Analytical Study of Quasi-One-Dimensional Flat Band Networks and Slow Light Analogue

Abstract

Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite size cluster of atomic sites is decoupled from the rest of the system by the special 'non-permissible' vertex having zero amplitude. This immediately leads to the self-trapping of the incoming excitation. We work out an analytical scheme to discern the localizing character of the diffraction free dispersionless modes using real space renormalization group technique. Supportive numerical calculations of spectral profile and transport are demonstrated to substantiate the essence of compact localized states. Possible experimental scope regarding the photonic analogue of the tight-binding electronic case is also discussed elaborately. This eventually unfolds the concepts of slow light and the related re-entrant mode switching from the study of optical dispersion.

Tunable zero modes and quantum interferences in flat-band topological insulators

“…The -CSSH ladder, when either J or J are zero, reduces to the orthogonal dimer chain [Fig. 2 (f)], a topological model that is usually studied as a chain of interacting spins [44][45][46][47][48][49][50][51][52]. The -CSSH ladder model connects the topological phases of the orthogonal dimer chain and of the π-flux Creutz ladder in an adiabatic way, without losing the topological protection of the edge states at any point 2 .…”

“…It is topological when φ = π and m < √ 2J (assuming J = 0). As mentioned above, this model is usually studied in the context of interacting spins [45,47,48,50,52]. The -CSSH ladder connects the topological phases of the Creutz ladder (obtained when θ = π/4) and the orthogonal dimer chain (θ = 0, π/2), two previously unrelated models.…”

“…The -CSSH ladder, when either J or J are zero, reduces to the orthogonal dimer chain [Fig. 2 (f)], a topological model that is usually studied as a chain of interacting spins [42][43][44][45][46][47][48][49]. The spin-1/2 SSH chain with spin-orbit [50][51][52][53] is isomorphic to the hourglass CSSH ladder when the spin-orbit coupling constants are equal to the tunneling amplitudes.…”

Compact localized boundary states in a quasi-1D electronic diamond-necklace chain

“…This chain bears some resemblance with the diamond chain, although in the latter the compact localized states are bulk modes [ 10 , 13 , 22 – 24 ]. The diamond-necklace chain has been studied in the context of spin chains [ 25 – 27 ], where it is known as the dimer-plaquette chain, and recently in the context of flat bands in a non-interacting lattice [ 28 ]. The end modes that we find are doubly degenerate, have an energy in the insulating bulk gap, are compactly localized at the extremities of the lattice (no bulk decay) and are robust against a large number of perturbations.…”

Compact localized boundary states in a quasi-1D electronic diamond-necklace chain

“…This chain bares some resemblance with the diamond chain, although in the latter the compact localized states are bulk modes 9,12,17 . The diamond-necklace chain has been studied in the context of spin chains [18][19][20] , where it is known as the dimer-plaquette chain, and recently in the context of flat bands in a non-interacting lattice 21 . The end modes that we find are doubly degenerate, have an energy in the insulating bulk gap, are compactly localized at the extremities of the lattice (no bulk decay), and are robust against a large number of perturbations.…”