Topological electronic structure and Weyl semimetal in the TlBiSe$_2$
  class of semiconductors

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Abstract

We present an analysis of bulk and surface electronic structures of thallium based ternary III-V-VI$_2$ series of compounds TlMQ$_2$, where M=Bi or Sb and Q=S, Se or Te, using the ab initio density functional theory framework. Based on parity analysis and (111) surface electronic structure, we predict TlSbSe$_2$, TlSbTe$_2$, TlBiSe$_2$ and TlBiTe$_2$ to be non-trivial topological insulators with a single Dirac cone at the $\Gamma$-point, and TlSbS$_2$ and TlBiS$_2$ to be trivial band insulators. Our predicted topological phases agree well with available angle-resolved photoemission spectroscopy (ARPES) measurements, in particular the topological phase changes between TlBiSe$_2$ and TlBiS$_2$. Moreover, we propose that Weyl semimetal can be realized at the topological critical point in TlBi(S$_{1-x}$Se$_x$)$_2$ and TlBi(S$_{1-x}$Te$_x$)$_2$ alloys by breaking the inversion symmetry in the layer by layer growth in the order of Tl-Se(Te)-Bi-S, yielding six Dirac cones centered along the $\Gamma-L$ directions in the bulk band structure.

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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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Classification of topological insulators and superconductors in three spatial dimensions

Andreas Ludwig, Akira Furusaki, Shinsei Ryu … (2008)

We systematically study topological phases of insulators and superconductors (SCs) in 3D. We find that there exist 3D topologically non-trivial insulators or SCs in 5 out of 10 symmetry classes introduced by Altland and Zirnbauer within the context of random matrix theory. One of these is the recently introduced Z_2 topological insulator in the symplectic symmetry class. We show there exist precisely 4 more topological insulators. For these systems, all of which are time-reversal (TR) invariant in 3D, the space of insulating ground states satisfying certain discrete symmetry properties is partitioned into topological sectors that are separated by quantum phase transitions. 3 of the above 5 topologically non-trivial phases can be realized as TR invariant SCs, and in these the different topological sectors are characterized by an integer winding number defined in momentum space. When such 3D topological insulators are terminated by a 2D surface, they support a number (which may be an arbitrary non-vanishing even number for singlet pairing) of Dirac fermion (Majorana fermion when spin rotation symmetry is completely broken) surface modes which remain gapless under arbitrary perturbations that preserve the characteristic discrete symmetries. In particular, these surface modes completely evade Anderson localization. These topological phases can be thought of as 3D analogues of well known paired topological phases in 2D such as the chiral p-wave SC. In the corresponding topologically non-trivial and topologically trivial 3D phases, the wavefunctions exhibit markedly distinct behavior. When an electromagnetic U(1) gauge field and fluctuations of the gap functions are included in the dynamics, the SC phases with non-vanishing winding number possess non-trivial topological ground state degeneracies.

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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.

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Publication date Created: 26 September 2012

Article

DOI: 10.1103/PhysRevB.86.115208

ArXiV ID: 1209.5896

SO-VID: 210e6fc8-e344-4e20-85f1-7eba745d0871

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Journal reference Phys. Rev. B 86, 115208 (2012)

Comments 9 pages, 10 figures,Accepted for publication in Physical Review B (2012)

Topological electronic structure and Weyl semimetal in the TlBiSe\(_2\) class of semiconductors

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Most cited references 24

Topological Insulators

Classification of topological insulators and superconductors in three spatial dimensions

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

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