Compact localized states and magnetic flux-driven topological phase transition in a diamond-dodecagon lattice geometry

TL;DR

The paper addresses how to realize and control flat-band physics and flux-induced topology in a 2D diamond-dodecagon lattice. It combines a tight-binding description with analytic CLS constructions, Berry-curvature analysis, and transport calculations to show that, at zero flux, three exact flat bands coexist with compact localized states, while applying magnetic flux gaps the bands and generates topological nearly-flat bands with nonzero Chern numbers (for example $C_1=+1$, $C_5=-1$ at $\Phi=\Phi_0/4$ and $C_2=+1$, $C_5=-1$ at $\Phi=\Phi_0/2$). The two-terminal transport spectra exhibit flux-tunable resonances and suppression tied to the flat bands, illustrating the interplay between localization, topology, and transport. The results propose a robust, tunable platform for exploring flat-band physics and lattice Chern insulators in photonic or ultracold-atom experiments, with potential extensions to interactions and non-equilibrium driving.

Abstract

We propose and investigate a novel two-dimensional (2D) tight-binding model defined on a diamond-dodecagon lattice geometry that hosts multiple flat bands (FBs) and supports topological phase transitions driven by a magnetic flux. This lattice exhibits three completely flat, non-dispersive bands in the band structure in the absence of magnetic flux due to destructive interference in the electron hoppings, leading to the emergence of compact localized states (CLS). These CLS are analytically constructed and exhibit real-space confinement of the electrons, arising solely due to the lattice's geometrical frustration. It has been shown that these FBs are very robust against the introduction of weak random onsite disorder in the system. By tuning the uniform magnetic flux threaded through the diamond plaquettes, we demonstrate a tunable evolution of the band structure and show that certain bands develop nontrivial topological features with nonzero integer values of the Chern number. Additionally, we have computed the multi-terminal transport properties for this 2D lattice system, which display the flux-tunable resonances and transmission suppression linked to the FBs, establishing a clear interplay between the localization, topology, and transport. Our findings put forward the diamond-dodecagon lattice as a robust and tunable platform for studying the flat-band physics and magnetic flux-controlled topological phenomena, offering promising experimental feasibility in photonic lattices and ultracold atomic systems.

Figures (8)

• Figure 1: Schematic diagram of a two-dimensional (2D) diamond-dodecagon lattice model. The unit cell of the lattice containing six atomic sites is highlighted with light blue color. Each diamond plaquette is pierced by a uniform magnetic flux $\Phi$. The solid black lines represents the nearest-neighbor hopping and the dotted lines represent the next-nearest-neighbor hopping.
• Figure 2: Electronic band structure for a 2D diamond-dodecagon lattice for three different values of the magnetic flux, viz., (a) $\Phi=0$, (b) $\Phi=\Phi_{0}/4$, and (c) $\Phi=\Phi_{0}/2$. For $\Phi=0$, we have three completely flat, non-dispersive bands appearing in the system marked by the red color, while the remaining three dispersive bands are shown in blue color. For $\Phi \ne 0$, gap opens up between all the bands in the system, and the FBs are no longer completely flat; they acuire quasi-flatness. We have set $\varepsilon_{i}=0$ for all sites and $t = \lambda = 1$.
• Figure 3: Distribution of the compact localized states (CLS) corresponding to the flat bands at the energies (a) $E = 1$, (b) $E = -1$, and (c) $E = -2$ in the absence of magnetic flux. The black sites denote the nodes with zero wavefunction amplitudes, while the dark and light green sites indicate nonzero positive wavefunction amplitudes (normalized to $+2$ and $+1$, respectively), and the dark and light orange sites indicate nonzero negative wavefunction amplitudes (normalized to $-2$ and $-1$, respectively).
• Figure 4: The variation of the average density of states (ADOS) $\rho(E)$ of the system as a function of the energy ($E$) for $\Phi=0$. (a) is for the perfectly ordered system and (b) is for a random disordered distribution of the onsite energies with a disorder strength $\Delta=0.2$ (measured in units of $t$). The sharp peaks in the spectrum indicate the flat band states. The system size considered here is $30 \times 30$ unit cells (i.e., $\mathcal{N}=5400$ sites).
• Figure 5: Distribution of the Berry curvatures (BC) in the first Brillouin zone for all the six bands ($n = 1$ to $6$) in the diamond-dodecagon lattice at a magnetic flux $\Phi = \Phi_{0}/4$, corresponding to the band structure shown in Fig. \ref{['fig:band-structure']}(b). The upper panel corresponds to the band index $n=1$ to $3$ and the lower panel corresponds to the band index $n=4$ to $6$. The system exhibits nontrivial topology with Chern numbers $C_{1} = +1$ and $C_{5} = -1$, while the remaining bands are topologically trivial ($C_{n} = 0$ for $n=2,3,4,6$).