AC Frequency Modulated Phase Transitions in Topolectrical Circuits

Abstract

Topolectrical (TE) circuits have not only bridged the seemingly different disciplines of electrical circuits and topological condensed matter but also allowed the realization of highly tunable lattice systems with desired topological properties based on the parameters of the corresponding TE circuit lattices [1, 2]. The frequency dependence of the electrical inter-node couplings (i.e., the admittance of capacitors and inductors) suggests that the circuits can be switched between the insulating, semimetallic, and Chern insulator phases by varying the frequency of the alternating signal [3]. Here, we propose a TE circuit lattice that exhibits this switching within a single circuit set-up. We consider a 2-dimensional (2D) TE circuit containing two types of nodes A and B (Fig. 1a) with complex nearest-neighbor couplings (combination of capacitive and resistive) realized via negative impedance converters (NICs) (Fig. 1b) and capacitive next-nearest neighbor (NNN) couplings. The critical frequency of the circuit depends only on the grounding inductor and NNN capacitor (Fig. 1c). In the absence of resistive coupling, the TE circuit respects time-reversal symmetry (TRS) and hosts insulating and semimetallic phases when the frequency is less than, and greater or equal to the critical frequency, respectively. Furthermore, the 2D Weyl points in the semimetallic phase are connected by topological edge states in the admittance spectra (Fig. 2b,e). However, a non-zero Rd breaks TRS and a bulk bandgap appears. Chiral edge states emerge under open boundary conditions and the circuit exhibits the quantum anomalous Hall effect at ω > ωc (Fig. 2f). Moreover, the Chern number of the system changes signs when the frequency crosses the critical value.  a. Schematic of frequency-dependent Chern circuit. b. NIC and grounding connections. c. System Hamiltonian and critical frequency.  a-f. Admittance dispersion of a finite system at different frequencies. The top and bottom rows correspond to zero and non-zero resistive couplings, respectively. Common parameters: C1=1.5 mF, C2=1 mF and Lm=1 nH.