2020/01/13(Mon) 10:30 -12:30 五樓第一會議室 5F, 1st Meeting Room
Title
Nielsen-Ninomiya Theorem for the 17 wallpaper groups
Speaker
Dr. Ching-Kai Chiu (Kavli Institute for Theoretical Sciences)Abstract
In a 2D Brillouin zone, chiral symmetry and space-time inversion symmetry can properly define topological invariants as charges characterizing the stability of the nodal points so that the non-zero charges protect the nodal points. Due to the charge neutralization, the Nielsen-Ninomiya Theorem leads to the presence of at least two stable nodal points in the entire Brillouin zone. However, additional crystalline symmetries might duplicate nodal points. In this regard, for wallpaper groups with crystalline symmetries, the minimal numbers of the nodal points in the Brillouin zone might be more than two. In this work, we determine the minimal numbers of the nodal points for the 17 wallpaper groups in chiral-symmetric and space-time-inversion- symmetric systems separately. This generalized Nielsen-Ninomiya Theorem provides a guide to searching for 2D Dirac materials and topological nodal superconductors. Furthermore, we show the Nielsen-Ninomiya Theorem can be extended to 2D non-Hermitian systems hosting Fermi points and exceptional points for the 17 wallpaper groups.
Language
演講語言 (Language): in English
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