Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

Abstract

A non-Hermitian system is characterized by the violation of energy conservation. As a result of unbalanced gain or loss in the forward and backward directions due to non-reciprocal couplings, the eigenmodes of such systems exhibit extreme localization, also known as non-Hermitian skin effect (NHSE). This work explores unconventional scenarios where the interplay of multiple asymmetric couplings can cause the NHSE to vanish, with the admittance spectra taking identical dispersion under open boundary conditions (OBC) and periodic boundary conditions (PBC). This is unlike known non-Hermitian models where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE, with the overall eigenmode localization determined by the geometric mean of the cumulative contributions of all asymmetric coupling segments. In the limit of large unit cells, our results provide a route towards the NHSE caused by asymmetric hopping textures, rather than single asymmetric hoppings alone. Furthermore, our generalized model can be transformed into a square-root lattice simply by tuning the coupling capacitors, where the topological edge states occur at a non-zero admittance, in contrast to the zero-admittance states of conventional topological insulators. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, optics and quantum circuits.

Chiral surface and hinge states in higher-order Weyl semimetallic circuits

“…In the search for alternative platforms to serve as experimental testbeds for investigating topological states, lattice arrays with lossless electrical components such as inductors and capacitors known as topolectrical (TE) circuits have emerged as a frontrunner [23,[55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71] as they offer better ability for tuning and modulating the system parameters. Because TE circuits are not constrained by physical dimensionality but rely solely on the mutual connectivities between the voltage nodes, HOTIs and higher-order gapless systems [36,37] (i.e, HODSMs and HOWSMs) can be readily implemented using conventional electrical components.…”

Critical hybridization of skin modes in coupled non-Hermitian chains

“…Interestingly, non-Hermitian systems host a plethora of unusual phenomena that include exceptional points [23,34,35], nodal rings [36,37], extensive localization of eigenstates [38][39][40][41], unidirectional transport [42,43], and the amplification and attenuation of quantum signals [44,45]. To date, one of the most iconic features of a non-Hermitian system is the non-Hermitian skin effect (NHSE) [41,[46][47][48][49][50][51][52][53][54][55], where the eigenstates experience extreme exponential localization in the vicinity of the boundaries. Several non-Hermitian systems have been realized in various platforms including topolectrical [56][57][58][59][60][61][62], photonics [63,64], optics [65,66], mechanical [58,67], acoustic [68,69] and superconductors [70,71], which offer broader accessibility and experimental flexibility in dynamic tuning of model parameters than condensed matter systems.…”