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Motivated by experimental reports on chirality induced spin selectivity, we investigate a minimal model that allows us to calculate the charge and spin conductances through helical molecules analytically. The spin–orbit interaction is assumed to be non-vanishing on the molecule and negligible in the reservoirs (leads). The band structure of the molecule features four helical modes with spin-momentum locking that are analogous of edge-currents in the quantum spin Hall effect. While charge is conserved and therefore the charge current is independent of where it is measured—reservoirs or molecule—our detailed calculations reveal that the spin currents in the left and right leads are equal in magnitudes but with opposite signs (in linear response). We predict that transport currents flowing through helical molecules are accompanied by a spin accumulation in the contact region with the same magnetization direction for source and drain. Furthermore, we predict that the spin-conductance can be extracted directly from measuring the (quasi-static) spin accumulation—rather than the spin current itself, which is very challenging to obtain experimentally. [ABSTRACT FROM AUTHOR]

The Zak phase serves as a reliable index for pinpointing topological phase transitions within one-dimensional chains, typically ascertained through numerical methods in complex situations. Nonetheless, in proximity to the transition threshold, the numerical Zak phase may become ambiguous. This ambiguity arises from the discrete nature of numerical approaches and the nonlinear relationship between the wave function's phase and the wave vector (k). In response, this paper presents an innovative method aimed at accurately determining the winding number, thereby facilitating the identification of topological phase transitions. Our approach hinges on analyzing the evolution of the phase difference between the projections of the Bloch wave function onto two distinct sublattices. We demonstrate the efficacy of this method through three illustrative examples: the Su–Schrieffer–Heeger model, a magnetic vortex chain, and a trimer lattice chain. The results indicate that our proposed numerical lagging-phase examination method achieves superior precision in identifying topological phase transitions, particularly at critical junctures, compared to the conventional numerical Zak phase approach. [ABSTRACT FROM AUTHOR]

This paper explores the emergence of topological interface states in one-dimensional locally resonant lattices incorporating inerters in both nearest neighbor (NN) and beyond-nearest neighbor (BNN) coupling. The investigation focuses on the unique wave propagation characteristics of these lattices, particularly the presence and behavior of interface states. The non-trivial topological behavior due to broken inversion symmetry within the unit cell of the locally resonant lattice is comprehensively investigated in the presence of inerters in NN and BNN coupling. The emerging interface states in the supercell analysis exhibit specific spatial and frequency localization properties due to inerter-based BNN interactions. Additionally, the study demonstrates the ability of inerter elements with weak inertance to control the frequency of interface states while maintaining the fundamental topological properties of the lattice. The identified topological interface states in lattices with BNN coupling present an opportunity for designing diverse devices, such as waveguides, filters, sensors, and energy harvesting systems. Overall, this research enhances our comprehension of topological phenomena in inerter-based locally resonant lattices with BNN interactions and introduces possibilities for creating robust and versatile devices based on topologically protected edge/interface states. [ABSTRACT FROM AUTHOR]

The semiconductor quantum well based on mercury telluride is characterized by two distinct phases: conventional insulating phase and topological insulating phase with helical edge states. The system undergoes a topological quantum phase transition from one phase to the other, tuned by the critical geometric parameters of the quantum well. It is shown that the quantum states in each phase exhibit distinct flavors of Bloch oscillations, depending strongly on the geometric parameters and crystal momentum of the system. In particular, the group and Berry velocities and the real-space trajectories exhibit pronounced Bloch oscillations. Interestingly, the x - and y -components of the group velocity are interchanged by interchanging their corresponding components of the crystal momentum. In addition, a Gaussian wave packet undergoes distinct time evolution in each quantum phase of the HgTe quantum well. Moreover, the effects of applied in-plane electric and transverse magnetic fields are determined within the framework of Newtonian mechanics, leading to the geometric visualization of such an oscillatory motion. We find that in the presence of both applied in-plane electric and transverse magnetic fields simultaneously, the system undergoes a dynamic phase transition between confined and de-confined states, tuned by the relative strength of the fields. It is argued that the distinct Bloch oscillations originate from the peculiar band structure of HgTe quantum wells in each quantum phase. Furthermore, we find that the direct-current drift velocity in each quantum phase exhibits negative differential conductivity, a hallmark of the Bloch oscillation regime. [ABSTRACT FROM AUTHOR]

Establishing the (non)existence of a spectral gap above the ground state in the thermodynamic limit is one of the fundamental steps for characterizing the topological phase of a quantum lattice model. This is particularly challenging when a model is expected to have low-lying edge excitations, but nevertheless a positive bulk gap. We review the bulk gap strategy introduced in [S. Warzel and A. Young, The spectral gap of a fractional quantum Hall system on a thin torus, J. Math. Phys.63 (2022) 041901; S. Warzel and A. Young, A bulk spectral gap in the presence of edge states for a truncated pseudopotential, Ann. Henri Poincaré24 (2023) 133–178], while studying truncated Haldane pseudopotentials. This approach is able to avoid low-lying edge modes by separating the ground states and edge states into different invariant subspaces before applying spectral gap bounding techniques. The approach is stated in a general context, and we reformulate specific spectral gap methods in an invariant subspace context to illustrate the necessary conditions for combining them with the bulk gap strategy. We then review its application to a truncation of the 1/3-filled Haldane pseudopotential in the cylinder geometry. [ABSTRACT FROM AUTHOR]

The electronic structure of silicene supported by monolayer of different monochalcogenide MX (GaS, GaSe, GaTe and InSe) substrates has been investigated by first principle density functional theory. By calculating the formation energies and phonons, it has been seen that silicene supported by monolayer of MX remains stable. The systems retain their almost 2 D planner configurations with small buckling as that of the free standing silicene and also the Bader charge analysis shows that silicene hardly interacts with any of the MX substrates. The Dirac cone with a small gap (∼ 3 0 – 5 0   meV) has been observed in each of the cases. All the systems show quantum spin Hall effect and the quantum spin Hall conductivities have been estimated to be within the range ∼ 2 − 5 ℏ e S/cm, which are larger than that of the free standing silicene. Our calculations show that even if the systems have bulk band gaps but the edge states are conducting in nature. [ABSTRACT FROM AUTHOR]

