A new mechanism of the magnetoelectric effect based on the spin supercurrent is theoretically presented in terms of a microscopic electronic model for noncollinear magnets. The electric polarization ${\overrightarrow{P}}_{ij}$ produced between the two magnetic moments ${\overrightarrow{S}}_i$ and ${\overrightarrow{S}}_j$ is given by $\overrightarrow{P}\propto {\overrightarrow{e}}_{ij}\times ({\overrightarrow{S}}_i\times {\overrightarrow{S}}_j)$ with ${\overrightarrow{e}}_{ij}$ being the unit vector connecting the sites $i$ and $j$. Applications to the spiral spin structure and the gauge theoretical interpretation are discussed.

We report the theoretical discovery of a class of 2D tight-binding models containing nearly flatbands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Because of the similarity with 2D continuum Landau levels, these topologically nontrivial nearly flatbands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flatband aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

Observing the Magnon Hall Effect: The anomalous thermal Hall effect occurs when transverse heat transport is generated in the absence of an external magnetic field. The transport may be mediated by free carriers, phonons, or spin waves (magnons). Onose et al. (p. 297 ) observed this effect in an insulating ferromagnet and were able to rule out free carriers and phonons as the mediators of the thermal transport. Instead, the observations are consistent with a theory ascribing its origin to magnon propagation. This thermal magnon Hall effect is caused by the spin-orbit interaction, which acts in a fashion similar to the magnetic field in the conventional Hall effect. Its observation in an insulator may enable the elimination of losses in spintronic applications.

We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order. The other type is allowed in a spin liquid which is a novel quantum state since there is no order even at zero temperature. For this case, the deconfined spinons contribute to the thermal Hall response due to Lorentz force. These results offer a clear experimental method to prove the existence of the deconfined spinons via a thermal transport phenomenon.

We consider ($2+1$)-dimensional topological quantum states which possess edge states described by a chiral ($1+1$)-dimensional conformal field theory, such as, e.g., a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state conformal field theory which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system and by viewing the cutting process as a sudden “quantum quench” into a conformal field theory, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.

We study theoretically the electronic states in a $5d$ transition metal oxide ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, in which both the spin-orbit interaction and the electron correlation play crucial roles. A tight-binding model analysis together with the first-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Because of the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.