Matrix-element selection rule for sublattice-selective leakage suppression in flat-band Lieb mechanical lattices

Area of Science:

• Condensed Matter Physics
• Mechanical Metamaterials
• Wave Phenomena

Background:

• Flat-band lattices exhibit compact localized states with sublattice-selective properties.
• The protection of boundary resonances from disorder-induced bulk leakage in these lattices remains an open question.

Purpose of the Study:

• To identify a mechanism for suppressing disorder-induced leakage from boundary resonances in flat-band lattices.
• To investigate the role of lattice geometry and disorder type in leakage suppression.

Main Methods:

• Analysis of a gyroscopic Lieb mechanical lattice with a boundary resonance.
• Introduction of sublattice-resolved onsite disorder and bond-stiffness disorder.
• Application of Fermi's golden rule to analyze eigenmodes and matrix elements.

Main Results:

• A matrix-element selection rule for sublattice-selective leakage suppression was identified.
• Significant suppression of leakage was observed for both onsite and bond-stiffness disorder, with selectivity ratios up to 58 and 34, respectively.
• The suppression mechanism is geometric, robust against spring anisotropy, and attributed to a suppressed matrix element.

Conclusions:

• A geometric selection rule effectively suppresses bulk leakage from boundary resonances in flat-band lattices.
• This mechanism offers a pathway to engineer robust mechanical, phononic, and photonic flat-band platforms.
• The findings are generalizable to multi-sublattice systems.