Materials with large Rashba spin splitting (RSS) and quantum spin Hall effect (QSHE) are extremely important in spintronic device applications. Based on first-principles calculations, we present H–Pb–OH, a two-dimensional (2D) hexagonal lattice material capable of achieving complete coexistence of massive RSS and QSHE. The RSS phenomenon (αR = 3.66 eV Å) in the electronic band of H–Pb–OH occurs when the system's spatial inversion symmetry is broken and there is an intrinsic electric field present. Furthermore, biaxial stress can modulate the RSS of H–Pb–OH (−8 to 8%). By examining the electronic characteristics of H–Pb–OH, we discover that there is a significant bandgap (1.12 eV) around the Fermi surface, and the system exhibits a topological invariant Z2 = 1 due to the inversion of the s-p orbitals of the Pb atoms, indicating that H–Pb–OH is a 2D topological insulator with a large topological bandgap. Our findings provide an outstanding candidate material for investigating and implementing the coexistence of RSS and QSHE. [ABSTRACT FROM AUTHOR]

In this work, we propose a method for regulating topological states in acoustic systems by introducing airflow circulation. Composed of hollow rings linked with subwavelength rectangular waveguides, the proposed acoustic topological meta-crystals support multi-dimensional boundary states where the corner states merge into the edge ones. With the airflow introduced, the corner states separate from the edge states. We give the relationship between the frequency of the corner state and the speed of airflow and test the result by calculating eigenmodes of the supercell and finite lattice. Simulations for the acoustic field excited by a point source in a finite lattice also agree the relationship we give. The introduction of airflow in a topological system provides a method for manual control of the topological corner states. [ABSTRACT FROM AUTHOR]

Rainbow trapping, observed in elastic waves, has attracted considerable scientific interest owing to its potential applications in energy harvesting, buffering, and wavelength-division multiplexing devices. However, previous approaches have often necessitated complex geometric modifications to the scatterer, such as altering dimensions or shifting along diagonals to corners, limiting practical utility. Here, we realize the coupled topological edge states (CTESs) of elastic waves in a two-dimensional (2D) solid phononic crystal (PC) with inversion center changes. Changing the inversion center along the x or y directions by a specific distance can induce the topological phase transition. The topological edge states (TESs) arise at the interface by combining PCs with different topologies positioned adjacent to each other. Furthermore, it is demonstrated that TES exhibits topological robustness against defects. By introducing a gradient into the PC structure by altering the geometrical parameters of scatterers along the interface, the topological rainbow trapping of elastic waves is achieved. Finally, the CTES are generated by the interaction between TESs of different interfaces, which can lead to coupled topological rainbow trapping in phononic heterostructures with different displacement parameters along the multiple interface gradient. Our results pave the way for manipulating the symmetric and antisymmetric topological modes of elastic waves in topologically coupled waveguides, which offers potential applications in selective filtering and multiband waveguiding. [ABSTRACT FROM AUTHOR]

Characterizing topologically nontrivial photonic lattices by measuring their topological invariants is crucial in topological photonics. In conservative one-dimensional systems, a widely used observable to extract the winding number is the mean-chiral displacement. In many realistic photonic systems, however, losses can hardly be avoided, and little is known on how one can extend the mean-chiral displacement to a driven-dissipative context. Here we theoretically propose an experimentally viable method to directly detect the topological winding number of one-dimensional chiral photonic lattices. The method we propose is a generalization of the mean-chiral displacement to a driven-dissipative context with coherent illumination. By integrating the mean-chiral displacement of the steady state over the pump light frequency, one can obtain the winding number with a correction of the order of the loss rate squared. We demonstrate that this method can be successfully applied to lattices along synthetic frequency dimensions. While various photonic lattices with topologically nontrivial band structures have been realized, how to measure topological invariants in such systems with photon losses has not been clearly understood. We find that the topological winding number can be measured even in the presence of photon loss by generalizing the concept of the mean-chiral displacement originally developed for lossless systems. [ABSTRACT FROM AUTHOR]

Topological rainbow trapping, which can separate and trap different frequencies of topological states into different positions, plays a key role in topological acoustic devices. However, few schemes have been proposed to realize multidimensional topological rainbow trapping effects with the hierarchy of edge and corner, which has partly restricted their practical applications in multifunctional integrated acoustic devices. Herein, a tactic to realize a multidimensional topological rainbow trapping of acoustic wave with the hierarchy of edge and corner in the second‐order topological sonic crystals is proposed. Based on the designing of a self‐ordering structure to both induce the topological phases of the bulk and edge states in the rectangular lattice, the edge states and corner states are obtained. Furthermore, the regularity between the located frequency of topological edge and corner states and the geometric parameters are discussed in detail. Finally, the rainbow trapping effects for topological edge states and corner states are investigated, respectively, in which different frequencies of topological acoustic edge and corner states are well separated and trapped in different positions without overlap. This proposal may provide a novel way for multidimensional wave manipulation and the integration of multifunctional acoustic devices. [ABSTRACT FROM AUTHOR]

PtN4C2 is a recently predicted two-dimensional (2D) Dirac semimetal exhibiting significant topological quantum spin and valley Hall effects. Herein, we explore its topological phonon states and thermal transport properties from first-principles calculations. In terms of symmetry arguments, we predict the existence of multiple topologically protected phononic Dirac points in the frequency range of 0–20 THz, which are evidenced by the relevant irreducible representations and calculated nontrivial edge states on the (100) surface. In addition, anharmonic phonon renormalization is found to play a significant role in determining the phonon spectrum, especially for the out-of-plane flexural acoustic (ZA) branch. Moreover, we explicitly consider three-phonon scattering, four-phonon scattering, and phonon renormalization to predict the lattice thermal conductivity κl of PtN4C2, by solving the Boltzmann transport equation. With the incorporation of four-phonon scattering, we predict that the intrinsic κl is 68 W/mK at room temperature, which is reduced by about 45% as compared to the value obtained by only including three-phonon scattering. This reduction is found to arise mainly from the ZA phonons, whose contribution to κl is significantly suppressed by four-phonon scattering, due to the restriction of the mirror symmetry-induced selection rules on three-phonon processes. We also unveil that the presence of Dirac points steepens the surrounding phonon dispersion and thus greatly increases the phonon group velocities, thereby making a considerable contribution to κl. This work establishes a thorough understanding of intrinsic topological phonons and thermal transport in PtN4C2 and highlights the importance of phonon renormalization and higher-order anharmonicity in determining the phonon transport properties of 2D materials. [ABSTRACT FROM AUTHOR]

