Observation of fractional disclination charges induced by gain and loss

Fractional charge, a hallmark of modern electric polarization theory, provides a topological framework for understanding quantized polarization. Until recently has it been recognized that real-space topological defects, like disclinations, can further modify charge fractionalization, as an interplay between momentum-space and real-space topologies. So far, all demonstrated mechanisms leading to fractional disclination charges have been limited to Hermitian, or energy-conserved, systems. While the non-Hermiticity has theoretically been predicted as a new route to modifying fractional disclination charge, experimental evidence remains lacking, primarily due to challenges in measuring biorthogonal bases and precisely controlling gain/loss. Here, on a circuit metamaterial platform, we experimentally demonstrate the fractional disclination charge modification solely by manipulating the gain/loss. In experiments, negative resistors are employed as on-site gain, while positive ones as on-site loss. Via measuring admittance and calculating the local density of states, we observe the topological disclination states and the associated fractionalized disclination charge. Moreover, by precisely tuning the spatial distribution of gain and loss, we observe a transition in disclination charge from fractional to integer values, with the vanishing of localized states and a topological phase transition from nontrivial to trivial. Our experimental observations demonstrate a distinctive interplay between non-Hermiticity and real-space topological defects.