Weyl semimetals (WSMs) are a recent addition to the family of topological materials, and the physical realization of heterojunctions between different types of WSMs is challenging. Here, we use electrical components to create topoelectrical (TE) circuits for modeling and studying the transmission across heterojunctions, consisting of a Type I WSM source to a drain in the Type II or intermediary Type III WSM phase. For transport from a Type I WSM source to a Type II WSM drain, valley-independent (dependent) energy flux transmission occurs when the tilt and transmission directions are perpendicular (parallel) to each other. Furthermore, “anti-Klein” tunneling occurs between a Type I source and Type III drain where the transmission is totally suppressed for certain valleys at normal incidence. Owing to their experimental accessibility, TE circuits offer an excellent testbed for transport phenomena in WSM-based heterostructures.

In this work, we demonstrate a simple and effective method to design and realize various Weyl semimetal (WSM) states in a three-dimensional periodic circuit lattice composed of passive electric circuit elements such as inductors and capacitors (LC). The experimental accessibility of such LC circuits offers a ready platform for the realization of not only various WSM phases but also for exploring transport properties in topological systems. The characteristics of such LC circuits are described by the circuit admittance matrices, which are mathematically related to the Hamiltonian of the quantum tight-binding model. The system can be switched between the Type-I and Type-II WSM phases simply by an appropriate choice of inductive or capacitive coupling between certain nodes. A peculiar phase with a flat admittance band emerges at the transition between the Type-I and Type-II Weyl phases. Impedance resonances occur in the LC circuits at certain frequencies associated with vanishing eigenvalues of the admittance matrix. The impedance readout can be used to classify the Type-I and Type-II WSM states. A Type-I WSM shows impedance peaks only at the Weyl points (WPs) whereas a Type-II WSM exhibits multiple secondary peaks near the WPs. This impedance behaviour reflects the vanishing and non-vanishing density of states at the Weyl nodes in the Type-I and Type-II WSM phases, respectively.

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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.

Topoelectrical (TE) circuits consisting of capacitors and inductors can be designed to exhibit various Weyl semimetal (WSM) phases in their admittance dispersion. We consider a TE heterojunction circuit consisting of a central region sandwiched by source and drain regions. The energy flux transmission across the heterojunction can be tuned to exhibit perfect transmission near normal incidence (Klein tunneling) for one valley and perfect reflection (anti-Klein tunneling) for the other valley by controlling the WSM phases of the heterojunction. Perfect valley-polarized transmission occurs when the dispersion tilt to Fermi velocity ratio in the source region is reciprocal to that in the central barrier region. This unusual flux transmission is ascribed to two factors, i.e., perfect pseudospin (sublattice) polarization at normal incidence and complete decoupling of one of the sublattice polarizations at the critical velocity ratio. The emergence of anti-Klein tunneling by design in TE circuits suggests a possible realization of the effect in real WSM materials.