Flat bands host compact localized states arising from destructive interference and exhibit enhanced sensitivity to weak perturbations, making them a versatile arena for band-geometry engineering. The present geometry-tunable splitting provides a linear-wave analog of flat-band reconstruction, enabling controllable gaps without invoking intrinsic nonlinearity. This work demonstrates that in a two-dimensional periodic conductor array of Lieb lattice, interlayer inductive coupling enables the single-layer zeroth-order flat band to split into two Even-Odd branches that are continuously tunable. Due to the mutual inductance depending on the interlayer spacing, geometry-induced hybridization gap is realized without nonlinear elements. Circuit theory and numerical analysis validate the approach, advancing geometry-based band engineering and reconfigurable photonics.

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• Flat bands
• Plasmonics
• Topological materials