Flattened band in band structure What does a flattened band in a band structure plot imply? I've been reading this paper https://doi.org/10.1016/j.apsusc.2012.06.092 and one of the primary results is the flattening of bands however it does not say anything about the significance of the band flattening. can anyone help me with this?

 A: The emergence of a flat band, i.e. a band with low dispersion, can be understood in terms of a tight binding picture. Bringing a set of atoms together, the initially discrete energy levels of the isolated atoms begin to broaden because of overlap of the orbitals between the atoms. The stronger this overlap / hybridization, the broader the band will be. A very flat band is formed from states that have very little orbital overlap between the lattice sites. As a first approximation, the width of a band is proportional to the overlap integrals (also called hopping integrals) between the nearest neighboring sites (overlap between sites further apart typically leads to somewhat smaller corrections to the band shape).
A derivation of the dependence of the band width on the nearest neighbor hopping (and an introduction in general) can be found in "Crystal-Field Theory, Tight-Binding Method and Jahn-Teller Effect" by Eva Pavarini (the bandwidth dependence (the factor $2t$ in front of the cosine) is introduced on pages 6.25/6.26).
