  Wave localization is a fundamental phenomenon that appears universally in
both natural materials and artificial structures and plays a crucial role in
understanding the various physical properties of a system. Usually, a localized
state has an exponential profile with a localization length independent of the
system size. Here, we experimentally demonstrate a new class of localized
states called scale-free localized states, which has an unfixed localization
length scaling linearly with the system size. Using circuit lattices, we
observe that a non-Hermitian defect added to a Hermitian lattice induces an
extensive number of states with scale-free localization. Furthermore, we
demonstrate that, in a lattice with a parity-time-symmetric non-Hermitian
defect, the scale-free localization emerges because of spontaneous parity-time
symmetry breaking. Our results uncover a new type of localized states and
extend the study of defect physics to the non-Hermitian regime.
