Twisted topology and Bipolar Non-Hermitian Skin Effect induced by long-range asymmetric coupling

We investigate the twisted topology of the complex eigenspectrum of a one-dimensional non-Hermitian system under the influence of long-range unidirectional coupling. Unlike the complex energy spectrum of the conventional Hatano-Nelson chain, which takes the form of a single loop with a topological winding index of a definite sign, the introduction of long-range unidirectional hopping results in the creation of multiple twisted loops. These twisted loops exhibit opposite signs of the topological winding index, which correlate to alternating clockwise and anticlockwise energy windings. The simultaneous presence of both signs of the winding index translates into a bipolar non-Hermitian skin effect (NHSE), which challenges the conventional wisdom that the NHSE localization is dependent on the direction of the dominant nearest-neighbor interactions. In this bipolar NHSE, the exponents of the complex energy eigenvectors corresponding to clockwise and anti-clockwise windings, lie inside and outside of the complex unit circle, respectively. Interestingly, at the intersections of oppositely oriented energy loops where the sign of the topological winding index flips, the energy becomes real-valued, leading to a suppression of the NHSE. This marks the emergence of Bloch-like contact points, where both the bipolar NHSE and the traditional NHSE vanish. Based on the non-Hermitian model we provide analytical insights into the effects of long-range unidirectional coupling to the winding topology of its complex energy spectra and their broader implications for the field of condensed matter physics.Comment: 11 pages, 3 figure

Impedance responses and size-dependent resonances in topolectrical circuits via the method of images

Resonances in an electric circuit occur when capacitive and inductive components are present together. Such resonances appear in admittance measurements depending on the circuit's parameters and the driving AC frequency. In this study, we analyze the impedance characteristics of nontrivial topolectrical circuits such as one- and two-dimensional Su-Schrieffer-Heeger circuits and reveal that size-dependent anomalous impedance resonances inevitably arise in finite $LC$ circuits. Through the \textit{method of images}, we study how resonance modes in a multi-dimensional circuit array can be nontrivially modified by the reflection and interference of current from the structure and boundaries of the lattice. We derive analytic expressions for the impedance across two corner nodes of various lattice networks with homogeneous and heterogeneous circuit elements. We also derive the irregular dependency of the impedance resonance on the lattice size, and provide integral and dimensionally-reduced expressions for the impedance in three dimensions and above.Comment: 24 pages, 10 figure

TOPOLOGICAL MATERIALS AND THEIR TOPOLECTRICAL CIRCUIT MODELS

Ph.DDOCTOR OF PHILOSOPHY (FOE

A new rain attenuation conversion technique for tropical regions

Rain attenuation is one of the most crucial factors to be considered in the link budget estimation for microwave satellite communication systems, operating at frequencies above 10 GHz. This paper presents a mathematical model for converting terrestrial rain attenuation data to be used for satellite applications at Ku-band. In the proposed technique, the ITU-R P 618-9, together with a combination of ITU-R P 530-12 and the revised Moupfouma model have been adopted for satellite and terrestrial rain attenuation predictions, respectively. The model has been used for transforming the measured rain attenuation data of some DIGI MINI-LINKS operating at 15 GHz in Malaysia, to be used for MEASAT 2 applications. It was found that the model predictions are fairly reasonable when compared with direct beacon measurements in Malaysia and similar tropical locations. The model will provide a relatively accurate method for transforming the measured terrestrial rain attenuation to be used for satellite applications; and therefore substantially reduce the cost of implementing Earth-satellite links in some tropical regions that have suffcient rain attenuation data for the terrestrial links

Non-Hermitian topological phases and exceptional lines in topolectrical circuits

10.1088/1367-2630/abe6e4New Journal of Physics2333301

Terminal-coupling induced critical eigenspectrum transition in closed non-Hermitian loops

