Non-Hermitian topological phases and exceptional lines in topolectrical circuits

Abstract

We propose a scheme to realize various non-Hermitian topological phases in a topolectrical (TE) circuit network consisting of resistors, inductors, and capacitors. These phases are characterized by topologically protected exceptional points and lines. The positive and negative resistive couplings R g in the circuit provide loss and gain factors which break the Hermiticity of the circuit Laplacian. By controlling R g, the exceptional lines of the circuit can be modulated, e.g. from open curves to closed ellipses in the Brillouin zone. In practice, the topology of the exceptional lines can be detected by the impedance spectra of the circuit. We also considered finite TE systems with open boundary conditions, the admittance spectra of which exhibit highly tunable zero-admittance states demarcated by boundary points (BPs). The phase diagram of the system shows topological phases that are characterized by the number of their BPs. The transition between different phases can be controlled by varying the circuit parameters and tracked via the impedance readout between the terminal nodes. Our TE model offers an accessible and tunable means of realizing different topological phases in a non-Hermitian framework and characterizing them based on their boundary point and exceptional line configurations.

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

“…Note that the sign of the non-Hermitian part of the couplings C ni can be flipped by reversing the biasings of the operational amplifier in the inter-cell and intracell segment couplings with respect to each other. This sign flipping of C ni in the asymmetric coupling is also known as negative impedance converter with current inversion (INIC) [63,64]. For notational convenience, we denote (iω) −1 L(β, ω) as H(β, ω) and call it the "normalized Laplacian" where ω is the frequency of the driving AC signal:…”

Critical non-Hermitian Skin Effect in a Single Closed non-Hermitian Chain

“…Non-Hermitian phenomena [1][2][3][4] are one of the most exciting topics that have emerged in condensed matter physics. In general, the breaking of Hermiticity by non-reciprocal couplings between lattice sites or onsite gain/loss terms [5][6][7] can induce a plethora of unusual phenomena that include exceptional points [5,8,9], nodal rings [10], and the extensive localization of eigenstates [11][12][13][14][15], also known as the non-Hermitian skin effect (NHSE). The NHSE can be exploited for ultra-sensitive sensors [16,17], unidirectional transport [18], and the amplification and attenuation of quantum signals [19,20].…”

Complex–Real Transformation of Eigenenergies and Topological Edge States in Square‐Root Non‐Hermitian Topolectrical Circuits

“…For example, first‐order topological states involve 1D Su–Schrieffer–Heeger (SSH) models, [ 28–30 ] 2D topological insulators, [ 31–34 ] and 3D Weyl and nodal line semimetals, [ 35–37 ] higher‐order topological states, [ 38–42 ] and non‐Hermitian topological states. [ 43–49 ]…”