The Jaynes–Cummings Model (JCM) is a fundamental model and building block for light‐matter interactions, quantum information and quantum computation. The present work analytically analyzes the topological feature manifested by the JCM in the presence of non‐Hermiticity which may arise from dissipation and decay rates. Indeed, the eigenstates of the JCM are topologically characterized by spin windings in 2D plane. The non‐Hermiticity tilts the spin‐winding plane and induces an out‐of‐plane component, while the topological feature is maintained. In particular, besides the invariant spin texture nodes, the study reveals a non‐Hermiticity‐induced reversal transition of the tilting angle and spin winding direction with a fractional phase gain at gap closing, a partially level‐independent reversal transition without gap closing, and a completely level‐independent super‐invariant point with untilted angle and also without gap closing. The result demonstrates that the topological feature is robust against non‐Hermiticity, which may be favorable in practical applications. On the other hand, one may conversely make use of the disadvantageous dissipation and decay rates to reverse the spin winding direction, which may add a controlled way for topological manipulation of quantum systems in light‐matter interactions. [ABSTRACT FROM AUTHOR]

PtN4C2 is a recently predicted two-dimensional (2D) Dirac semimetal exhibiting significant topological quantum spin and valley Hall effects. Herein, we explore its topological phonon states and thermal transport properties from first-principles calculations. In terms of symmetry arguments, we predict the existence of multiple topologically protected phononic Dirac points in the frequency range of 0–20 THz, which are evidenced by the relevant irreducible representations and calculated nontrivial edge states on the (100) surface. In addition, anharmonic phonon renormalization is found to play a significant role in determining the phonon spectrum, especially for the out-of-plane flexural acoustic (ZA) branch. Moreover, we explicitly consider three-phonon scattering, four-phonon scattering, and phonon renormalization to predict the lattice thermal conductivity κl of PtN4C2, by solving the Boltzmann transport equation. With the incorporation of four-phonon scattering, we predict that the intrinsic κl is 68 W/mK at room temperature, which is reduced by about 45% as compared to the value obtained by only including three-phonon scattering. This reduction is found to arise mainly from the ZA phonons, whose contribution to κl is significantly suppressed by four-phonon scattering, due to the restriction of the mirror symmetry-induced selection rules on three-phonon processes. We also unveil that the presence of Dirac points steepens the surrounding phonon dispersion and thus greatly increases the phonon group velocities, thereby making a considerable contribution to κl. This work establishes a thorough understanding of intrinsic topological phonons and thermal transport in PtN4C2 and highlights the importance of phonon renormalization and higher-order anharmonicity in determining the phonon transport properties of 2D materials. [ABSTRACT FROM AUTHOR]

Many of the most exciting materials discoveries in fundamental condensed matter physics are made in systems hosting some degree of intrinsic disorder. While disorder has historically been regarded as something to be avoided in materials design, it is often of central importance to correlated and quantum materials. This is largely driven by the conceptual and theoretical ease to handle, predict, and understand highly uniform systems that exhibit complex interactions, symmetries, and band structures. In this Perspective, we highlight how flipping this paradigm has enabled exciting possibilities in the emerging field of high entropy materials, focusing primarily on high entropy oxide and chalcogenide quantum materials. These materials host high levels of cation or anion compositional disorder while maintaining unexpectedly uniform single crystal lattices. The diversity of atomic scale interactions of spin, charge, orbital, and lattice degrees of freedom are found to emerge into coherent properties on much larger length scales. Thus, altering the variance and magnitudes of the atomic scale properties through elemental selection can open new routes to tune global correlated phases, such as magnetism, metal–insulator transitions, ferroelectricity, and even emergent topological responses. The strategy of embracing disorder in this way provides a much broader pallet from which functional states can be designed for next-generation microelectronic and quantum information systems. [ABSTRACT FROM AUTHOR]

We evaluated topological protection for edge and higher-order corner states in topological diffusion systems based on the breathing kagome lattice. In the kagome lattice, the corner states appear at the corner boundary where all three Wannier centers in nontrivial unit cells are located. The three Wannier centers in a unit cell can be placed on the obtuse- and acute-corner boundaries utilizing the armchair boundary, generating topological acute- and obtuse-corner states. For another representative zigzag boundary, only the acute-corner unit cell has three Wannier centers located at the boundary; hence, only the acute-corner state appears. Our band analysis and numerical studies show that the topologically protected decay behavior for armchair boundaries is as robust as that for zigzag boundaries, unlike wave phenomena with space and time periodicities. Our findings can guide the flexible design of topological diffusion applications such as heat localization and recovery systems. [ABSTRACT FROM AUTHOR]

We propose a controllable topological add-drop filter based on magnetic–optical photonic crystals. This add-drop filter is composed of two straight waveguides and a hexagonal photonic crystal ring resonator. The waveguide and ring resonator are constructed by three different honeycomb magnetic–optical photonic crystals. The expanded lattice is applied with an external magnetic field so that it breaks time-reversal symmetry and the analogous quantum spin Hall effect simultaneously. While the standard one and the compressed one are not magnetized and trivial, the straight waveguide supports pseudospin-down (or pseudospin-up) one-way states when the expanded lattice is applied with an external magnetic field of +H (or −H). The ring resonator possesses multiple resonant modes which can be divided into travelling modes and standing modes. By using the travelling modes, we have demonstrated the function of the add-drop filter and realized the output port control by changing the direction of the magnetic field. Moreover, a large tunable power ratio from near 0 to 52.6 is achieved by adjusting the strength of the external magnetic field. The structure has strong robustness against defects due to the topological protection property. These results have potential in wavelength division multiplexing systems and integrated topological optical devices. [ABSTRACT FROM AUTHOR]

Polymorphism in transition metal dichalcogenides (TMDs) allows unique physical properties to be controlled, such as artificial heavy fermion phenomena, the quantum spin Hall effect, and optimized device operations with 2D materials. Besides lattice structural and metal‐semiconductor polymorphs, intriguing charge density wave (CDW) states with different electronic and magnetic phases are demonstrated in TMDs. Typically, the "normal" state is stabilized at high temperature above the CDW energy scale, and therefore, is not relevant to many low‐temperature quantum phenomena, such as magnetic ordering and the heavy fermion Kondo state. Here, a local and robust phase manipulation of the normal (1T) and CDW (1T') states of VTe2 is reported by laser irradiation, and polymorphic Kondo effects are demonstrated with the two phases at low temperatures. The theoretical calculations show that Kondo screening of vanadium 3d electron moments is markedly enhanced in 1T'‐VTe2, which is responsible for the observed transport properties distinct from its 1T counterpart. Controlling the spin‐lattice coupling and Kondo physics via laser‐driven CDW phase patterning allows the design of correlated electronic and magnetic properties in TMDs. [ABSTRACT FROM AUTHOR]

