Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

0583171 - ÚJF 2025 RIV GB eng J - Journal Article
Jakubský, Vít - Zelaya, Kevin
Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions.
Physica Scripta. Roč. 99, č. 3 (2024), č. článku 035220. ISSN 0031-8949. E-ISSN 1402-4896
R&D Projects: GA MŠMT EF18_053/0017163
Institutional support: RVO:61389005
Keywords : lieb lattice * pseudospin-1 systems * flat band * Darboux transformations * SUSY QM * Reflectionless Dirac systems
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 2.9, year: 2022
Method of publishing: Limited access
https://doi.org/10.1088/1402-4896/ad224a

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.
Permanent Link: https://hdl.handle.net/11104/0351167