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Added by
Henrik Ronellenfitsch
Publication date
2019
fields
Physics
and research's language is
English
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The transfer of topological concepts from the quantum world to classical mechanical and electronic systems has opened fundamentally new approaches to protected information transmission and wave guidance. A particularly promising technology are recently discovered topolectrical circuits that achieve robust electric signal transduction by mimicking edge currents in quantum Hall systems. In parallel, modern active matter research has shown how autonomous units driven by internal energy reservoirs can spontaneously self-organize into collective coherent dynamics. Here, we unify key ideas from these two previously disparate fields to develop design principles for active topolectrical circuits (ATCs) that can self-excite topologically protected global signal patterns. Realizing autonomous active units through nonlinear Chua diode circuits, we theoretically predict and experimentally confirm the emergence of self-organized protected edge oscillations in one- and two-dimensional ATCs. The close agreement between theory, simulations and experiments implies that nonlinear ATCs provide a robust and versatile platform for developing high-dimensional autonomous electrical circuits with topologically protected functionalities.
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Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological drumhead surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment that maps out the topological drumhead region of a Hopf-link.
Higher-order topological insulators are a new class of topological phases of matter, originally conceived for electrons in solids. It has been suggested that $mathbb{Z}_N$ Berry phase (Berry phase quantized into $2pi/N$) is a useful tool to characterize the symmetry protected topological states, while the experimental evidence is still elusive. Recently, topolectrical circuits have emerged as a simple yet very powerful platform for studying topological physics that are challenging to realize in condensed matter systems. Here, we present the first experimental observation of second-order corner states characterized by $mathbb{Z}_3$ Berry phase in topolectrical circuits. We demonstrate theoretically and experimentally that the localized second-order topological states are protected by a generalized chiral symmetry of tripartite lattices, and they are pinned to zero energy. By introducing extra capacitors within sublattices in the circuit, we are able to examine the robustness of the zero modes against both chiral-symmetry conserving and breaking disturbances. Our work paves the way for testing exotic topological band theory by electrical-circuit experiments.
The study of the laws of nature has traditionally been pursued in the limit of isolated systems, where energy is conserved. This is not always a valid approximation, however, as the inclusion of features like gain and loss, or periodic driving, qualitatively amends these laws. A contemporary frontier of meta-material research is the challenge open systems pose to the established characterization of topological matter. There, one of the most relied upon principles is the bulk-boundary correspondence (BBC), which intimately relates the properties of the surface states to the topological classification of the bulk. The presence of gain and loss, in combination with the violation of reciprocity, has recently been predicted to affect this principle dramatically. Here, we report the experimental observation of BBC violation in a non-reciprocal topolectric circuit. The circuit admittance spectrum exhibits an unprecedented sensitivity to the presence of a boundary, displaying an extensive admittance mode localization despite a translationally invariant bulk. Intriguingly, we measure a non-local voltage response due to broken BBC. Depending on the AC current feed frequency, the voltage signal accumulates at the left or right boundary, and increases as a function of nodal distance to the current feed.
Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness - topological protection, as well as the non-Hermitian skin effect. In this work, we report the first experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various novel states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for new applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.
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.
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