Fig. 4: Flat band enabled by the EC with hybrid coupling.

a Schematic of periodic chain composed of on-site resonator A (\({\omega }_{0}\)) and detuning coupled resonator B (\({\omega }_{r}\)). b Experimental design of ring-like coupled resonance system with four on-site resonators (i.e., resonators A, C, E, and G) and four detuning coupled resonators (i.e., resonators B, D, F, and H). c The corresponding band structure of the ring-like system for different coupling strength: \(\kappa /2\pi =18\) kHz (\(\kappa < {\kappa }_{c}\)), 46 kHz (\(\kappa ={\kappa }_{c}\)), 60 kHz (\(\kappa > {\kappa }_{c}\)), which are marked by blue, black and red lines, respectively. d Measured DOS of system with \(\kappa /2\pi =18\) kHz (blue), 46 (black), and 60 (red). Red and blue area represents band in (c), and they overlap from 1.618 MHz to 1.628 MHz. e Measured field intensity of coils in ring-like system with coil A excited. Solid lines and dotted lines represent site A and site B separately. The green dashed line represents flat band with \(f=1.454\) MHz.