Honeycomb lattice spin-orbit Mott insulators

H. L. Nourse, Ross H. McKenzie, Benjamin James Powell

We study the interplay of strong electron correlations and intratriangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-1 Mott insulator, a metal, and a spin-0 Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intratriangle multiorbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenough-Kanamori rules, may occur in coordination polymers from kinetic exchange via the ligands. We characterize the magnetism in the regime where spin triplets dominate. For small $U$ a spin-1 Slater insulator occurs with antiferromagnetic order between triangles. Magnetism in the spin-1 Mott insulator is described by a spin-1 Heisenberg model on a honeycomb lattice, whose ground state is N\'eel ordered.

H. Takagi

Zheng Zhu, D. N. Sheng, Liang Fu

Inspired by the recent discovery of correlated insulating states in twisted bilayer graphene, we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group simulation, we identify a metal-insulator transition around U_{c}/t=2.5-3. In the vicinity of U_{c}, we find strong spin-orbital density wave fluctuations at commensurate wave vectors, accompanied by weaker incommensurate charge density wave fluctuations. The spin-orbital density wave fluctuations are enhanced with increasing system sizes, suggesting the possible emergence of long-range order in the two-dimensional limit. At larger U, our calculations indicate a possible nonmagnetic Mott insulator phase without spin or orbital polarization. Our findings offer new insight into correlated electron phenomena in twisted bilayer graphene and other multiorbital honeycomb materials.

Shenghan Jiang, Hyun-Yong Lee, Panjin Kim +2 more

W. M. H. Natori, Rajah P. Nutakki, Rodrigo G. Pereira +1 more

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the ${e}_{g}$ Mott insulator ${\mathrm{Ba}}_{3}{\mathrm{CuSb}}_{2}{\mathrm{O}}_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.

Dorota Gotfryd