Interplay of U with large SOC fulfills the requirements of proposed Chern Mott insulators with bandgaps an order of magnitude larger than those studied so far.Īn efficient design strategy must seek to identify promising candidates. Some of these energy scales have been included in model studies, 9 but the coupling to lattice that we find to be a determining factor is too intricate for model Hamiltonian studies. This list includes more than ten parameters, and the treatment of them from a model Hamiltonian viewpoint, even within mean field, is formidable. Altogether, these couple to the lattice to provide two more scales, the Jahn-Teller ( λ JT) and breathing ( λ br) distortion strengths. 2L XO, on the other hand, presents a multi-orbital system with a number of additional degrees of freedom: intraatomic Coulomb repulsion U and Hund’s rule spin interaction J H, cubic crystal field splitting Δ cf, trigonal crystal field splitting δ cf, spin-orbit coupling (SOC) strength ξ, orbital-dependent interatomic hopping amplitudes, and band filling n d. Graphene has a hopping amplitude, or equivalently a velocity, that sets the energy scale, and a two-valley degree of freedom. The degree of generalization from graphene is huge. The advent of (111)-oriented growth of oxides 17, 18, 19, 20, 21, 22, 23, 24, 25 provides a new platform for design of new materials, and especially Chern insulators. A number of model 6, 7, 8, 9 and material-specific studies 10, 11, 12, 13, 14, 15, 16 have probed the possibilities that such systems may offer. 4, 5 The origin of the buckled honeycomb lattice is depicted in Fig.

The recognition that a perovskite (111) bilayer of La XO 3 encased in LaAlO 3 (we use the notation 2L XO for an X bilayer, X=transition metal ) provides a honeycomb lattice that led to a call for engineering ( i.e., design) of a Chern insulator in such systems. Yet the single band, uncorrelated case of graphene is only the simplest level of what can be realized on honeycomb lattices. The honeycomb lattice, 1, 2 particularly in conjunction with its Dirac points and two-valley nature in graphene, 3 has provided the basic platform for a great number of explorations into new phases of matter and new phenomena.

Recent growth of insulating, magnetic phases in closely related materials with this orientation supports the likelihood that synthesis and exploitation will follow. Symmetry lowering in the course of structural relaxation hampers obtaining quantum anomalous Hall character, as pointed out previously there is only mild structural symmetry breaking of the bilayer in these robust Chern phases. We find, in this class, that a trade-off between larger spin-orbit coupling and strong interactions leads to a larger gap, whereas the stronger spin-orbit coupling correlates with the larger magnitude of the Hall conductivity.

Building on accumulated knowledge of the behavior of the 3 d series, we tune spin-orbit and interaction strength together with strain to design two Chern insulator systems with bandgaps up to 130 meV and Chern numbers C = −1 and C = 2. Honeycomb lattice systems such as we discuss here, occupied by heavy transition-metal ions, have been proposed as Chern insulators, but finding a concrete example has been challenging due to an assortment of broken symmetry phases that thwart the topological character. Chern insulators are attracting interest both as a novel electronic phase and for their novel and potentially useful boundary charge and spin currents. 49, 405–408 (1982)), provide the quantum Hall anomalous effect without an applied magnetic field. Quantum anomalous Hall insulators, which display robust boundary charge and spin currents categorized in terms of a bulk topological invariant known as the Chern number (Thouless et al Phys.

Wide gapped