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

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 FB physics and magnetic flux-controlled topological phenomena, offering promising experimental feasibility in photonic lattices and ultracold atomic systems.