Polymorphism in transition metal dichalcogenides (TMDs) allows unique physical properties to be controlled, such as artificial heavy fermion phenomena, the quantum spin Hall effect, and optimized device operations with 2D materials. Besides lattice structural and metal‐semiconductor polymorphs, intriguing charge density wave (CDW) states with different electronic and magnetic phases are demonstrated in TMDs. Typically, the "normal" state is stabilized at high temperature above the CDW energy scale, and therefore, is not relevant to many low‐temperature quantum phenomena, such as magnetic ordering and the heavy fermion Kondo state. Here, a local and robust phase manipulation of the normal (1T) and CDW (1T') states of VTe2 is reported by laser irradiation, and polymorphic Kondo effects are demonstrated with the two phases at low temperatures. The theoretical calculations show that Kondo screening of vanadium 3d electron moments is markedly enhanced in 1T'‐VTe2, which is responsible for the observed transport properties distinct from its 1T counterpart. Controlling the spin‐lattice coupling and Kondo physics via laser‐driven CDW phase patterning allows the design of correlated electronic and magnetic properties in TMDs. [ABSTRACT FROM AUTHOR]

We unveil that the holey graphyne (HGY), a two-dimensional carbon allotrope where benzene rings are connected by two −C≡C− bonds fabricated recently in a bottom-up way, exhibits topological electronic states. Using first-principles calculations and Wannier tight-binding modeling, we discover a higher-order topological invariant associated with C 2 symmetry of the material, and show that the resultant corner modes appear in nanoflakes matching to the structure of precursor reported previously, which are ready for direct experimental observations. In addition, we find that a band inversion between emergent g -like and h -like orbitals gives rise to a nontrivial topology characterized by Z 2 invariant protected by an energy gap as large as 0.52 eV, manifesting helical edge states mimicking those in the prominent quantum spin Hall effect, which can be accessed experimentally after hydrogenation in HGY. We hope these findings trigger interests towards exploring the topological electronic states in HGY and related future electronics applications. [ABSTRACT FROM AUTHOR]

In systems exhibiting the non-Hermitian skin effect (NHSE), the bulk spectrum under open boundary conditions (OBC) significantly differs from that of its periodic counterpart. This disparity renders the conventional bulk-boundary correspondence (BBC) inapplicable. Here we propose an intuitive approach called doubling and swapping to restore the BBC, using the non-Hermitian Su-Schrieffer-Heeger model as an example. Explicitly, we construct a modified system free of NHSE by swapping the asymmetric intracell hoppings in every second primitive unit cell. Importantly, this change does not alter the OBC spectrum. As a result, the modified periodic system can serve as the bulk for defining topological invariants that accurately predict edge states and topological phase transitions. The basic principle is applicable to many other systems. By extending the study to disordered systems in which the asymmetric hoppings are randomly swapped, we show that two types of winding numbers can also be defined to account for the NHSE and topological edge states, respectively. Non-Hermitian (NH) systems have recently attracted great attention, and the NH bulk-boundary correspondence is a key question. The authors propose an approach to restore NH bulk-boundary correspondence by a "doubling and swapping" construction which eliminates the NH skin effect, resulting in a new NH Hamiltonian with the same energy spectrum. [ABSTRACT FROM AUTHOR]

Non-Hermitian systems have been employed to construct a high-sensitivity sensor. To evaluate the performance of the sensors, the quantum Fisher information per photon, or equivalently signal-to-noise ratio per photon, is provided as a "true" sensing criterion, which avoids the trivial contribution from the photon numbers. The specific properties of non-Hermitian systems, e.g., exceptional points and skin effect, have been connected to the true exponentially enhanced sensing performance. To date, the relation between the non-Hermitian topological phase and the true sensing performance has not been reported clearly. Here, we construct the high-sensitivity sensor based on the non-Hermitian Su–Schrieffer–Heeger lattice and establish the relationship between the exponentially enhanced sensing and the non-Hermitian topologically nontrivial phase. The saturation of sensing with the size emerges in the sense of one perturbation. Such a limitation can be surpassed through the change of incident positions of driving fields, and the exponentially enhanced sensing reappears. [ABSTRACT FROM AUTHOR]

We consider a disordered waveguide consisting of trivial dielectric and non-trivial magnetically anisotropic material. A topologically protected edge mode appears owing to the broken time-reversal symmetry of the non-trivial lattice. While the edge mode maintains under other position and radius disorders, the protection is immediately broken by applying a radius disorder to the non-trivial lattice. This breakdown originates from donor and acceptor modes occupying the topological bandgap. Furthermore, via the calculation of the Bott index, we show that Anderson localization occurs as a metal conducting gap changes to a topological gap along with increasing disorders. [ABSTRACT FROM AUTHOR]

Topological boundary modes in electronic and classical-wave systems exhibit fascinating properties. In photonics, topological nature of boundary modes can make them robust and endows them with an additional internal structure--pseudo-spins. Here, we introduce heterogeneous boundary modes, which are based on mixing two of the most widely used topological photonics platforms--the pseudo-spin-Hall-like and valley-Hall photonic topological insulators. We predict and confirm experimentally that transformation between the two, realized by altering the lattice geometry, enables a continuum of boundary states carrying both pseudo-spin and valley degrees of freedom (DoFs). When applied adiabatically, this leads to conversion between pseudo-spin and valley polarization. We show that such evolution gives rise to a geometrical phase associated with the synthetic gauge fields, which is confirmed via an Aharonov-Bohm type experiment on a silicon chip. Our results unveil a versatile approach to manipulating properties of topological photonic states and envision topological photonics as a powerful platform for devices based on synthetic DoFs. [ABSTRACT FROM AUTHOR]

Topological photonics has been widely investigated due to its profound physical significance and great number of potential applications. Microwaves have long wavelengths, so it is relatively easy to manufacture large-sized microwave photonic crystals, enabling researchers to observe and measure phenomena such as topological boundary states. Nevertheless, the quality factors (QFs) of most resonators composed of traditional materials in the microwave region are relatively low, leading to topological edge states with high decay rates. In this study, we present a one-dimensional topological photonic crystal in the microwave region based on coupled superconducting resonators. A topological state with a QF as high as 6000 is observed, which proves this to be a new platform for the investigation of topological photonics with low decay rates in the microwave regime. [ABSTRACT FROM AUTHOR]

