Rational design of phononic flat-band materials

Electronic Flat band (FB) is of great interest in the field of condensed matter physics. Here, using spring-mass model and symmetry analysis, we prescribe a generic recipe to realize FB in both line-graph (LG) lattices and non-LG phononic lattices. We first demonstrate the design principle in several two-dimensional (2D) LG and non-LG model lattices. Then we carry out first-principles calculations, guided by the newly developed recipe, to search for phononic FB materials and discover that 2D Kagome BN is a perfect candidate to host phononic FB. Our work will not only offer a comprehensive understanding of phononic FB and enrich the FB physics, but also pave a path for exploring phononic FB materials.