Recent progress in understanding the topological properties of condensed matter has led to the discovery of time-reversal-invariant topological insulators. A remarkable and useful property of these materials is that they support unidirectional spin-polarized propagation at their surfaces. Unfortunately topological insulators are rare among solid-state materials. Using suitably designed electromagnetic media (metamaterials) we theoretically demonstrate a photonic analogue of a topological insulator. We show that metacrystals-superlattices of metamaterials with judiciously designed properties-provide a platform for designing topologically non-trivial photonic states, similar to those that have been identified for condensed-matter topological insulators. The interfaces of the metacrystals support helical edge states that exhibit spin-polarized one-way propagation of photons, robust against disorder. Our results demonstrate the possibility of attaining one-way photon transport without application of external magnetic fields or breaking of time-reversal symmetry. Such spin-polarized one-way transport enables exotic spin-cloaked photon sources that do not obscure each other.

Mott physics is characterized by an interaction-driven metal-to-insulator transition in a partially filled band. In the resulting insulating state, antiferromagnetic orders of the local moments typically develop, but in rare situations no long-range magnetic order appears, even at zero temperature, rendering the system a quantum spin liquid. A fundamental and technologically critical question is whether one can tune the underlying energetic landscape to control both metal-to-insulator and Néel transitions, and even stabilize latent metastable phases, ideally on a platform suitable for applications. Here we demonstrate how to achieve this in ultrathin films of NdNiO 3 with various degrees of lattice mismatch, and report on the quantum critical behaviours not reported in the bulk by transport measurements and resonant X-ray spectroscopy/scattering. In particular, on the decay of the antiferromagnetic Mott insulating state into a non-Fermi liquid, we find evidence of a quantum metal-to-insulator transition that spans a non-magnetic insulating phase.

Motivated by recent experiments probing anomalous surface states of Dirac semimetals (DSMs) Na 3 Bi and Cd 3 As 2 , we raise the question posed in the title. We find that, in marked contrast to Weyl semimetals, the gapless surface states of DSMs are not topologically protected in general, except on time-reversal-invariant planes of surface Brillouin zone. We first demonstrate this finding in a minimal four-band model with a pair of Dirac nodes at k = (0,0, ± Q), where gapless states on the side surfaces are protected only near k z = 0. We then validate our conclusions about the absence of a topological invariant protecting double Fermi arcs in DSMs, using a K-theory analysis for space groups of Na 3 Bi and Cd 3 As 2 . Generically, the arcs deform into a Fermi pocket, similar to the surface states of a topological insulator, and this pocket can merge into the projection of bulk Dirac Fermi surfaces as the chemical potential is varied. We make sharp predictions for the doping dependence of the surface states of a DSM that can be tested by angle-resolved photoemission spectroscopy and quantum oscillation experiments. Of particular interest are 3D semimetals where the bulk electronic dispersion exhibits point nodes at the Fermi level and the low-energy physics are effectively described by a Weyl or Dirac Hamiltonian (9).A striking feature of 3D Weyl semimetals (WSMs), which necessarily break either time-reversal or inversion symmetry, is the existence (5) of topologically protected surface "Fermi arcs." Here the Fermi contour in the surface Brillouin zone breaks up into disconnected pieces, which connect the projection of two Weyl nodes with opposite chirality. The Fermi arcs have been recently observed in angle-resolved photoemission spectroscopy (ARPES) studies of noncentrosymmetric TaAs (10-15).Here we focus on another outstanding example, the Dirac semimetal (DSM), which is the 3D analog of graphene. In the presence of both time-reversal and inversion symmetries, the electronic excitations near each node are described by a four-component Dirac fermion, and a dispersion that is linear in all directions in k space (16)(17)(18). ARPES has clearly observed linearly dispersing bands near Dirac nodes in two DSM materials, Na 3 Bi (19, 20) and Cd 3 As 2 (21-23). The signatures of Fermi arcs by ARPES in Na 3 Bi (24) and by their peculiar quantum oscillations (25) in Cd 3 As 2 (26) have recently been reported. Although DSM can in principle appear in a system with spin rotational symmetry (27), here we focus on DSMs in spinorbit-coupled systems that are more closely related to material realizations.We can understand the Dirac fermions as two degenerate Weyl fermions with opposite chirality, where crystal symmetries forbid the two Weyl nodes from hybridizing and opening up a gap at each Dirac point (16,28). Given this picture of the bulk, it is natural to expect the surface states in a DSM (17, 18) as two copies of the chiral Fermi arc on the WSM surface: i.e., the "double Fermi arcs" shown schematically in Fig. 1A.In thi...

In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the pyrochlore lattice, such as those of the form A2M2O7, where A is a rare earth element and M is a transition metal element. We focus on the competition between Coulomb interaction, spin-orbit coupling, and lattice distortion when these energy scales are comparable. Strong spin-orbit coupling entangles the spin and the t2g d-orbitals giving rise to doublet j = 1/2 and quadruplet j = 3/2 states. In contrast to previous works which focused on the doublet manifold, we also discuss the quadruplet manifold which is relevant for several pyrochlore oxides. The Coulomb interaction is taken into account by use of the slave-rotor mean field theory and different classes of lattice distortions which further split the levels of the quadruplet j = 3/2 manifold are studied. Various topological phases are predicted, including exotic strong and weak topological Mott insulating phases. We discuss the general structure of the phase diagram for several values of d-shell filling and various symmetry classes of lattice distortions. Our results are relevant to the search for exotic topological insulators and quantum spin liquids in strongly correlated materials with strong spin-orbit coupling.

We consider the electromagnetic response of a topological Weyl semimetal (TWS) with a pair of Weyl nodes in the bulk and corresponding Fermi arcs in the surface Brillouin zone. We compute the frequency-dependent complex conductivities σαβ(ω) and also take into account the modification of Maxwell equations by the topological θ-term to obtain the Kerr and Faraday rotations in a variety of geometries. For TWS films thinner than the wavelength, the Kerr and Faraday rotations, determined by the separation between Weyl nodes, are significantly larger than in topological insulators. In thicker films, the Kerr and Faraday angles can be enhanced by choice of film thickness and substrate refractive index. We show that, for radiation incident on a surface with Fermi arcs, there is no Kerr or Faraday rotation but the electric field develops a longitudinal component inside the TWS, and there is linear dichroism signal. Our results have implications for probing the TWS phase in various experimental systems.