Symmetry-Protected Locally Confined Eigenstates Oscillation in Topolectrical Heterosystem

We demonstrate a controllable novel local confinement of voltage oscillations in a topolectrical (TE) heterosystem constructed with typical RLC circuit components by exploiting the underlying symmetries of its admittance spectrum. The system comprises of TE Su-Schrieffer-Heeger chain with different inter- and intra-unit cell coupling capacitances in which alternating onsite gain and loss are introduced through resistors coupled to operational amplifiers in the non-Hermitian (NH) half of the chain while the Hermitian part remains resistor-free. By adjusting the resistance in the NH segment, the admittance spectrum of the system can be made to exhibit parity-time (PT) symmetry in which all the admittance eigenvalues of the entire chain are real, and the corresponding voltage eigenstates are delocalized throughout all the circuit nodes. In contrast, when the NH segment is tuned to an anti-PT symmetric configuration, the eigenmodes with imaginary eigenvalues are localized exclusively within the NH segments while those with real eigenvalues are localized within only the Hermitian segment. This remarkable phenomenon represents a novel symmetry-protected and controlled confinement of voltage oscillations in TE heterojunctions, which is of practical utility in topological electronics.