Exchange couplings and edge states in two-dimensional topological insulators.

We consider two-dimensional honeycomb-lattice topological insulators of electrons which are exposed to exchange couplings at the edges, paying particular attention to the energy dispersions of edge states. The energy band structure of edge states is found to depend strongly on the direction of exchange couplings. Energy band splitting occurs for the exchange couplings perpendicular to the plane of topological insulators. In contrast, the parallel exchange couplings turn out to generate a finite energy gap in the edge-state bands for zigzag edges while armchair nanoribbons does not show such energy gaps. We also discuss the dependence of energy band structures of edge states on the magnetic structure of exchange couplings as well as the disorder effects on the edge-state density of states.

Correlation effects on 3D topological phases: from bulk to boundary.

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

Spin wave measurements over the full Brillouin zone of multiferroic BiFeO3.

Using the inelastic neutron scattering technique, we measured the spin wave dispersion over the entire Brillouin zone of room temperature multiferroic BiFeO(3) single crystals with magnetic excitations extending to as high as 72.5 meV. The full spin waves can be explained by a simple Heisenberg Hamiltonian with a nearest-neighbor exchange interaction (J=4.38 meV), a next-nearest-neighbor exchange interaction (J'=0.15 meV), and a Dzyaloshinskii-Moriya-like term (D=0.107 meV). This simple Hamiltonian determined, for the first time, for BiFeO(3) provides a fundamental ingredient for understanding the novel magnetic properties of BiFeO(3).

Observation of a multiferroic critical end point.

The study of abrupt increases in magnetization with magnetic field known as metamagnetic transitions has opened a rich vein of new physics in itinerant electron systems, including the discovery of quantum critical end points with a marked propensity to develop new kinds of order. However, the electric analogue of the metamagnetic critical end point, a "metaelectric" critical end point, has been rarely studied. Multiferroic materials wherein magnetism and ferroelectricity are cross-coupled are ideal candidates for the exploration of this novel possibility using magnetic-field (H) as a tuning parameter. Herein, we report the discovery of a magnetic-field-induced metaelectric transition in multiferroic BiMn(2)O(5), in which the electric polarization (P) switches polarity along with a concomitant Mn spin-flop transition at a critical magnetic field H(c). The simultaneous metaelectric and spin-flop transitions become sharper upon cooling but remain a continuous cross-over even down to 0.5 K. Near the P = 0 line realized at mu(0)H(c) approximately 18 T below 20 K, the dielectric constant (epsilon) increases significantly over wide field and temperature (T) ranges. Furthermore, a characteristic power-law behavior is found in the P(H) and epsilon(H) curves at T = 0.66 K. These findings indicate that a magnetic-field-induced metaelectric critical end point is realized in BiMn(2)O(5) near zero temperature.

Suppression of magnetic ordering in XXZ-type antiferromagnetic monolayer NiPS3.

How a certain ground state of complex physical systems emerges, especially in two-dimensional materials, is a fundamental question in condensed-matter physics. A particularly interesting case is systems belonging to the class of XY Hamiltonian where the magnetic order parameter of conventional nature is unstable in two-dimensional materials leading to a Berezinskii-Kosterlitz-Thouless transition. Here, we report how the XXZ-type antiferromagnetic order of a magnetic van der Waals material, NiPS3, behaves upon reducing the thickness and ultimately becomes unstable in the monolayer limit. Our experimental data are consistent with the findings based on renormalization-group theory that at low temperatures a two-dimensional XXZ system behaves like a two-dimensional XY one, which cannot have a long-range order at finite temperatures. This work provides the experimental examination of the XY magnetism in the atomically thin limit and opens opportunities of exploiting these fundamental theorems of magnetism using magnetic van der Waals materials.

Spontaneous phase oscillation induced by inertia and time delay.

We consider a system of coupled oscillators with finite inertia and time-delayed interaction, and investigate the interplay between inertia and delay both analytically and numerically. The phase velocity of the system is examined; revealed in numerical simulations is the emergence of spontaneous phase oscillation without external driving, which turns out to be in good agreement with analytical results derived in the strong-coupling limit. Such self-oscillation is found to suppress synchronization, and its frequency is observed to decrease with inertia and delay. We obtain the phase diagram, which displays oscillatory and stationary phases in the appropriate regions of the parameters.

Effective projection theory in a correlated electron system.

We propose an efficient method for nonperturbative calculation of Green's function in a correlated electron system. The key idea of the method is to project out irrelevant operators having zero norm in the ground state, which we refer to as effective projection theory. We apply the method to a mesoscopic Anderson model and show that for a given wavefunction ansatz, equations of motion can be closed only by relevant operators, allowing easy calculation of the zero-temperature Green's function. It turns out that the resulting Green's functions reproduce exact limits of both weak and strong interactions. The accuracy is also verified for small systems by comparison with exact diagonalization results, revealing that effective projection theory captures the essential correlated features in the entire regime of interactions.

Properties of the one-dimensional Hubbard model: cellular dynamical mean-field description.

The one-dimensional half-filled Hubbard model is considered at zero temperature within the cellular dynamical mean-field theory (CDMFT). By the computation of the spectral gap and the energy density with various cluster and bath sizes we examine the accuracy of the CDMFT in a systematic way, which proves the accurate description of the one-dimensional systems by the CDMFT with small clusters. We also calculate the spectral weights in a full range of the momentum for various interaction strengths. The results do not only account for the spin-charge separation, but they also reproduce all the features of the Bethe ansatz dispersions, implying that the CDMFT provides an excellent description of the spectral properties of low-dimensional interacting systems.

Microscopic verification of topological electron-vortex binding in the lowest Landau-level crystal state.

When two-dimensional electrons are subjected to a very strong magnetic field, they are believed to form a triangular crystal. By a direct comparison with the exact wave function, we demonstrate that this crystal is not a simple Hartree-Fock crystal of electrons but an inherently quantum mechanical crystal characterized by a nonperturbative binding of quantized vortices to electrons. It is suggested that this has qualitative consequences for experiment.

Fractional statistics in the fractional quantum Hall effect.

A microscopic confirmation of the fractional statistics of the quasiparticles in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at nu=1/3 and nu=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.