Abstract A hallmark feature of non-Hermitian (NH) systems is the non-Hermitian skin effect (NHSE), in which the eigenenergy spectra of the system under open boundary conditions (OBC) and periodic boundary conditions (PBC) differ markedly from each other. In particular, the critical NHSE occurs in systems consisting of multiple non-Hermitian chains coupled in parallel where even an infinitesimally small inter-chain coupling can cause the thermodynamic-limit eigenenergy spectrum of the system to deviate significantly from the OBC spectra of the individual component chains. We overturn the conventional wisdom that multiple chains are required for such critical transitions by showing that such a critical effect can also be induced in a single finite-length non-Hermitian chain where its two ends are connected together by a weak terminal coupling to form a closed loop. An infinitesimally small terminal coupling can induce the thermodynamic-limit energy spectrum of the closed loop to switch from the OBC to the PBC spectrum of the chain. Similar to the critical NHSE, this switch occurs abruptly when the chain length exceeds a critical size limit. We explain analytically the underlying origin of the effect in a Hatano–Nelson chain system, and demonstrate its generality in more complex one-dimensional non-Hermitian chains. Our findings illustrate the generality of critical size-dependent effects in finite NH systems that arise from the interplay between the interfacial boundary conditions and the influence of edge localization

Interfacial skin modes at a non-Hermitian heterojunction

We uncover a non-Hermitian skin mode in which the eigenmodes of a nonreciprocal topoelectrical (TE) heterojunction circuit array are localized at the heterojunction interface under both open boundary condition (OBC) and periodic boundary condition (PBC). This is in marked contrast to the conventional non-Hermitian skin effect (NHSE) in homogenous non-Hermitian systems that exists under OBC but vanishes in PBC. The interfacial non-Hermitian skin effect is induced when two non-Hermitian circuit chain segments with dissimilar NHSE decay lengths are cascaded together. It is shown analytically that the interfacial NHSE decay rates are directly associated with the asymmetric intracell couplings in the TE segments. Such nonreciprocal directional couplings can be realized in practical circuits by means of negative impedance converters with current inversion (INIC). In contrast to the conventional NHSE in homogeneous systems, the TE heterojunction circuit allows for a voltage profile localized at the interface, that is independent of the boundary conditions and whose decay length can be modulated by circuit parameters. Finally, the results presented are general and applicable to other analogous non-Hermitian platforms such as photonic and condensed matter nanoscale systems

Critical hybridization of skin modes in coupled non-Hermitian chains

Non-Hermitian topological systems exhibit a plethora of unusual topological phenomena including the extreme localization of eigenstates, known as the non-Hermitian skin effect (NHSE), which occurs in open chains. However, the non-Hermitian characteristics of coupled non-Hermitian chains remain largely unexplored. Here, we report on the eigenstate localization in coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on and off by modulating the interchain coupling strength. In the limit of small interchain strength, the NHSE is present at both ends of the coupled system because of the weak hybridization of the eigenstates of the individual chains. The eigenspectrum under open boundary conditions (OBC) exhibits a discontinuous jump known as the critical NHSE (CNHSE) as the chain length increases. However, when the interchain coupling strength and hence, the hybridization between eigenstates become significant, the NHSE and CNHSE vanish. Instead, a peculiar “half-half skin localization” occurs in composite chains with opposite signs of inverse skin lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide new insights into the non-Hermitian phenomena in coupled systems

Unconventional skin modes in generalized topolectrical circuits with multiple asymmetric couplings

The eigennmodes in a non-Hermitian system containing nonreciprocal couplings may exhibit an extreme localization, also known as non-Hermitian skin effect (NHSE), under open boundary conditions. Here, we ex- plore unconventional scenarios where the interplay between multiple asymmetric couplings can cause the NHSE to vanish, unlike in known models with nonreciprocal couplings, where the NHSE vanishes only when the non-Hermiticity is turned off. We derive general conditions for the NHSE in a non-Hermitian superlattice in which the overall eigenmode localization is 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. We provide explicit electrical circuit setups for realizing our observations, which also extend to other established platforms such as photonics, mechanics, and optics systems, and quantum circuits