title: Flatbands under correlated perturbations.
abstract: Flatband networks are characterized by the coexistence of dispersive and flatbands. Flatbands (FBs) are generated by compact localized eigenstates (CLSs) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLSs without additional renormalization, yet with surprising consequences: (i) states are expelled from the FB energy E_{FB}, (ii) the localization length of eigenstates vanishes as ξ∼1/ln(E-E_{FB}), (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), and (iv) mobility edge curves show algebraic singularities at E_{FB}. Our analytical results are based on perturbative expansions of the CLSs and supported by numerical data in one and two lattice dimensions.
authors.affiliation: New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland, 0745 New Zealand.
authors.forename: Joshua D
authors.initials: JD
authors.lastname: Bodyfelt
authors.affiliation: Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
authors.forename: Daniel
authors.initials: D
authors.lastname: Leykam
authors.affiliation: New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland, 0745 New Zealand.
authors.forename: Carlo
authors.initials: C
authors.lastname: Danieli
authors.affiliation: New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland, 0745 New Zealand.
authors.forename: Xiaoquan
authors.initials: X
authors.lastname: Yu
authors.affiliation: New Zealand Institute for Advanced Study, Centre for Theoretical Chemistry and Physics, Massey University, Auckland, 0745 New Zealand.
authors.forename: Sergej
authors.initials: S
authors.lastname: Flach