Superexchange Mechanism in Coupled Triangulenes Forming Spin-1 Chains.

We show that the origin of the antiferromagnetic coupling in spin-1 triangulene chains, which were recently synthesized and measured by Mishra et al. ( Nature 2021, 598, 287-292), originates from a superexchange mechanism. This process, mediated by intertriangulene states, opens the possibility to control parameters in the effective bilinear-biquadratic spin model. We start from the derivation of an effective tight-binding model for triangulene chains using a combination of tight-binding and Hartree-Fock methods fitted to hybrid density functional theory results. Next, correlation effects are investigated within the configuration interaction method. Our low-energy many-body spectrum for NTr = 2 and NTr = 4 triangulene chains agree well with the bilinear-biquadratic spin-1 chain antiferromagnetic model when indirect coupling processes and superexchange coupling between triangulene spins are taken into account.

Nonlocal Interactions in Moiré Hubbard Systems.

Moiré materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron density and interaction strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moiré materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, nonlocal interaction terms like interaction-assisted hopping and intersite exchange are more relevant. We theoretically demonstrate the possibility of tuning the strength of these coupling constants to favor unusual states of matter, including spin liquids, insulating ferromagnets, and superconductors.

Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene.

We report on finite-size exact-diagonalization calculations in a Hilbert space defined by the continuum-model flat moiré bands of magic angle twisted bilayer graphene. For moiré band filling 3>|ν|>2, where superconductivity is strongest, we obtain evidence that the ground state is a spin ferromagnet. Near |ν|=3, we find Chern insulator ground states that have spontaneous spin, valley, and sublattice polarization, and demonstrate that the anisotropy energy in this order-parameter space is strongly band-filling-factor dependent. We emphasize that inclusion of the remote band self-energy is necessary for a reliable description of magic angle twisted bilayer graphene flat band correlations.

Entanglement entropy and entanglement spectrum of Bi1-x Sb x (1 1 1) bilayers.

We study topological properties of Bi1-x Sb x bilayers in the (1 1 1) plane using entanglement measures. Electronic structures are investigated within multi-orbital tight-binding model and structural stability is confirmed through first-principles calculations. The topologically non-trivial nature of the bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum. We consider topological phase transitions driven by a composition change x, an applied external electric field in Bi bilayers and strain in Sb bilayers. Composition- and strain-induced phase transitions reveal a finite discontinuity in the entanglement entropy. This quantity remains a continuous function of the electric field strength, but shows a finite discontinuity in the first derivative. We relate the difference in behavior of the entanglement entropy to the breaking of inversion symmetry in the last case.

Stability of topological properties of bismuth (1 1 1) bilayer.

We investigate the electronic and transport properties of the bismuth (1 1 1) bilayer in the context of the stability of its topological properties against different perturbations. The effects of spin-orbit coupling variations, geometry relaxation and interaction with a substrate are considered. The transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within the multi-orbital tight-binding model and density functional theory methods. A band inversion process in the bismuth (1 1 1) infinite bilayer and an evolution of the edge state dispersion in ribbons as a function of spin-orbit coupling strength are analyzed. A significant change in the orbital composition of the conduction and valence bands is observed during a topological phase transition. The topological edge states are shown to be weakly affected by the effect of ribbon geometry relaxation. The interaction with a substrate is considered for narrow ribbons on top of another bismuth (1 1 1) bilayer. This corresponds to a weakly interacting case and the effect is similar to an external perpendicular electric field. Robust quantized conductance is observed when the Fermi energy lies within the energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, scattering is possible between the channels lying close in the k-space. When the energy of the edge states overlaps the valence states, no topological protection is observed.