Topological photonic crystals have great potential in the application of on-chip integrated optical communication devices. Here, we successfully construct the on-chip transmissible topological edge states using one-dimensional Su–Schrieffer–Heeger (SSH) photonic crystals with defect cavities on silicon-on-insulator slab. Different coupling strengths between the lateral modes and diagonal modes in photonic crystal defect cavities are used to construct the SSH model. Furthermore, two photonic SSH-cavity configurations, called α and β configurations, are designed to demonstrate the topological edge states. Leveraging the capabilities of photonic crystal transverse electric modes with on-chip transmission, we introduced a waveguide to excite a boundary defect cavity and found that the transmission peak of light, corresponding to the topological edge state, can be received in another boundary defect cavity, which is caused by the tunnel effect. Moreover, the position of this peak experiences a blue shift as the defect cavity size increases. Therefore, by tuning the size of the SSH defect cavity, on-chip wavelength division multiplexing function can be achieved, which is demonstrated in experiments. The ultrafast response time of one operation can be less than 20 fs. This work harmonizes the simplicity of one-dimensional SSH model with the transmissibility of two-dimensional photonic crystals, realizing transmissible on-chip zero-dimensional topological edge states. Since transmission peaks are highly sensitive to defect cavity size, this configuration can also serve as a wavelength sensor and a reconfigurable optical device, which is of substantial practical value to on-chip applications of topological photonics. [ABSTRACT FROM AUTHOR]

The concept of "rainbow trapping" has generated considerable interest in wave propagation and energy harvesting, offering new possibilities for diverse and efficient acoustic wave operations. In this work, we investigate a dual-channel topological rainbow trapping device implemented within an underwater two-dimensional phononic crystal based on synthetic dimension. The topological edge states with different frequencies are separated and trapped at different spatial locations. Acoustic waves propagate simultaneously along two boundaries due to the degeneracy of the edge states. In particular, the propagation of a dual-channel topological rainbow is also realized by using a bend design. This work contributes to the advancement of multi-channel devices in synthetic space and provides a reference for the design of highly efficient underwater acoustic devices. [ABSTRACT FROM AUTHOR]

Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non-Hermitian physical systems. In contrast to previous classifications that only incorporate the eigenstate exchange effect, our proposed classification gives rise to finer Z 2 classifications depending on the presence of a π Berry phase after the encircling of the EPs. Moreover, by mapping arbitrary one-dimensional systems to the adiabatic encircling of EPs, we can classify one-dimensional non-Hermitian systems characterized by topological phase transitions involving EPs. Applying our exceptional classification to various multiband systems, we expect to enhance the understanding of topological phases in non-Hermitian systems. Large efforts have been placed on topological phases in non-Hermitian systems, where the appearance of exceptional points (EPs) and nontrivial Berry phase gather great interest. This study proposes an exhaustive classification framework for EPs, which connects eigenstate switching and Berry phase and reveals topological phase transitions accompanying EPs. [ABSTRACT FROM AUTHOR]

Topological charges of nodal lines in a multigap system are represented by non-Abelian numbers, and the Euler class, a topological invariant, can be used to explain their topological phase transitions, such as pair-annihilation of nodal lines. Up until now, no discussion of phase transitions of nodal lines in photonic crystals using the Euler class has been reported, despite the fact that the Euler class and topological phase transition have recently been addressed in metallic or acoustic crystals. Here, we show how the deformation of a photonic crystal causes topological phase transitions in the nodal lines, and the Euler class can be used to theoretically predict the nodal lines' stability based on the non-Abelian topological charge theory. Specifically, by manipulating the separation between the two single diamond structures and the extent of structural distortion, we numerically demonstrate the topological transition of nodal lines, e.g., from nodal lines to nodal rings. We then demonstrate that the range of surface states is strongly influenced by the topological phase transition of nodal lines. Moreover, the Zak phase was used to explain the surface states' existence. [ABSTRACT FROM AUTHOR]

Two linked gear wheels in a micromachine can be simultaneously rotated in opposite directions by using a laser beam that has in its section areas the spin angular momentum (SAM) of the opposite sign. However, for instance, a cylindrical vector beam has zero SAM in the focus. We alter a cylindrical vector beam so as to generate areas in its focus where the SAM is of opposite signs. The first alteration is adding to the cylindrical vector beam a linearly polarized beam. Thus, we study superposition of two rotationally symmetric beams: those with cylindrical and linear polarization. We obtain an expression for the SAM and prove two of its properties. The first property is that changing superposition coefficients does not change the shape of the SAM density distribution, whereas the intensity changes. The second property is that maximal SAM density is achieved when both beams in the superposition have the same energy. The second perturbation is adding a spatial carrier frequency. We study the SAM density of a cylindrical vector beam with a spatial carrier frequency. Due to periodic modulation, upon propagation in space, such a beam is split into two beams, having left and right elliptic polarization. Thus, in the beam transverse section, areas with the spin of different signs are separated in space, which is a manifestation of the spin Hall effect. We demonstrate that such light beams can be generated by metasurfaces, with the transmittance depending periodically on one coordinate. [ABSTRACT FROM AUTHOR]

Rainbow trapping is a significant strategy for capturing waves of different frequencies at different spatial positions. It offers significant potential for multi-frequency on-chip nanophotonic devices in the era of big data and has attracted much interest recently, and topological rainbow trapping that is immune to disorder has been observed in optics and acoustics. Reported here is the topological rainbow trapping of elastic waves using gradient valley phononic crystal plates (PCPs) with a hexagonal lattice, based on valley edge states that are localized at the boundary between two PCPs with opposite valley topological phases. The gradient valley PCPs are achieved by gradually adjusting the height of the scatterers or the thickness of the PCPs. The topological rainbow trapping of elastic waves is shown by applying vertical vibration to the studied gradient PCPs, which are simple in structure and easily fabricated, providing a good solution for manipulating and trapping elastic waves. [ABSTRACT FROM AUTHOR]

