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The 390th forum: Stiefel-Whitney classes and topological phases in systems with space-time inversion symmetry

Date: 2019-12-30
Time: 10:00
Venue: M236
Speaker: Bohm-Jung Yang

Department of Physics and Astronomy, Seoul National University


Prof. Bohm-Jung Yang obtained his Ph.D. from Seoul National University in 2008. After that, he did his postdoc in University of Toronto and RIKEN. In 2015, he joined Seoul National University as an assistant Professor and became an associate Professor in 2019. He has received many awards, honors and fellowships, including a membership of Young Korean Academy of Sciences and Technology, Award for excellent research from SNU, Award for young physicists from Korean Physical Society. His research interests include emergent topological phenomena in correlated quantum matters, symmetry protected topological quantum states, and frustrated quantum magnets.


I am going to talk about novel topological properties of spinless fermion systems with space time inversion IST symmetry which is the combination of time-reversal symmetry with additional inversion or two-fold rotation symmetry. First, in three dimensions, the band topology of IST symmetric systems can support nodal lines with Z2 monopole charges. Here we show that the Z2 monopole charge is equivalent to the second Stiefel Whitney invariant [1]. Also using the mathematical properties of the Stiefel-Whitney classes, we show the intriguing linking structure of monopole nodal lines. In the second part, we will show that the second Stiefel-Whitney number defined over the Brillouin zone torus can serve as a well-defined 2D topological invariant, and propose a new 2D topological insulator, which we call a 2D Stiefel-Whitney insulator (2D SWI) characterized by a nontrivial second Stiefel-Whitney number. We show that 2D SWI has fragile band topology and supports corner charges. We propose that both the topological property of monopole nodal lines of 3D nodal line semimetals and the fragile topology of 2D SWIs originate from the underlying mathematical structure of the IST symmetric real wave functions, that is, the Stiefel-Whitney classes [1,2].


[1] J. Ahn, D. W. Kim, Y.K.Kim and B. –J. Yang, “Band topology and linking structure of  nodal line semimetals with Z2 monopole charges”, Phys. Rev. Lett. 121, 106403 (2018)..

[2] Junyeong Ahn, Sungjoon Park, Dongwook Kim, Youngkuk Kim, Bohm-Jung Yang, “Stiefel-Whitney class and topological phases in band theory”, arXiv:1904.00336.

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