Exact flatness of energy bands implies some reasons behind. Here we present one of them, "molecular orbital (MO) representation", which seems to be applied for various classes of tight binding models. Mathematically if the rank of the hamiltonian as a linear operator is less than the number of atomic sites, the kernel of the linear operator has a finite dimension. This is the zero mode flat band. The MO rep. presents nice physical reasons for it. Original proposal by YH with Isao Maruyama in 2011 in EPL and arXiv is counting dimensions of non-orthogonal projections but the hopping of the MO's is allowed as we pointed out (it should be). It's a fun to guess what kinds of the MO representation is possible for a known flat band system. Try ! Also several physical reason why the flat band crosses/touches to dispersive bands in many cases are discussed. Our new paper has appeared in EPL, "Molecular-orbital representation of generic flat-band models", by T. Mizoguchi and Y. Hatsugai , also arXiv.

I wrote a small article "So Small Implies So Large: For a Material Design" in the "News and comment" section of the JPSJ in relation to a recent interesting paper by Toshikaze Kariyado. Material deformation induces a gauge field that modifies electronic structure and may result in the Landau levels without breaking time reversal. Have a look at.

Our paper "Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion" by Tomonari Mizoguchi, Hiromu Araki, and Yasuhiro Hatsugai, has appeared in J. Phys. Soc. Jpn. 88, 104703 (2019). One can access also via arXiv:1906.07928. Z₆ quantization in honeycomb structure is the key. Have a look at.

Ryo Okugawa (WPI-AIMR, Tohoku Univ.) will be telling us on his recent work as a title "Chiral-symmetry protected second-order topological phases" on Sep. 18 (2019). Rm. D301 from 13:30pm. Join us.

Due to an intrinsic symmetry of a mechanical system with friction governed by the Newton equation, exceptional rings appear in two dimensions. We have demonstrated it and classification of symmetry-protected non-Hermitian degeneracies is addressed putting a focus on the symmetry. The paper is published in Physical Review B, "Exceptional rings protected by emergent symmetry for mechanical systems" by Tsuneya Yoshida and Yasuhiro Hatsugai. You may find also here arXiv:1904.10764.