Dispersion relations of strained as well as complex Lieb lattices

TL;DR

This paper systematically studies the dispersion relations of strained and complex Lieb lattices using tight-binding models, revealing the absence of edge states in strained lattices and the impossibility of achieving PT-symmetry in these systems.

Contribution

It provides a detailed analysis of how strain and complex modifications affect the dispersion and edge states in Lieb lattices, highlighting limitations in PT-symmetry realization.

Findings

Edge states do not appear in strained Lieb lattices.

PT-symmetry Lieb lattices cannot be realized.

Strain and complex modifications significantly alter dispersion relations.

Abstract

We investigate the dispersion relations of strained as well as complex Lieb lattices systematically based on the tight-binding method when the nearest-neighbor approximation is adopted. We find that edge states will no appear for strained Lieb lattices and $\mathcal{PT}$-symmetry Lieb lattice cannot be obtained.