Proximity-induced flat bands and topological properties in a decorated diamond chain

TL;DR

This work shows that a strain-induced proximity effect can control multiple flat bands in a quasi-one-dimensional decorated diamond chain without magnetic flux. Using a tight-binding model with tunable horizontal diagonal hopping $d_H$ (and $d_V=0$), the authors produce gapless and gapped flat bands at energies such as $E=0$, $-1$, and $-2$, and construct corresponding compact localized states. The flat bands are robust to weak on-site disorder, though strong disorder collapses them, indicating an inverse Anderson transition regime. Topological analysis via Wilson loops reveals nontrivial winding numbers and the emergence of in-gap edge states at $E=-\sqrt{2}$ under open boundaries, illustrating a bulk-boundary correspondence in this proximity-engineered lattice. The results point to feasible photonic-lattice realizations and provide a tunable platform for exploring flat-band physics and topology in low-dimensional systems.

Abstract

In the present study, we propose a unique scheme to generate and control multiple flat bands in a decorated diamond chain by using a strain-induced proximity effect between the diagonal sites of each diamond plaquette. This is in complete contrast to the conventional diamond chain, in which the interplay between the lattice topology and an external magnetic flux leads to an extreme localization of the single-particle states, producing the flat bands in the energy spectrum. Such a strain-induced proximity effect will enable us to systematically control one of the diagonal hoppings in the decorated diamond chain, which will lead to the formation of both gapless and gapped flat bands in the energy spectrum. These gapless or gapped flat bands have been corroborated by the computation of the compact localized states amplitude distribution as well as the density of states of the system using a real space calculation. We have also shown that these flat bands are robust against the introduction of small amounts of random onsite disorder in the system. In addition to this, we have also classified the nontrivial topological properties of the system by calculating the winding numbers and edge states for the gapped energy spectrum. These findings could be easily realized experimentally using the laser-induced photonic lattice platforms.

Figures (10)

• Figure 1: Schematic diagram of a quasi-one-dimensional decorated diamond lattice. The segment inside the dotted box indicates the unit cell of the lattice structure, consisting of four atomic sites. $t$ denotes the coupling along the periphery of each diamond (rhombic) structure, while $d_H$ and $d_V$ depict the diagonal couplings along the horizontal and vertical directions, respectively, inside a diamond structure. $\lambda$ represents the coupling in between two consecutive diamond structures.
• Figure 2: Electronic band structure of the decorated diamond lattice model. (a) A gapless FB appears at $E=0$ for $d_H=0$, (b) one gapless and one gapped FB appear at $E=0$ and $E=-2$, respectively, for $d_H=1$, (c) the FB at $E=0$ is gapped out for $d_H=1.5$, (d) two gapped FBs emerge at $E=0$ and $E=-1$, respectively, for $d_H=2$. We have set $d_V=0$ and $\lambda=t=1$ in all the four cases.
• Figure 3: The real-space wave function amplitude distribution corresponding to the flat bands at the energies (a) $E=0$ (for all possible values of $d_H$), (b) $E=-1$ (for $d_H=2$), and (c) $E=-2$ (for $d_H=1$). Zero wave function amplitudes are denoted by grey-shaded circles, while the nonzero wave function amplitudes are marked by green (for positive amplitudes) and red (for negative amplitudes) circles, respectively. We have taken $d_V=0$ and $\lambda=t=1$ in all the three cases.
• Figure 4: Variation of the average density of states (ADOS) as a function of the energy ($E$) for the decorated diamond chain. The total number of unit cells considered here is $100$ (i.e., $\mathcal{N} =400$ sites). The plots are done for different values of the horizontal diagonal coupling $d_H$ (measured in units of $t$), viz., (a) $d_H=0$, (b) $d_H=1$, (c) $d_H=1.5$, and (d) $d_H=2$. The other parameters are chosen as $d_V=0$ and $\lambda=t=1$ in all four cases. The value of the small imaginary part $\eta$ is taken to be equal to 0.005.
• Figure 5: Variation of the average density of states (ADOS) as a function of the energy ($E$) for the decorated diamond chain by incorporating a random onsite (diagonal) disorder of strength $\Delta=0.2$ (measured in units of $t$) in the system. All other parameters are kept unaltered as in Fig. \ref{['fig:DOS']}.