Mechanism underlying supratransmission thresholds in nearly flat bands

Determine the precise mechanism responsible for the existence of a supratransmission threshold when the driving frequency lies within a nearly flat dispersive band in nonlinear flat-band lattices, specifically in the diamond and stub lattices governed by coupled discrete equations with Kerr (cubic) nonlinearity. Clarify how the interplay of nonlinearity and lattice topology (through coupling parameters c1, c2, and c3) enables or suppresses transmission when the band is not perfectly flat.

Background

This work studies in-band supratransmission in nonlinear lattices that host flat or nearly flat bands, focusing on diamond and stub geometries with cubic nonlinearity and boundary driving. In contrast to conventional supratransmission in band gaps (mediated by gap solitons), in-band supratransmission is mediated by nonlinear plane waves.

The authors report that, beyond perfectly flat bands, a supratransmission threshold also manifests when the band is nearly flat. However, the fundamental origin of this threshold in the nearly flat case is not yet established. Understanding the mechanism would elucidate how nonlinearity, topology, and band flatness collectively produce (or inhibit) transmission at in-band frequencies.