“Stiefel-Whitney classes and topological phases in condensed matter”

Dr. Bohm-Jung Yang
Department of Physics and Astronomy, Seoul National University

May. 31 (Fri.), 02:30 PM
E6-2. 1st fl. #1323

Abstract:
I am going to talk about novel topological properties of spinless fermions systems with space time inversion IST symmetry, which is basically a combination of time-reversal symmetry with additional inversion or two-fold rotation symmetry. In three dimensions, the band topology of IST symmetric systems can support nodal lines with Z2 monopole charges [1]. Here we show the intriguing linking structure of monopole nodal line and propose a general mechanism for pair-creation and pair-annihilation. In the case of two dimensional systems with IST symmetry, we show that the nontrivial band topology of two band systems can be characterized by Euler class. We prove that a two-band system with nontrivial Euler class has band crossing points with nonzero total vorticity, which naturally violates the well-known Nielsen-Ninomiya theorem[2]. We propose that both the topological property of monopole nodal lines and the fragile topology of 2D insulators with nontrivial Euler class originate from the underlying mathematical structure of the IST symmetric real wave functions, dubbed the second Stiefel-Whitney class[3,4].

REFERENCES:
[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] J. Ahn, S. J. Park and B. –J. Yang, “Failure of Nielsen-Ninomiya theorem and fragile topology in systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle”, Phys. Rev. X, 9, 021013 (2019)
[3]. Junyeong Ahn, Sungjoon Park, Dongwook Kim, Youngkuk Kim, Bohm-Jung Yang, “Stiefel-Whitney class and topological phases in band theory”, arXiv:1904.00336.
[4]. Eunwoo Lee, Rokyeon Kim, Junyeong Ahn, Bohm-Jung Yang, “Higher-order band topology and corner charges in monolayer graphdiyne”, arXiv:1904.11452.