Fermion space charge in narrow-band gap semiconductors, Weyl semimetals
  and around highly charged nuclei

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Abstract

The field of charged impurities in narrow-band gap semiconductors and Weyl semimetals can create electron-hole pairs when the total charge \(Ze\) of the impurity exceeds a value \(Z_{c}e\). The particles of one charge escape to infinity, leaving a screening space charge. The result is that the observable dimensionless impurity charge \(Q_{\infty}\) is less than \(Z\) but greater than \(Z_{c}\). There is a corresponding effect for nuclei with \(Z >Z_{c} \approx 170\), however in the condensed matter setting we find \(Z_{c} \simeq 10\). Thomas-Fermi theory indicates that \(Q_{\infty} = 0\) for the Weyl semimetal, but we argue that this is a defect of the theory. For the case of a highly-charged recombination center in a narrow band-gap semiconductor (or of a supercharged nucleus), the observable charge takes on a nearly universal value. In Weyl semimetals the observable charge takes on the universal value \(Q_{\infty} = Z_{c}\) set by the reciprocal of material's fine structure constant.

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Is Open Access

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

Ashvin Vishwanath, Ari M. Turner, Xiangang Wan … (2010)

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.