Abstract
The dice lattice supports Aharonov-Bohm caging when all the energy bands are flat for the half-quantum magnetic flux enclosed in each plaquette of the lattice. We analytically investigate the eigenstates and discuss the localization dynamics. We find that arbitrary excitation is compactly confined within the excited-site-related snowflake structures of the dice lattice; as a consequence that the nonzero-energy flatband localizes in the single snowflake, whereas the zero-energy flatband localizes in three nearest snowflakes that are connected in the form of a trident star. The localization dynamics of an arbitrary excitation is grasped from two dynamical behaviors of single-site excitation. For the single-site excitation at the center of a snowflake, the excitation is localized in that snowflake; whereas for the single-site excitation at the branch site of a snowflake, the excitation is localized in the three snowflakes that the branch site belongs to. Our findings deepen the understanding of destructive interference and the dynamics of Aharonov-Bohm caging in the dice lattice.
Highlights
Flatbands are dispersiveless, fully constituted by degenerate energies and independent of the momentum [1]
We systematically demonstrate the properties of compact localized states (CLSs) and the confinement dynamics of AB caging in the 2D dice lattice
The dice (T3) lattice supports AB caging when the halfquantum magnetic flux is enclosed in the diamond plaquette of the dice lattice
Summary
Fully constituted by degenerate energies and independent of the momentum [1]. The Lieb lattice [30] possesses a zeroenergy flatband [31,32,33,34,35,36] and is realized in optical systems for cold atoms [26,37,38] and trapped ions [6]. When a half-quantum magnetic flux π is introduced into a quasi-1D rhombic lattice, all the energy bands become flat [49]; and the excitations that are not limited to be the eigenstates of the system can be completely confined in certain regions, referred to as the Aharonov-Bohm (AB) caging. We systematically demonstrate the properties of CLSs and the confinement dynamics of AB caging in the 2D dice lattice. V, results of the CLSs and the localization dynamics in the dice lattice are summarized
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