The search for magnetic topological materials has been at the forefront of condensed matter research for their potential to host exotic states such as axion insulators, magnetic Weyl semimetals, Chern insulators, etc. To date, the MnBi2 n Te3 n +1 family is the only group of materials showcasing van der Waals-layered structures, intrinsic magnetism and non-trivial band topology without trivial bands at the Fermi level. The interplay between magnetism and band topology in this family has led to the proposal of various topological phenomena, including the quantum anomalous Hall effect, quantum spin Hall effect and quantum magnetoelectric effect. Among these, the quantum anomalous Hall effect has been experimentally observed at record-high temperatures, highlighting the unprecedented potential of this family of materials in fundamental science and technological innovation. In this paper, we provide a comprehensive review of the research progress in this intrinsic magnetic topological insulator family, with a focus on single-crystal growth, characterization of chemical disorder, manipulation of magnetism through chemical substitution and external pressure, and important questions that remain to be conclusively answered. [ABSTRACT FROM AUTHOR]

Topological materials, which feature robust surface and/or edge states, have now been a research focus in condensed matter physics. They represent a new class of materials exhibiting nontrivial topological phases, and provide a platform for exploring exotic transport phenomena, such as the quantum anomalous Hall effect and the quantum spin Hall effect. Recently, magnetic topological materials have attracted considerable interests due to the possibility to study the interplay between topological and magnetic orders. In particular, the quantum anomalous Hall and axion insulator phases can be realized in topological insulators with magnetic order. MnBi2Te4, as the first intrinsic antiferromagnetic topological insulator discovered, allows the examination of existing theoretical predictions; it has been extensively studied, and many new discoveries have been made. Here we review the progress made on MnBi2Te4 from both experimental and theoretical aspects. The bulk crystal and magnetic structures are surveyed first, followed by a review of theoretical calculations and experimental probes on the band structure and surface states, and a discussion of various exotic phases that can be realized in MnBi2Te4. The properties of MnBi2Te4 thin films and the corresponding transport studies are then reviewed, with an emphasis on the edge state transport. Possible future research directions in this field are also discussed. [ABSTRACT FROM AUTHOR]

Topological phononic crystals (PnCs) with topologically protected boundary states have important applications in the fields of acoustic wave transmission and control. However, previous studies based on solid‐state PnC systems are mostly limited by fixed structures, resulting in the difficulty to deform the edge states, which partly limits its practical applications. Herein, a 2D solid topological PnC coupled with the defect is designed to achieve the adjustable valley edge state and rainbow trapping. First, by breaking the spatial inversion symmetry, the valley Hall phase transition of elastic wave is realized and valley edge states are obtained. Next, by introducing defects of different widths between the two different valleys' topological PnCs, both the defect‐adjusted valley edge state and defect state are achieved. Then, by designing different topological PnCs waveguides, the robust transport characteristics of the two above states are compared. Subsequently, a new power divider based on the defect‐adjusted valley edge state is designed, which is found to possess various manners of operation such as equal and unequal power divisions. Finally, based on defect adjustment of the edge states, a rainbow trapping is implemented. This research provides an important guidance for ultrasonic devices, such as waveguides, energy harvesters, and power dividers. [ABSTRACT FROM AUTHOR]

Volkov–Pankratov (VP) states are a family of sub-gap states that appear at the smooth interface/domain wall between topologically distinct gaped states. We carry out quantum transport simulations on one- and two-dimensional lattice models to demonstrate the emergence of such states in the edge spectrum of a quantum spin Hall system subjected to a smoothly varying exchange field that switches its sign at a given spatial point. We show the VP states possess non-trivial spin textures that can be characterized by a winding number in real space. It is further demonstrated that the application of an electric field along the edge provides control of this spin texture without altering the winding number. Finally, we illuminate how these spin textures can be read off via the local tunnel magnetoresistance (TMR) response of spin-polarized tunnel probes attached to the edge and the TMR can be controlled by purely electrical means akin to a Datta–Das type spin transistor. [ABSTRACT FROM AUTHOR]

It has been known that the bulk-boundary correspondence (BBC) of the non-Hermitian skin effect is characterized by the topology of the complex eigenvalue spectra, while the topology of the wave function gives rise to Hermitian BBC with conventional boundary modes. In this work, we go beyond the known description of the non-Hermitian topological phase and find a different type of BBC that appears in generalized boundary conditions. The generalized Brillouin zone (GBZ) possesses non-trivial topological structures in the intermediate boundary condition between open and periodic boundary conditions. Unlike the conventional BBC, the topological phase transition is characterized by the generalized momentum touching of GBZ, which manifests as exceptional points. As a realization of our proposal, we suggest the non-reciprocal Kuramoto oscillator lattice, where phase slips accompany exceptional points as a signature of such topological phase transition. Our work establishes an understanding of non-Hermitian topological matter by complementing the non-Hermitian BBC as a general foundation of the non-Hermitian topological systems. A key problem in non-Hermitian lattice physics is restoring bulk-boundary correspondence. Here, the authors study two non-Hermitian models with a generalized boundary condition, proving that these systems can continuously be tuned from a periodic to an open boundary condition, showing a phase transition characterized by an exceptional point. [ABSTRACT FROM AUTHOR]

This research explores how two-dimensional honeycomb materials can be used in advanced electronics, focusing on zigzag honeycomb nanoribbons. These nanoribbons can create zero-energy band gaps, enabling helical spin current edge states. The study investigates the quantum spin Hall state, showcasing the adaptability of the Kane-Mele model in various honeycomb lattices. In addition to the theoretical discussions, this study presents a detailed Hamiltonian, performs band structure computations, and introduces a novel spin-filtering technique for zigzag nanoribbons. This method enhances our understanding of edge-localized quantum states and can revolutionize spintronics. By revealing the quantum states in honeycomb nanoribbons, this study contributes to the advancement of electronics and offers a promising path for highly efficient spinbased technologies. [ABSTRACT FROM AUTHOR]

This study reports a modified Haldane model that supports transitions between valley and Chern topological phases in photonic crystals. Berry curvatures of this system can be flexibly diffused, converged, or flipped by endowing different model parameters, thus exhibiting exotic topological interface/edge behaviors, such as topological bound states with ideally zero dispersion. Importantly, the coexistence of chiral and antichiral edge states preserved simultaneously by valley and Chern topological phases is achieved by splicing together two kinds of topological structures as an entirety. It further employs a honeycomb lattice comprising gyromagnetic and ceramic cylinders at microwave frequencies, where inversion and time‐reversal symmetries can be flexibly manipulated. Topological interface transport is demonstrated, including two opposite signs of group velocities jointly protected by topologically distinct regimes. These results bridge the gap between valley and Chern topological physics and shed light on developing reconfigurable integrated device applications for classical (quantum) information processing and photonic computing. [ABSTRACT FROM AUTHOR]

