Topological phases with higher winding numbers in nonreciprocal one-dimensional topolectrical circuits

We propose the realization of higher winding number topological states in a one-dimensional system by means of a non-Hermitian, nonreciprocal topoelectrical (TE) circuit lattice. The crucial element of the circuit is a directional intercell pi-phase coupling which is realized by operational amplifiers (op-amps). The phase of the coupling coefficients can be modulated by the choice of capacitive or inductive hoppings between the voltage nodes. The resulting topological state has a winding number of 2 compared to its Hermitian counterpart, which can have at most a winding number of one. Furthermore, in this system the nontrivial topological eigenmodes are localized at the edges. This localization can coexist with the non-Hermitian skin effect, the latter of which is induced by having different magnitudes of the left- and right-directional couplings. In practice, the higher winding number topological state can be distinguished from the trivial phase by the much higher resonant impedance values. Furthermore, by shunting the op-amps, we can recover the Hermiticity of the system and the conventional topological phase. The experimental accessibility and unprecedented tunability of the model parameters in our TE model provide a ready platform for the realization and detection of higher winding number topological phases in one-dimensional systems.

Automated summary

We propose the realization of higher winding number topological states in a one-dimensional system using a non-Hermitian, nonreciprocal topoelectrical (TE) circuit lattice. The crucial element is a directional intercell pi-phase coupling achieved through operational amplifiers (op-amps). The resulting topological state has a winding number of 2 compared to its Hermitian counterpart, and the nontrivial topological eigenmodes are localized at the edges in this system.