both insulating and superconducting behavior. The origins of these phases, and how they relate to one another, are the subject of much experimental and theoretical work. However, there is much confusion regarding the essential ingredients needed to explain these remarkable phenomena. Current numerical methods have severe limitations and theoretical approaches to realistic models are necessarily approximate. An unbiased numerical approach that can tackle large enough system sizes as well as realistic interactions would be a boon to making progress. Here, we present the first realistic simulations of twisted bilayer graphene that captures all necessary ingredients.

Our approach is based on a momentum-space description, which enables it to accurately capture nontrivial electronic band topology and evade problems that plague real-space descriptions of the lattice. In this momentum-space model, we establish the absence of the “sign problem” that often discourages simulations of fermionic quantum systems. Therefore, we can perform numerically exact simulations of hundreds of electrons and access not only zero-temperature but also finite-temperature properties. We have gone beyond this breakthrough, applying the technique to access a great many physical quantities of interest, which provide surprises and much fodder for future research.

Our results pave the way toward uncovering the physics of “magic-angle” graphene through exact simulations of over 300 electrons across a wide temperature range.