This is an update of a previous review (Naumis et al 2017 Rep. Prog. Phys. 80 096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisation P on hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials. [ABSTRACT FROM AUTHOR]

Topological phases of matter have attracted significant attention in recent years, due to the unusual robustness of their response to defects and disorder. Various research efforts have been exploring classical and quantum topological wave phenomena in engineered materials, in which different degrees of freedom (DoFs) – for the most part based on broken crystal symmetries associated with pseudo-spins – induce synthetic gauge fields that support topological phases and unveil distinct forms of wave propagation. However, spin is not the only viable option to induce topological effects. Intrinsic orbital DoFs in spinless systems may offer a powerful alternative platform, mostly unexplored to date. Here we reveal orbital-selective wave-matter interactions in acoustic systems supporting multiple orbital DoFs, and report the experimental demonstration of disorder-immune orbital-induced topological edge states in a zigzag acoustic 1D spinless lattice. This work expands the study of topological phases based on orbitals, paving the way to explore other orbital-dependent phenomena in spinless systems. The researchers demonstrate orbital-dependent sound-matter interactions in acoustic systems. They unveil duality symmetry and topological phase transitions beyond the conventional SSH model expanding the fundamental understanding of sound-matter interaction. [ABSTRACT FROM AUTHOR]

We have utilized the density functional theory (DFT) in conjunction with graph‐theoretical techniques to compute the vibrational, electronic and topological properties of porous nanographenes starting with the building blocks of kekulene, septulene, extended kekulenes, and circumkekulene. Furthermore, graph theoretically based spectral polynomials and other topological properties including Kekulé counts, delocalization energies, and resonance energies are computed for such structures and larger tessellations of kekulenes which are precursors to nanographene belts with multiple pores. The success of the DFT methods is demonstrated with the computed vibrational modes and infrared and Raman spectra of several of these structures. The computed spectral polynomials and the spectra reveal the underlying patterns of the energy levels and structural features and hence suggest the possibility of integration of graph theory with quantum chemical techniques for the computations of properties of large porous graphenes including the possibility of the Pariser–Parr–Pople (PPP) method with parameters extracted from machine learning of the DFT computations on a combinatorial library of precursors. Finally, the computations reveal that the porous structures can be tailored for sequestration of various ions including heavy metal ions for environmental remediation. [ABSTRACT FROM AUTHOR]

Higher‐order corner‐bound states in a 2D structure have been found to possess robust and exotic properties beyond the "ordinary" topological edge states, giving rise to a promising applicative potential. For example, the topological nanocavity designed based on the corner states exhibits much better performance than that of the conventional photonic crystal cavity. However, the corner states in the finite Hermitian system are usually coupled with each other, which results in the weakening of their localization. As such, the contradiction between the performance and footprint of topological devices is vexing. Here, it shows that introducing non‐Hermiticity in the higher‐order topological insulators is an effective strategy to enhance the localization of corner states in finite systems. By designing and analyzing the 2D finite Su‐Schriffer‐Heeger optical lattices with two types of non‐Hermitian configuration, the localization degree of higher‐order corner states is found to depend on the gain/loss strength. This is experimentally demonstrated by observing the distribution of corner states in the femtosecond‐laser‐writing loss‐controlled waveguide arrays. This scheme tuning localization of higher‐order corner‐bound states by non‐Hermiticity may offer a new avenue to design robust and compact devices, such as topological nano‐lasers with an ultra‐low threshold. [ABSTRACT FROM AUTHOR]

Exploring the interaction between topological phases and non-Hermitian potentials such as gain and loss can benefit designing robust optical devices. Recent studies have revealed topological phases can be simply from gain and loss in non-Hermitian systems. Here, we propose an extended kagome lattice model, where the non-Hermitian potentials drive the system from a trivial phase to a higher-order topological phase. Higher-order topological insulators exhibit lower-dimensional boundary states on corners or hinges. We construct two-dimensional higher-order topological insulators on different arrays of the extended kagome lattice model. Topologically protected states emerge at the corner with a 1/3 fractional charge at each corner as the strength of the gain and loss increases. The topologically protected corner states are characterized by the quantized polarization as the topological index. We find that non-Hermitian potentials provide an extra degree of freedom to switch on and off the higher-order topological corner states. The proposed system can be verified through many experimental platforms, including coupled optical resonating cavities and waveguides. Our work indicates the great prospects for constructing integrated photonics platforms and designing actively reconfigurable photonic devices. [ABSTRACT FROM AUTHOR]

The investigation of topological state transition in carefully designed photonic lattices is of high interest for fundamental research, as well as for applied studies such as manipulating light flow in on‐chip photonic systems. Herein, the topological phase transition between symmetric topological zero modes (TZM) and antisymmetric TZMs in Su–Schrieffer–Heeger mirror symmetric waveguides is reported. The transition of TZMs is realized by adjusting the coupling ratio between neighboring waveguide pairs, which is enabled by selective modulation of the refractive index in the waveguide gaps. Bidirectional topological transitions between symmetric and antisymmetric TZMs can be achieved with proposed switching strategy. Selective excitation of topological edge mode is demonstrated owing to the symmetry characteristics of the TZMs. The flexible manipulation of topological states is promising for on‐chip light flow control and may spark further investigations on symmetric/antisymmetric TZM transitions in other photonic topological frameworks. [ABSTRACT FROM AUTHOR]

Floquet topological insulators (FTIs) have richer topological properties than static systems. In this work, we designed different domain wall (DW) structures consisting of a Floquet photonic lattice with opposite helical directions. We investigated the existence and types of edge states in three shared coupling structures and the impact of these shared coupling structures on edge states. When two opposite helical lattices share a straight waveguide array coupling, the edge states are localized on the straight waveguide. When two opposite helical lattices share a clockwise (or anticlockwise) helical waveguide array coupling, the DWs consist of zigzag and bearded edges, but the positions of the zigzag and bearded edges of the shared clockwise waveguide array are different from those of the shared anticlockwise waveguide array. The slope and transmission rate of the edge states both vary with the degree of coupling between the shared waveguides. The characteristics of these edge states, such as transmission speed and band gap width, are also affected by the incidence angle, modulation phase factor, and helical radii, and the methods for controlling the edge states in different shared coupling structures are provided. This will help deepen our understanding of how topological structures influence the electronic and photonic properties of materials. This could also lead to combining topology with metasurface-based structured light, which would highlight many novel properties with great application potential for various fields, such as imaging, metrology, communication, quantum information processing, and light–matter interaction. [ABSTRACT FROM AUTHOR]

