Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene

Abstract

Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions ν of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of ν and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality, ν = 0, with additional spin-polarization being present at quarter (ν = −2) or three quarter (ν = +2) fillings of the quasi-flat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene. CONTENTS 1. Continuum model and low-energy degrees of freedom 2. Single-particle symmetries 3. Interaction and form factors B. Exact statements about the interacting groundstates 1. Turning on the coupling between the subsystems 2. Behavior of Goldstone modes C. Hartree-Fock functional 1. General form

Interaction-induced velocity renormalization in magic angle twisted trilayer graphene

“…We predict that this velocity renormalization leads to an increase of the slow and decrease of the fast Dirac velocity in TTG. We remark that a U(1) generalization of our Gross-Neveu theory would correspond to intervalley coherent order in TTG 34 , which is expected to display qualitatively similar behavior to the velocity renormalization and critical exponents we have found based on studies of the XY-Gross-Neveu model 35,[56][57][58][59][60][61] . The generalization of our theory to experimentally relevant 17,18 twisted pentalayar graphene and other van-der-Waals materials with more than two Dirac velocities is left for future work.…”

“…26 Theoretically, different candidate states for a gap opening at charge neutrality in TBG have similar energies. [27][28][29][30][31][32][33] Among them, (sublattice-polarized) quantum valley Hall or intervalley coherent order have also been discussed to gap out the slow bands in TTG, based on extensions of the effective, exactly soluble models from TBG to TTG 34 .…”

Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene

“…We should stress regarding the appropriateness of the approximation in Eq. (29). When the band structure resulting from this approximation was compared to band structures resulting from a full extended space treatment of the time dependent problem such as in [60] it was found that even at driving strengths as high as η = AaAA = 4 the approximation yielded results that were almost indistinguishable from the exact extended space treatment.…”

“…In fact, it has been discovered that at certain, so-called magic angles, flat energy bands occur which then give rise to a plethora of highly correlated phases. An exciting example is a superconducting phase that occurs at the first magic twist angle [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. This superconducting state was first discovered in a land-mark paper in Nature Physics [20].…”

Unconventional superconductivity due to interband polarization

“…Strong-coupling superconductivity can arise from repulsive interactions, as a result of enhanced fluctuations near insulating ordered phases driven by these interactions. This picture has been extensively discussed in connection to the superconducting cuprates [18], pnictides [19][20][21], and also twisted bilayer graphene and other graphitic systems [22][23][24][25][26][27][28][29][30][31][32]. Superconductivity can also arise from repulsive interactions through virtual transition of electron pairs from the Fermi surface to distant or incipient bands [33,34].…”