Competing phases of interacting electrons on triangular lattices in moiré heterostructures

Abstract

We study the quantum many-body instabilities of interacting electrons with SU(2)×SU(2) symmetry in spin and orbital degrees of freedom on the triangular lattice near van-Hove filling. Our work is motivated by effective models for the flat bands in hexagonal moiré heterostructures like twisted bilayer boron nitride and trilayer graphene-boron nitride systems. We consider an extended Hubbard model including onsite Hubbard and Hund's couplings, as well as nearest-neighbor exchange interactions and analyze the different ordering tendencies with the help of an unbiased functional renormalization group approach. We find three classes of instabilities controlled by the filling and bare interactions. For a nested Fermi surface at van-Hove filling, Hund-like couplings induce a weak instability towards spin or orbital density wave phases. An SU(4) exchange interaction moves the system towards a Chern insulator, which is robust with respect to perturbations from Hundlike interactions or deviations from perfect nesting. Further, in an extended range of fillings and interactions, we find topological d ± id and (spin-singlet)-(orbital-singlet) f -wave superconductivity.arXiv:1902.05350v1 [cond-mat.str-el]

SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators

“…We close this paper with remarks about two solid-state platforms that would be described by similar KK models: the trilayer graphene/hexagonal boron nitrite heterostructures (TLG/hBN) [27][28][29][30] and the j = 3/2 compound α-ZrCl 3 [19]. KK models for TLG/hBN also display twofold orbital degeneracy, but these Wannier orbitals are located on a triangular lattice, which implies that our results are not extendable to this system.…”

Quantum Geometry and Flat Band Bose-Einstein Condensation

“…Indeed, previous studies have shown that the superfluid density of flat band systems is determined by the Chern number, quantum metric, or Berry curvature [17][18][19], despite the fact that effective mass of the electrons in a flat band is infinite. Recently, it has been proposed [20][21][22][23] that the observed superconductivity in twisted bilayer graphene [24,25] stems from quantum geometric properties of quasiflat Bloch bands.…”

Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in kagome metals $\text{AV}_3\text{Sb}_5$

“…Whether these topological states can arise as the leading instability at the Van Hove doping becomes an interesting topic to explore. It has been shown that the imaginary charge density wave is degenerate with the real spin density wave with spin flavors N f = 2, and is further dominant universally at larger number of flavors N f ≥ 4 [28,30]. Meanwhile, the staggered currents have also been proposed in a π-flux triangular lattice [11], as well as in the doped chiral spin liquid [31].…”