Topological phononic crystals and acoustic metamaterials have attracted enormous research attention in recent years due to the presence of robust and disorder-immune wave propagation. In this study, a sinusoidal lightweight elastic topological insulator with protected interface modes is investigated at a subwavelength frequency region. By a wave dispersion study, the dual Dirac cones are observed at a subwavelength frequency region due to the employment of two distinct cylinders connected with sinusoidal ligaments. Both cylindrical masses and sinusoidal ligaments are found responsible for opening low-frequency bandgaps that manipulate elastic wave wavelengths almost 30 times larger than the lattice size. Consequently, the subwavelength bandgap closing-and-reopening phenomenon with phase transitions is further captured and opposite signs of the valley Chern numbers are obtained for different structural parameters. A supercell structure is constructed based on the phase transition, and dual topologically protected interface modes (TPIMs) are captured with different quality factors. The comparison of topologically protected interface modes shows that TPIM I is in a higher and wider frequency range, while TPIM II is positioned in a comparatively narrow and extremely low-frequency range. Finally, the robust elastic wave propagation along various designated paths is demonstrated. The proposed lightweight topologically protected phononic lattice may spark future investigation of topological edge states in metadevices at a subwavelength frequency region. [ABSTRACT FROM AUTHOR]

Ferroelectricity and band topology are hot topics in condensed matter physics, and the nonvolatile regulation of topological orders through ferroelectric properties is crucial for the design of next-generation miniature electronic devices. Here, using first-principles calculations, we demonstrate the coexistence of intrinsic ferroelectric and topological properties in two-dimensional (2D) In2TeS2. Interestingly, in single-layer In2TeS2, the spin flipping of chiral edge states occurs when the direction of ferroelectric polarization is reversed. While for In2TeS2 homobilayers, we find that the topological properties are stacking-dependent, and the ferroelectric order can be served as an effective means to achieve topological phase transition between trivial and nontrivial states. Our work not only shed light on the intrinsic 2D ferroelectric topological insulator but also put forward it as a promising candidate for high-efficiency and low-energy consumption electronic devices. [ABSTRACT FROM AUTHOR]

Ferroelectricity and band topology are hot topics in condensed matter physics, and the nonvolatile regulation of topological orders through ferroelectric properties is crucial for the design of next-generation miniature electronic devices. Here, using first-principles calculations, we demonstrate the coexistence of intrinsic ferroelectric and topological properties in two-dimensional (2D) In2TeS2. Interestingly, in single-layer In2TeS2, the spin flipping of chiral edge states occurs when the direction of ferroelectric polarization is reversed. While for In2TeS2 homobilayers, we find that the topological properties are stacking-dependent, and the ferroelectric order can be served as an effective means to achieve topological phase transition between trivial and nontrivial states. Our work not only shed light on the intrinsic 2D ferroelectric topological insulator but also put forward it as a promising candidate for high-efficiency and low-energy consumption electronic devices. [ABSTRACT FROM AUTHOR]

Recently, topological insulators (TIs) KHgX (X = As, Sb, Bi) with hourglass-shaped dispersion have attracted great interest. Different from the TIs protected by either time-reversal or mirror crystal symmorphic symmetry tested in previous experiments, these materials were proposed as the first material class whose band topology relies on nonsymmorphic symmetries. As a result, KHgX shows many exotic properties, such as hourglass-shaped electronic channels and three-dimensional doubled quantum spin Hall effects. To date, high-pressure experimental studies on these nonsymmorphic TIs are minimal. Here, we carried out high-pressure electrical measurements up to 55 GPa, together with high-pressure X-ray diffraction measurements and high-pressure structure prediction on KHgAs. We found a pressure-induced semiconductor-metal transition between ~16 and 20 GPa, followed by the appearance of superconductivity with a Tc of ~3.5 K at approximately 21 GPa. The superconducting transition temperature was enhanced to a maximum of ~6.6 K at 31.8 GPa and then slowly decreased until 55 GPa. Furthermore, three high-pressure phases within 55 GPa were observed, and their crystal structures were established. Our results showed the high-pressure phase diagram of KHgAs and determined the pressure-induced superconductivity in nonsymmorphic TIs. Thus, our study can be used to facilitate further research on superconductivity and topologically nontrivial features protected by nonsymmorphic symmetries. We observed a pressure-induced semiconductor-metal transition, which was followed by the emergence of superconductivity in the nonsymmorphic topological insulator KHgAs. The superconducting transition temperature reaches a maximum of approximately 6.6 K at 31.8 GPa, after which it slightly decreases up to 55 GPa. We identified the pressure-induced phase transitions and determined the structures of three high-pressure phases of KHgAs through structure prediction. Our findings establish the high-pressure phase diagram of the hourglass fermion compound KHgAs and demonstrate the potential coexistence of superconductivity with a topologically nontrivial feature protected by nonsymmorphic symmetries. [ABSTRACT FROM AUTHOR]

Spin angular momenta play important roles in light–matter interactions, leading to the emergence of the spin Hall effect and topological quasiparticles in modern optics. The typical approach is to decompose the spins of plane electromagnetic waves into longitudinal and transverse components, yet this description is not easily transferable to more structured electromagnetic environments. Here, we developed a field theory to reveal the physical origin and topological properties of longitudinal and transverse spins for arbitrary electromagnetic waves (including water waves and acoustic waves) in both near-field and free space. For electromagnetic waves carrying intrinsic helicity, we observed the emergence of helicity-dependent transverse spin possessing helicity-dependent spin-momentum locking. To verify that the number of spin-momentum locking states coincides with the spin Chern number, we experimentally measured the three-dimensional spin angular momentum densities of Bloch-type optical skyrmions. Our findings yield valuable insight for constructing spin-based field theory and exploiting optical topological quasiparticle-based applications. The task of mapping solid-state spin-orbit coupling (SOC) into photonic systems has sparked intense research efforts. The authors propose a unified theory to study SOC in photonic and classical wave systems, that is validated numerically and through ad hoc experiments with Bloch-type photonic skyrmions, showing excellent agreement between the two. [ABSTRACT FROM AUTHOR]