Robustness of flat bands on the perturbed Kagome and the perturbed Super-Kagome lattice
arXiv:2301.05076 · doi:10.1007/s00023-023-01399-7
Abstract
We study spectral properties of perturbed discrete Laplacians on two-dimensional Archimedean tilings. The perturbation manifests itself in the introduction of non-trivial edge weights. We focus on the two lattices on which the unperturbed Laplacian exhibits flat bands, namely the Kagome lattice and the ``Super-Kagome'' lattice. We characterize all possible choices for edge weights which lead to flat bands. Furthermore, we discuss spectral consequences such as the emergence of new band gaps. Among our main findings is that flat bands are robust under physically reasonable assumptions on the perturbation and we completely describe the perturbation-spectrum phase diagram. The two flat bands in the Super-Kagome lattice are shown to even exhibit an ``all-or-nothing'' phenomenon in the sense that there is no perturbation which can destroy only one flat band while preserving the other.
arXiv comment19 pages, 6 figures
References in corpus (19)
- Time-reversal symmetry-breaking charge order in a kagome superconductor
- On the spectra of carbon nano-structures
- Line-Graph Lattices: Euclidean and Non-Euclidean Flat Bands, and Implementations in Circuit Quantum Electrodynamics
- Disordered flat bands on the kagome lattice
- Quantum geometry and flat band Bose-Einstein condensation
- Spectral Analysis of Percolation Hamiltonians
- A new class of bilayer kagome lattice compounds with Dirac nodal lines and pressure-induced superconductivity
- Topological flat band, Dirac fermions and quantum spin Hall phase in 2D Archimedean lattices
- Estimation of Bond Percolation Thresholds on the Archimedean Lattices
- Mathematics of magic angles in a model of twisted bilayer graphene
- Hidden symmetry and protection of Dirac points on the honeycomb lattice
- Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited. Enhanced superconductivity at boundaries with and without magnetic field
- On the growth constant for square-lattice self-avoiding walks
- Boundary Superconductivity in the BCS Model
- Spectral estimates for Schrödinger operators on periodic discrete graphs
- Spectral properties of soft quantum waveguides
- Soft quantum waveguides in three dimensions
- Kagome network with vertex coupling of a preferred orientation
- Unique continuation principles and their absence for Schrödinger eigenfunctions on combinatorial and quantum graphs and in continuum space