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Bulk-boundary correspondence is a concept for topological insulators and superconductors that determines the existence of topological boundary states within the tenfold classification table. Contrary to this belief, we demonstrate that topological domain-wall states can emerge in all forbidden 1D classes in the classification table using representative generalized Su-Schrieffer-Heeger and Kitaev models, which manifests as quantized electric dipole moments and Majorana zero modes, respectively. We first show that a zero-energy domain-wall state can possess a quantized polarization, even if the polarization of individual domains is not inherently quantized. A quantized Berry phase difference between the domains confirms the non-trivial nature of the domain-wall states, implying a general-bulk-boundary principle, further confirmed by the tight-binding, topological field, and low-energy effective theories. Our methodology is then extended to a superconducting system, resulting in Majorana zero modes on the domain wall of a generalized Kitaev model. Finally, we suggest potential systems where our results may be realized, spanning from condensed matter to optical.

Chirality, a fundamental concept from biological molecules to advanced materials, is prevalent in nature. Yet, its intricate behavior in specific topological systems remains poorly understood. Here, we investigate the emergence of hidden chiral domain wall states using a double-chain Su-Schrieffer-Heeger model with interchain coupling specifically designed to break chiral symmetry. Our phase diagram reveals single-gap and double-gap phases based on electronic structure, where transitions occur without topological phase changes. In the single-gap phase, we reproduce chiral domain wall states, akin to chiral solitons in the double-chain model, where chirality is encoded in the spectrum and topological charge pumping. In the double-gap phase, we identify hidden chiral domain wall states exhibiting opposite chirality to the domain wall states in the single-gap phase, where the opposite chirality is confirmed through spectrum inversion and charge pumping as the corresponding domain wall slowly moves. By engineering gap structures, we demonstrate control over hidden chiral domain states. Our findings open avenues to investigate novel topological systems with broken chiral symmetry and potential applications in diverse systems.

We investigate the roles of symmetry and bulk-boundary correspondence in characterizing topological edge states in generalized Jackiw-Rebbi (JR) models. We show that time-reversal ($T$), charge-conjugation ($C$), parity ($P$), and discrete internal field rotation ($Z_n$) symmetries protect and characterize the various types of edge states such as chiral and nonchiral solitons via bulk-boundary correspondence in the presence of the multiple vacua. As two representative models, we consider the JR model composed of a single fermion field having a complex mass and the generalized JR model with two massless but interacting fermion fields. The JR model shows nonchiral solitons with the $Z_2$ rotation symmetry, whereas it shows chiral solitons with the broken $Z_2$ rotation symmetry. In the generalized JR model, only nonchiral solitons can emerge with only $Z_2$ rotation symmetry, whereas both chiral and nonchiral solitons can exist with enhanced $Z_4$ rotation symmetry. Moreover, we find that the nonchiral solitons have $C, P$ symmetries while the chiral solitons do not, which can be explained by the symmetry-invariant lines connecting degenerate vacua. Finally, we find the symmetry correspondence between multiply-degenerate global vacua and solitons such that ${T}$, ${C}$, ${P}$ symmetries of a soliton inherit from global minima that are connected by the soliton, which provides a novel tool for the characterization of topological solitons.

In this work, we investigate collision processes and their mechanism among chiral and nonchiral kinks in the coupled double-field $\phi^4$ model and show that the kink collisions follow the $Z_4$ abelian group operation. Unlike the single-field $\phi^4$ model, this model has twelve kinks, which are classified into chiral and nonchiral kinks depending on their topological chiral charges. This enriches the variety of the collision processes. From the numerical simulation, we observe three kinds of collisions depending on the initial configuration and initial velocities of colliding kinks. During a collision, the topological chiral charges of kinks switch while preserving the $Z_4$ abelian group operation. To understand the collision and chirality switching mechanism, we investigate the detailed collision process, energy densities, the field gradients, internal modes, energy exchange between two fields, coherent vibration of two bions located in different fields, and the orbits of colliding kinks in the two-dimensional field space.

In this work, we propose a new signal routing method for solving routing problems that occur in the design process of semiconductor package substrates. Our work uses a topological transformation of the layers of the package substrate in order to simplify the routing problem into a problem of connecting points on a circle with non-intersecting straight line segments. The circle, which we call the Circular Frame, is a polygonal schema, which is originally used in topology to study the topological structure of 2-manifolds. We show through experiments that our new routing method based on the Circular Frame competes with certain grid-based routing algorithms., Comment: 24 pages, 22 figures, 3 tables

In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a topological transformation on the 2-dimensional planar routing environment that simplifies the routing problem into a problem of connecting points on a circle with straight line segments that do not intersect in the interior of the circle. These points are either the points that need to be connected by non-intersecting paths or special `reference' points that parametrize the topology of the original environment prior to the transformation. When all the necessary points on the circle are fully connected, the transformation is reversed such that the line segments combine to become the non-intersecting paths that connect the start and end points in the original environment. We interpret the transformed environment in which the routing problem is solved as a new data structure where any routing problem can be solved efficiently. We perform experiments and show that the routing time and success rate of the new routing algorithm outperforms the ones for the A*-algorithm., Comment: 15 pages, 10 figures

Topological phases and their topological features are enriched by the fundamental time-reversal, particle-hole, and chiral as well as crystalline symmetries. While one-dimensional (1D) generalized Su-Schrieffer-Heeger (SSH) systems show various topological phenomena such as topological solitons and topological charge pumping, it remains unclear how such symmetry protects and relates such topological phenomena. Here we show that the generalized time-reversal, particle-hole, and chiral symmetry operators consistently explain not only the symmetry transformation properties between the ground states but also the topological features of the topological solitons in prototypical quasi-1D systems such as the SSH, Rice-Mele, and double-chain models. As a consequence, we classify generalized essential operators into three groups: Class I and class II operators connect ground states in between after spontaneous symmetry breaking while class III operators give the generalized particle-hole and chiral symmetries to ground states. Furthermore, class I operators endow the equivalence relation between topological solitons while class II and III operators do the particle-hole relations. Finally, we demonstrate three distinct types of topological charge pumping and soliton chirality from the viewpoint of class I, II, and III operators. We build a general framework to explore the topological features of the generalized 1D electronic system, which can be easily applied in various condensed matter systems as well as photonic crystal and cold atomic systems., Comment: 18 pages, 7 figures, 8 tables

We study terahertz transmission through nano-patterned vanadium dioxide thin film. It is found that the patterning allows the lowering of the apparent transition temperature. For the case of the smallest width nano antennas, the transition temperature is lower by as many as ten degrees relative to the bare film, so that the nano patterned hysteresis curves completely separate themselves from their bare film counterparts. This early transition comes from the one order of magnitude enhanced effective dielectric constants by nano antennas. This phenomenon opens up the possibility of transition temperature engineering.