Flatbands under Correlated Perturbations

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 𝐸FB , (ii) the localization length of eigenstates vanishes as 𝜉∼1/ln⁡(𝐸−𝐸FB) , (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 𝐸FB . Our analytical results are based on perturbative expansions of the CLSs and supported by numerical data in one and two lattice dimensions.