Adler-Bell-Jackiw anomaly in Weyl semi-metals: Application to Pyrochlore
  Iridates

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Abstract

Weyl semimetals are three dimensional analogs of graphene where the energy of the excitations are a linear function of their momentum. Pyrochlore Iridates \((A_{2}Ir_{2}O_{7})\) with A =yttrium or lanthanide element) are conjectured to be examples of such a system, with the low energy physics described by twenty four Weyl nodes. An intriguing possibility is that these materials provide a physical realization of the Adler-Bell-Jackiw anomaly. In this letter we investigate the properties of pyrochlore iridates in an applied magnetic field. We find that the dispersion of the lowest landau level depends on the direction of the applied magnetic field. As a consequence the magneto-conductivity in an electric field, applied parallel to the magnetic field is highly anisotropic, providing a detectable signature of the semi-metallic state.

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Topological Insulators

, (2011)

Topological insulators are electronic materials that have a bulk band gap like an ordinary insulator, but have protected conducting states on their edge or surface. The 2D topological insulator is a quantum spin Hall insulator, which is a close cousin of the integer quantum Hall state. A 3D topological insulator supports novel spin polarized 2D Dirac fermions on its surface. In this Colloquium article we will review the theoretical foundation for these electronic states and describe recent experiments in which their signatures have been observed. We will describe transport experiments on HgCdTe quantum wells that demonstrate the existence of the edge states predicted for the quantum spin Hall insulator. We will then discuss experiments on Bi_{1-x}Sb_x, Bi_2 Se_3, Bi_2 Te_3 and Sb_2 Te_3 that establish these materials as 3D topological insulators and directly probe the topology of their surface states. We will then describe exotic states that can occur at the surface of a 3D topological insulator due to an induced energy gap. A magnetic gap leads to a novel quantum Hall state that gives rise to a topological magnetoelectric effect. A superconducting energy gap leads to a state that supports Majorana fermions, and may provide a new venue for realizing proposals for topological quantum computation. We will close by discussing prospects for observing these exotic states, a well as other potential device applications of topological insulators.

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Quantum Spin Hall Effect in Graphene

E. Mele, C. L. Kane (2004)

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the quantized transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are non chiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder and symmetry breaking fields are discussed.