Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions
arXiv:2307.02123 · doi:10.1088/1402-4896/ad224a
Abstract
This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is present in the spectrum of the initial system. Using the flat band state as one of the seed solutions substantially improves the applicability of the Darboux transformation, for it becomes necessary to ensure the Hermiticy of the new Hamiltonians. This is illustrated explicitly in four examples, where we show that the new Hamiltonians can describe quasi-particles in Lieb lattice with inhomogeneous hopping amplitudes.
References in corpus (32)
- Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
- Flat Bands in Slightly Twisted Bilayer Graphene
- Artificial flat band systems: from lattice models to experiments
- Geometric origin of superfluidity in the Lieb lattice flat band
- From dia- to paramagnetic orbital susceptibility of Dirac cones
- Experimental observation of bulk and edge transport in photonic Lieb lattices
- Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
- Massless Dirac-Weyl Fermions in a T_3 Optical Lattice
- Intertwining technique for the one-dimensional stationary Dirac equation
- Nontrivial topological flat bands in a diamond-octagon lattice geometry
- Unconventional phases in a Haldane model of dice lattice
- Dirac electron in graphene under supersymmetry generated magnetic fields
- Flat bands and nontrivial topological properties in an extended Lieb lattice
- Dirac electron in graphene with magnetic fields arising from first-order intertwining operators
- Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene
- Photoinduced Topological Phase Transitions in Topological Magnon Insulators
- Supersymmetric twisting of carbon nanotubes
- Darboux transformation for a general Dirac equation in two dimensions
- Confluent Crum-Darboux transformations in Dirac Hamiltonians with -symmetric Bragg gratings
- Twisted kinks, Dirac transparent systems and Darboux transformations
- Electron in bilayer graphene with magnetic fields leading to shape invariant potentials
- Direct optical probe of magnon topology in two-dimensional quantum magnets
- Bilayer graphene in magnetic fields generated by supersymmetry
- Magic angle twisted bilayer graphene as a highly efficient quantum Otto engine
- Flat-band solutions in -dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
- Topological Landau-Zener Bloch Oscillations in Photonic Floquet Lieb Lattices
- New solutions for graphene with scalar potentials by means of generalized intertwining
- Complex Supersymmetry in Graphene
- Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions
- Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators
- Landau levels and snake states of pseudo-spin-1 Dirac-like electrons in gapped Lieb lattices
- A New Class of Solvable Two-dimensional Scalar Potentials for Graphene