2014/07/31 by Joshua D. Bodyfelt, Daniel Leykam, Carlo Danieli +2 · 4 citations
Mathematics · Physics and Astronomy · #Algebraic number #CLs upper limits #Condensed matter physics #Eigenvalues and eigenvectors #Geometry #Gravitational singularity #Homogeneous space #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum and electron transport phenomena #Quantum mechanics #Quasiperiodic function #Renormalization #Symmetry (geometry) #Theoretical and Computational Physics #Topological Materials and Phenomena #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevlett.113.236403
published as Physical Review Letters 113, 236403 (2014)
arxiv created 2014/11/03 · openalex publication_date 2014/12/05 · arxiv updated 2014/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.