Multiple Topological Transitions Research Articles

Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems

Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems

Photonic Molecule Approach to Multiorbital Topology.

The concepts of topology provide a powerful tool to tailor the propagation and localization of the waves. While electrons have only two available spin states, engineered degeneracies of photonic modes provide novel opportunities resembling spin degrees of freedom in condensed matter. Here, we tailor such degeneracies for the array of femtosecond laser written waveguides in the optical range exploiting the idea of photonic molecules: clusters of strongly coupled waveguides. In our experiments, we observe unconventional topological modes protected by the Z3 invariant arising due to the interplay of interorbital coupling and geometric dimerization mechanism. We track multiple topological transitions in the system with the change in the lattice spacings and excitation wavelength. This strategy opens an avenue for designing novel types of photonic topological phases and states.

Multiple topological transitions and topological edge states of triple-site honeycomb lattice photonic crystals

We propose a two-dimensional (2D) triple-site honeycomb lattice (TSHL) photonic crystal (PC) by rotating the three dielectric rods six times, forming unit cell, and then arraying the unit cells in the triangular lattice. The TSHL PC structure can achieve topological phase transitions in three ways, which are changing the position or size of the rods, and rotating the rods. By calculating the band structure under different parameters, the law of topological phase transition for TSHL PC is analyzed. The topological edge state can be adjusted by changing the rotation angle of the dielectric rods. Based on this, a frequency-selective beam splitter is designed. Compared with previous studies, this flexible topological system shows more abundant physical phenomena, enriches the implementation of topological photonics , and promotes the research of topological edge states and the development of topological insulators in practical applications. • We propose a two-dimensional triple-site honeycomb lattice photonic crystal, which has the high degrees of freedom. • The triple-site honeycomb lattice unit cell can achieve topological phase transitions in three ways, which are changing the position or size of the cylinders, and rotating the cylinders. • We design a frequency-selective beam splitter, by changing the rotation angle of the dielectric rods.

Manipulation of Antiskyrmion Phase in Mn2+xNi1−xGa Tetragonal Heusler System

The inhomogeneous magnetization distribution in antiskyrmions helps in nullifying the unwanted skyrmion Hall effect generally found in the current driven motion of skyrmions. At present, the observation of room-temperature antiskyrmion phase is limited to only a very few materials. Here, we present the evidence of a tunable antiskyrmion phase in the ${D}_{2d}$-symmetry-based tetragonal Heusler system ${\mathrm{Mn}}_{2+x}{\mathrm{Ni}}_{1\ensuremath{-}x}\mathrm{Ga}$. With the help of dc magnetization, ac susceptibility, and topological Hall effect measurements, we demonstrate that the potential antiskyrmion phase can be tuned over a wide compositional range with magnetic ordering temperature of above 600 K. In addition, we find the existence of multiple topological phase transitions for a certain Mn/Ni ratio where the magnetic anisotropy attains its maxima. Our micromagnetic simulations suggest that the transition from antiskyrmionium and antiskyrmion pockets to the conventional antiskyrmion phase at the optimal value of magnetic anisotropy might be responsible for the observed multiple topological transitions in the present materials. The expected small size of antiskyrmions in the present low magnetic-moment-based ferrimagnetic system gives a great advantage over other skyrmion and antiskyrmion hosting materials for their potential application in racetrack-based memory devices.

Robust transport of the edge modes along the photonic topological interfaces of different configurations

Two-dimensional photonic crystals made of six air holes on a core-shell dielectric material has been proposed to study the newly emerged photonic quantum spin Hall insulator. Specifically, radii modification of the air holes and core-shell without breaking time-reversal (TR) symmetry are supported by the C6 point group symmetry upon a proposed scheme. It is shown that multiple topological transitions from an ordinary insulator with zero spin Chern number (Cs) to a topological insulator with a non-zero Cs can be achieved by modifying the geometry of the photonic structure. Studying the two counter-propagating helical edge modes which have the opposite group velocities are of individual importance for various optical purposes like scattering-free waveguides protected to various defects, disorders and strong light-matter interactions. We show that topological edge states demonstrate slow light characteristics. The findings emphasize the fact that exploring topological phase transition can be applied as a unique approach for realizing light transport, robust energy transportation and slow light in integrated photonic circuits and devices.

