We report the fabrication of (111)-oriented superlattice structures with alternating 2m-layers (m = 1, 2, and 3) of Ca0.5Sr0.5IrO3 perovskite and two layers of SrTiO3 perovskite on SrTiO3(111) substrates. In the case of m = 1 bilayer films, the Ir sub-lattice is a buckled honeycomb, where a topological state may be anticipated. The successful growth of superlattice structures on an atomic level along the [111] direction was clearly demonstrated by superlattice reflections in x-ray diffraction patterns and by atomically-resolved transmission electron microscope images. The ground states of the superlattice films were found to be magnetic insulators, which may suggest the importance of electron correlations in Ir perovskites in addition to the much discussed topological effects.
Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructi…
Artificial lattices have served as a platform to study the physics of unconventional superconductivity. We study semiconductor artificial graphene -- a honeycomb superlattice imposed on a semiconductor heterostructure -- which hosts the Dirac physics of graphene but with a tunable periodic potential strength and lattice spacing, allowing control of the strength of the electron-electron interactions. We demonstrate a new mechanism for superconductivity due to repulsive interactions which requires a strong lattice potential and a minimum doping away from the Dirac points. The mechanism relies on…
We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time our results directly apply to Kitaev's honeycomb model in a vortex superlattice.
We propose a two-orbital Hubbard model on an emergent honeycomb lattice to describe the low-energy physics of twisted bilayer graphene. Our model provides a theoretical basis for studying metal-insulator transition, Landau level degeneracy lifting and unconventional superconductivity that are recently observed.
Topological spin textures, like skyrmions, have significant potential for spintronics applications. The main purpose of this work is to study further the topological spin textures on the discrete lattice with magnetic fields. In this work, we study a classical rotated Heisenberg model with Dzyaloshinskii-Moriya interaction, bond-dependent anisotropy and easy-axis anisotropy on the honeycomb lattice via Monte Carlo simulations. We mainly focus on phase diagrams with magnetic fields, especially on the non-trivial phases only existing with fields. The results demonstrate the emergence of field-in…
We provide a comprehensive microscopic understanding of the nucleation of topological quantum liquids, a general mechanism where interactions between non-Abelian anyons cause a transition to another topological phase, which we study in the context of Kitaev's honeycomb lattice model. For non-Abelian vortex excitations arranged on superlattices, we observe the nucleation of several distinct Abelian topological phases whose character is found to depend on microscopic parameters such as the superlattice spacing or the spin exchange couplings. By reformulating the interacting vortex superlattice i…
We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped Z2 quantum spin liquid phase emerges at a finite Jc. We show that this phase survives in the well-controlled large-J limit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite-q inter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively `untwisting' the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev m…
Twisted moiré superlattices (TMSs) are fascinating materials with exotic physical properties. Despite tremendous studies on electronic, photonic and phononic TMSs, it has never been witnessed that TMSs can exhibit higher-order band topology. Here, we report on the experimental observation of higher-order topological states in acoustic TMSs. By introducing moiré twisting in bilayer honeycomb lattices of coupled acoustic resonators, we find a regime with designed interlayer couplings where a sizable band gap with higher-order topology emerges. This higher-order topological phase host unique topo…
\textit{Ab initio} calculations have been performed on hexagonal layers of M$_2$O$_3$ (M being several transition metals of the $5d$ series) sandwiched by a band insulator such as Al$_2$O$_3$ that provides the honeycomb lattice where the $5d$ electrons reside. This corundum-structure-based superlattice is the most obvious way to design a honeycomb lattice with transition metal cations avoiding the use of largely polar surfaces. We obtain that this system supports the presence of Dirac cones at the Fermi level that open up with the introduction of spin-orbit coupling at various fillings of the …
Moire superlattices of transition metal dichalcogenide (TMD) bilayers have been shown to host correlated electronic states, which arises from the interplay of emergent moire potential and long-range Coulomb interactions. Here we theoretically investigate structural relaxation and single-particle electronic properties in moire superlattices of transition metal dichalcogenide homobilayer and study the ground state charge orders in the effective honeycomb lattice of MX and XM region. From the large-scale density functional theory calculation and continuum model with layer degrees of freedom, we f…
We investigate the topological properties of Floquet-engineered twisted bilayer graphene above the magic angle driven by circularly polarized laser pulses. Employing a full Moiré-unit-cell tight-binding Hamiltonian based on first-principles electronic structure we show that the band topology in the bilayer, at twisting angles above 1.05$^\circ$, essentially corresponds to the one of single-layer graphene. However, the ability to open topologically trivial gaps in this system by a bias voltage between the layers enables the full topological phase diagram to be explored, which is not possible in…
We theoretically investigate the electronic band structures and magnetic properties of ilmenites with edge-sharing IrO$_6$ honeycomb layers, $A$IrO$_3$ with $A=$ Mg, Zn, and Mn, in comparison with a collinear antiferromagnet MnTiO$_3$. The compounds with $A=$ Mg and Zn were recently reported in Y.~Haraguchi {\it et al.}, Phys. Rev. Materials {\bf 2}, 054411 (2018), while MnIrO$_3$ has not been synthesized yet but the honeycomb stacking structure was elaborated in a superlattice with MnTiO$_3$ in K.~Miura {\it et al.}, Commun. Mater. {\bf 1}, 55 (2020). We find that, in contrast to MnTiO$_3$, w…
