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      Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations

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          Abstract

          We consider the tight-binding model with cubic symmetry that may be relevant for the description of a certain class of Weyl semimetals. We take into account elastic deformations of the semimetal through the modification of hopping parameters. This modification results in the appearance of emergent gauge field and the coordinate dependent anisotropic Fermi velocity. The latter may be interpreted as emergent gravitational field.

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          Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

          In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y\(_{2}\)Ir\(_{2}\)O\(_{7}\)) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y\(_{2}\)Ir\(_{2}\)O\(_{7}\) and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter \(\theta=\pi\), may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.
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            Discovery of a Three-dimensional Topological Dirac Semimetal, Na3Bi

            Three-dimensional (3D) topological Dirac semimetals (TDSs) represent a novel state of quantum matter that can be viewed as '3D graphene'. In contrast to two-dimensional (2D) Dirac fermions in graphene or on the surface of 3D topological insulators, TDSs possess 3D Dirac fermions in the bulk. The TDS is also an important boundary state mediating numerous novel quantum states, such as topological insulators, Weyl semi-metals, Axion insulators and topological superconductors. By investigating the electronic structure of Na3Bi with angle resolved photoemission spectroscopy, we discovered 3D Dirac fermions with linear dispersions along all momentum directions for the first time. Furthermore, we demonstrated that the 3D Dirac fermions in Na3Bi were protected by the bulk crystal symmetry. Our results establish that Na3Bi is the first model system of 3D TDSs, which can also serve as an ideal platform for the systematic study of quantum phase transitions between rich novel topological quantum states.
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              Topological response in Weyl semimetals and the chiral anomaly

              We demonstrate that topological transport phenomena, characteristic of Weyl semimetals, namely the semi-quantized anomalous Hall effect and the chiral magnetic effect (equilibrium magnetic-field-driven current), may be thought of as two distinct manifestations of the same underlying phenomenon, the chiral anomaly. We show that the topological response in Weyl semimetals is fully described by a \(\theta\)-term in the action for the electromagnetic field, where \(\theta\) is not a constant parameter, like e.g. in topological insulators, but is a field, which has a linear dependence on the space-time coordinates. We also show that the \(\theta\)-term and the corresponding topological response survive for sufficiently weak translational symmetry breaking perturbations, which open a gap in the spectrum of the Weyl semimetal, eliminating the Weyl nodes.
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                Author and article information

                Journal
                10.1016/j.aop.2016.01.006
                1508.04462

                High energy & Particle physics,Nanophysics
                High energy & Particle physics, Nanophysics

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