Gap-tuned exceptional skin effect in non-Hermitian flat bands.

Flat-band states in Hermitian systems exhibit compact localization in the bulk due to geometric or symmetry constraints, while non-Hermitian skin effects drive state accumulation at boundaries via asymmetric lattice hoppings. Despite extensive efforts devoted to studying these two effects separately, the interplay between these competing mechanisms remains largely unexplored. Here we reveal a tuneable interplay between them by introducing non-reciprocal hopping in low-dimensional lattice hosting isolated, symmetry-protected flat bands. We demonstrate that closure of the real or imaginary line gap between the flat band and dispersive bands induces exceptional skin effects (ESEs) - boundary localization of flat-band states despite their vanishing group velocity and intrinsic immunity to conventional skin effect. This phenomenon arises from exceptional points formed under periodic boundaries, where the flat band becomes enclosed by the spectral loop of dispersive states, enabling wavefunction mixing and skin accumulation. Supported by generalized Brillouin zone analysis, perturbation theory, and electrical circuit experiments, our findings establish band gaps as a primary tuning parameter for non-Hermitian localization, distinct from system size or reciprocity strength. These findings unveil a new class of gap-engineered non-Hermitian flat-band phenomena with implications for reconfigurable wave localization in photonic, acoustic, and electronic platforms.