Universal d=1 flat band generator from compact localized states

Wulayimu Maimaiti, Sergej Flach, and Alexei Andreanov
Phys. Rev. B 99, 125129 – Published 18 March 2019

Abstract

The band structure of some translationally invariant lattice Hamiltonians contains strictly dispersionless flat bands (FB). These are induced by destructive interference and typically host compact localized eigenstates (CLS) which occupy a finite number U of unit cells. FBs are important due to macroscopic degeneracy and consequently due to their high sensitivity and strong response to different types of weak perturbations. We use a recently introduced classification of FB networks based on CLS properties, and extend the FB Hamiltonian generator introduced in Phys. Rev. B 95, 115135 (2017) to an arbitrary number ν of bands in the band structure, and arbitrary size U of a CLS. The FB Hamiltonian is a solution to equations that we identify with an inverse eigenvalue problem. These can be solved only numerically in general. By imposing additional constraints, e.g., a chiral symmetry, we are able to find analytical solutions to the inverse eigenvalue problem.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 25 October 2018
  • Corrected 31 March 2021

DOI:https://doi.org/10.1103/PhysRevB.99.125129

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsNetworks

Corrections

31 March 2021

Correction: A minor typographical error in an inline equation in the fourth sentence of the fourth paragraph in Sec. IV has been fixed.

Authors & Affiliations

Wulayimu Maimaiti1,2, Sergej Flach1, and Alexei Andreanov1

  • 1Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea
  • 2Basic Science Program, Korea University of Science and Technology (UST), Daejeon 34113, Republic of Korea

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 12 — 15 March 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×