FYZIKÁLNY SEMINÁR

FMFI UK, Mlynská dolina 2, posl. C

Pondelok 29. januára 2018 o 13:00

Tomáš BzdušekStanford University

Homotopy classification of band-structure nodesAbstractRecent years have seen a surge of interest in understanding weakly-interacting gapless topologicalphases, such as Weyl and nodal-line semimetals or superconductors. In this talk, we are concerned witha systematic classification of stable band-structure nodes using homotopy theory – a mathematicaltechnique that has previously provided a solid understanding of topological defects in ordered media[1]. The two problems are mathematically equivalent, when the only major difference is the switch tomomentum space.

Most band-structure nodes carry a single topological charge such as a Chern number or a quantizedBerry phase. However, it was shown using homotopy theory [2] that nodal lines protected jointly bytime-reversal and inversion symmetry (without spin-orbit coupling) carry a pair of independent Z2

charges. A non-trivial value of the additional charge enhances the stability of such nodal lines, eventhough it does not entail new topological surface states. We generalize the corresponding argumentsto all ten inversion-symmetric Altland-Zirnbauer classes, and find that in 3D such “doubly charged”nodes (either nodal lines or nodal surfaces) are possible in four of them [3]. These are relevant forvarious semimetallic as well as superconducting phases – the peculiar Bogoliubov-Fermi surfaces [4]being one such an example. Nodes with a non-trivial value of the second charge can be removed onlyby a pairwise annihilation, thus leading to an analogue of the Nielsen-Ninomiya doubling.

We further generalize the homotopy description to systems with point group symmetries, whichallows us to understand the topological protection of most common species of band-structure nodesin a unified mathematical language. Without going deep into details, we outline in the talk someproperties of Weyl points, nodal lines and nodal chains that are easily deduced from this perspective.Similarly, by properly generalizing the discussion to multi-band systems, we show how one can emulatenon-Abelian vortices of biaxial nematics as nodal lines in momentum space. [5]

1N. D. Mermin, Rev. Mod. Phys. 51, 591 (1979)2C. Fang, Y. Chen, H.-Y. Kee, and L. Fu, Phys. Rev. B 92, 081201(R) (2015)3T. Bzdušek and M. Sigrist, Phys. Rev. B 96, 155102 (2017)4D. F. Agterberg, P. M. R. Brydon, and C. Timm, Phys. Rev. Lett. 118, 127001 (2017)5works with A. A. Soluyanov, X.-Q. Sun, Q.-S. Wu, and S.-C. Zhang, (in preparation)