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Flatbands under correlated perturbations.

Joshua D Bodyfelt1, Daniel Leykam2, Carlo Danieli1

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Summary
This summary is machine-generated.

Flatband networks with correlated disorder exhibit unique phenomena. Compact localized states are expelled from flatbands, leading to vanishing localization length and diverging density of states.

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Area of Science:

  • Condensed matter physics
  • Quantum mechanics
  • Disordered systems

Background:

  • Flatband networks feature both dispersive and flatbands.
  • Flatbands arise from compact localized eigenstates (CLSs) due to local symmetries and destructive interference.
  • Correlated disorder and quasiperiodic potentials can hybridize CLSs.

Purpose of the Study:

  • To investigate the effects of correlated disorder and quasiperiodic potentials on compact localized states in flatband networks.
  • To analytically and numerically explore the resulting changes in electronic properties.

Main Methods:

  • Perturbative expansion of compact localized states (CLSs).
  • Numerical simulations in one and two lattice dimensions.
  • Analysis of state expulsion, localization length, density of states, and mobility edges.

Main Results:

  • States are expelled from the flatband energy (E_{FB}).
  • Localization length vanishes as ξ∼1/ln(E-E_{FB}).
  • Density of states exhibits logarithmic (with particle-hole symmetry) and algebraic (without particle-hole symmetry) divergences.
  • Mobility edge curves display algebraic singularities at E_{FB}.

Conclusions:

  • Correlated disorder and quasiperiodic potentials lead to non-trivial hybridization of CLSs in flatband networks.
  • These hybridizations result in unique spectral and localization properties, including state expulsion and singularities.
  • The findings offer insights into the behavior of quantum systems with engineered disorder and symmetries.