Beyond Band Insulators: Topology of Semi-metals and Interacting Phases

By Ari M. Turner, Ashvin Vishwanath. 2013

171 citations recorded by the source corpus.

The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in identifying gapless systems with stable topological properties (such as novel surface states), using Weyl semimetals as an illustration. We then review recent progress in describing topological phases of interacting gapped systems. We explain how new types of edge states can be stabilized by interactions and symmetry, even though the bulk has only conventional excitations and no topological order of the kind associated with Fractional Quantum Hall states.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/1029cb151d83fe3ebbe2e98bd8dd3279e8db0f4b

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In Atomic and Molecular Physics, and Optics

1. Ashvin Vishwanath
2. Hsin Lin
3. Arun Bansil
4. J. Venderbos
5. Tanmoy Das
6. A. Grushin
7. Xiao-Liang Qi
8. P. Hosur

In Materials Chemistry

1. Ashvin Vishwanath
2. Hsin Lin
3. Arun Bansil
4. Tanmoy Das
5. J. Venderbos
6. A. Grushin
7. Xiao-Liang Qi
8. P. Hosur

Citations in the corpus

• Recent developments in transport phenomena in Weyl semimetals (2013, background): “This result has been derived in several recent works, both in lattice as well as in continuum models (Chen et al. [7], Xu et al. [43], Goswami and Tewari [13], Yang et al. [45], Vafek and Vishwanath [35], Burkov and Balents [3], Zyuzin and Burkov [49]), and has been accepted unanimously.”
• Classification of topological quantum matter with symmetries (2015, unknown): “…and Fu, 2015; Bernevig and Hughes, 2013; Franz and Molenkamp, 2013; Hasan et al., 2015; König et al., 2008; Mizushima et al., 2015; Moore, 2010; Schnyder and Brydon, 2015; Senthil, 2015; Shen, 2012; Turner and Vishwanath, 2013; Volovik, 2003; Witczak-Krempa et al., 2014; Zahid Hasan et al., 2014).”
• Giant Anomalous Hall Effect in the Chiral Antiferromagnet Mn 3 Ge (2015, background): “Notably, the zero-field AHE observed in Mn3Ge reaches nearly half of σH = e(2) 2πh |G| ∼ 800 Ω cm, a value expected for a 3D QHE with Chern number of unity where the pair of Weyl points are separated by the reciprocal lattice vector G [6, 26].”
• Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels (2016, background): “Many peculiar transport properties have been attributed to topological semimetals [10, 11], while not many of them have proven easy to measure.”
• Colloquium : Topological band theory (2016, background): “…realization of anomalous Hall effect (Yang, Lu, and Ran 2011; Burkov and Balents 2011b; Xu, Xia, et al. 2011), nontrivial electromagnetic responses (Turner and Vishwanath 2013), Majorana excitations (Meng and Balents 2012), a disconnected, yet protected, Fermi surface (FS) or a ‘Fermi arc’ (Wan et…”