Observation of Flatband Skin Effect in a Mechanical Lattice.

Symmetry-protected ideal flat bands in one-dimensional Hermitian lattices are populated by compact localized states-a special class of localization with wave functions confined within a small region. In this Letter, we demonstrate that the non-Hermitian skin effect can appear in a flat band. Unlike conventional non-Hermitian skin effects for dispersive bands that are protected by nontrivial point-gap topology, the flat-band skin effect (FBSE) emerges even though the flat band remains a point on the complex-energy plane with trivial spectral topology. The FBSE is intriguingly associated with the nontrivial spectral topology of the dispersive bands enclosing the flat band, so it only emerges within a finite range of non-Hermitian parameters and can counterintuitively disappear at large non-Hermiticity. We experimentally observe the FBSE and its parameter dependence in a non-Hermitian mechanical lattice. Our theoretical analyses further reveal that the gap between the flat and the dispersive bands can close at higher-order exceptional points under both periodic and open boundary conditions. The flat-band wave functions are discontinuous in quantum distance across these exceptional points, a property only found in singular flat bands in Hermitian systems. Our Letter reveals flat-band phenomena unique to non-Hermitian systems and highlights new possibilities in quantum geometry and localization control.