Multiple topological transitions driven by the interplay of normal scattering and Andreev scattering

The effect of multiple topological transitions for electron-hole excitations is discovered in full shell proximitized semiconducting nanowires with trapped superconducting vortices, recently shown to be a promising platform for the realization of Majorana states at moderate longitudinal magnetic fields. The mechanism of such multiple transitions is uncovered and explained to be governed by the interplay of normal and Andreev reflections from the shell and by the textured spin-orbit coupling inside the semiconductor. The extensive analysis of emerging propagating and Majorana-type evanescent quasiparticle modes in such Andreev waveguides is performed. Experimentally, these modes reveal themselves in peculiarities of charge and spin-polarized heat transport.

Reconfigurable Topological Phases in Two-Dimensional Dielectric Photonic Crystals

The extensive research on photonic topological insulators has opened up an intriguing way to control electromagnetic (EM) waves. In this work, we numerically demonstrate reconfigurable microwave photon analogues of topological insulator (TIs) in a triangular lattice of elliptical cylinders, according to the theory of topological defects. Multiple topological transitions between the trivial and nontrivial photonic phases can be realized by inhomogeneously changing the ellipse orientation, without altering the lattice structure. Topological protection of the edge states and reconfigurable topological one-way propagation at microwave frequencies, are further verified. Our approach provides a new route towards freely steering light propagations in dielectric photonic crystals (PCs), which has potential applications in the areas of topological signal processing and sensing.

Multiple topological transitions in twisted bilayer graphene near the first magic angle

Recent experiments have observed strongly correlated physics in twisted bilayer graphene (TBG) at very small angles, along with nearly flat electron bands at certain fillings. A good starting point in understanding the physics is a continuum model (CM) proposed by Lopes dos Santos et al. [Phys. Rev. Lett. 99, 256802 (2007)] and Bistritzer et al. [PNAS 108, 12233 (2011)] for TBG at small twist angles, which successfully predicts the bandwidth reduction of the middle two bands of TBG near the first magic angle $\theta_0=1.05^\circ$. In this paper, we analyze the symmetries of the CM and investigate the low energy flat band structure in the entire moir\'e Brillouin zone near $\theta_0$. Instead of observing flat bands at only one "magic" angle, we notice that the bands remain almost flat within a small range around $\theta_0$, where multiple topological transitions occur. The topological transitions are caused by the creation and annihilation of Dirac nodes at either $\text{K}$, $\text{K}^\prime$, or $\Gamma$ points, or along the high symmetry lines in the moir\'e Brillouin zone. We trace the evolution of the nodes and find that there are several processes transporting them from $\Gamma$ to $\text{K}$ and $\text{K}^\prime$. At the $\Gamma$ point, the lowest energy levels of the CM are doubly degenerate for some range of twisting angle around $\theta_0$, suggesting that the physics is not described by any two band model. Based on this observation, we propose an effective six-band model (up to second order in quasi-momentum) near the $\Gamma$ point with the full symmetries of the CM, which we argue is the minimal model that explains the motion of the Dirac nodes around $\Gamma$ as the twist angle is varied. By fitting the coefficients from the numerical results, we show that this six-band model captures the important physics over a wide range of angles near the first "magic" angle.

Self-ordering induces multiple topological transitions for in-plane bulk waves in solid phononic crystals

Topological defects with symmetry-breaking phase transitions have captured much attention. Vortex generated by topological defects exhibits exotic properties and its flow direction can be switched by altering the spin configurations. Contrary to electromagnetic and acoustic domains, the topological transport of elastic waves in periodic structures with topological defects is not well explored due to the mode conversion between the longitudinal and transverse modes. Here, we propose an elastic topological insulator with spontaneously broken symmetry based on the topological theory of defects and homotopy theory. Multiple topological transitions for elastic waves are achieved by topologically modifying the ellipse orientation in a triangular lattice of elliptical cylinders. The solid system, independent of the number of molecules in order parameter space, breaks through the limit of the point-group symmetry to emulate elastic pseudospin-orbit coupling. The transport robustness of the edge states is experimentally demonstrated. Our approach provides new possibilities for controlling and transporting elastic waves.

Topological transitions in continuously deformed photonic crystals

We demonstrate that multiple topological transitions can occur, with high-sensitivity, by continuous change of the geometry of a simple 2D dielectric-frame photonic crystal consisting of circular air-holes. By changing the radii of the holes and/or the distance between them, multiple transitions between normal and topological photonic band gaps (PBGs) can appear. The time-reversal symmetric topological PBGs resemble the quantum spin-Hall insulator of electrons and have two counter-propagating edge states. We search for optimal topological transitions, i.e., sharp transitions sensitive to the geometry, and optimal topological PBGs, i.e., large PBGs with clean spectrum of edge states. Such optimizations reveal that dielectric-frame photonic crystals are promising for optical sensors and unidirectional waveguides.