Fractional charge, a hallmark of modern electric polarization theory, provides a topological framework for understanding quantized polarization. It has only recently been recognized that real-space topological defects, such as disclinations, can further modify charge fractionalization, as an interplay between momentum-space and real-space topologies. So far, all the demonstrated mechanisms that lead to fractional disclination charges have been limited to Hermitian or energy-conserved systems. Although the non-Hermiticity has theoretically been predicted as a new route to modifying fractional disclination charge, experimental evidence remains lacking, mainly because of the 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. By 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, which coincided with the vanishing of localized disclination 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.
Li et al. (Sun,) studied this question.