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Fu and Kane have discovered that a topological insulator with induced s-wave superconductivity (gap Δ0, Fermi velocity v F, Fermi energy μ) supports chiral Majorana modes propagating on the surface along the edge with a magnetic insulator. We show that the direction of motion of the Majorana fermions can be inverted by the counterflow of supercurrent, when the Cooper pair momentum along the boundary exceeds \\({{\\Delta}}_{0}^{2}/\\mu {v}_{\\mathrm{F}}\\). The chirality inversion is signaled by a doubling of the thermal conductance of a channel parallel to the supercurrent. Moreover, the inverted edge can transport a nonzero electrical current, carried by a Dirac mode that appears when the Majorana mode switches chirality. The chirality inversion is a unique signature of Majorana fermions in a spinful topological superconductor: it does not exist for spinless chiral p-wave pairing.

Photonic crystal surface-emitting lasers (PCSELs) are promising light sources with numerous advantages, including vertical emission, single-mode operation, and high output power. However, the fabrication of PCSEL devices requires advanced techniques, such as wafer bonding or epitaxial regrowth, to form a photonic crystal (PhC) structure close to the central waveguide layer. This process is not only complicated but also necessitates multiple semiconductor epitaxies, which reduces fabrication yield and increases manufacturing costs. In this study, we introduce a simpler method for fabricating PCSELs that requires only a single dry-etch run on any standard edge-emitting laser diode epistructure. The key challenge of creating an array of PhC air holes deep enough to reach the waveguide layer is addressed through high-temperature, high-plasma-density dry etching. PCSEL devices fabricated using this method lased in single mode at a threshold current density as low as ∼0.8 kA/cm , which is comparable to or better than previously demonstrated devices. Our results offer a cost-effective, high-yield approach to PCSEL fabrication.

Hyperbolic polaritons (HPs) supported by van der Waals (vdW) materials enable exceptionally strong light–matter interactions through deep subwavelength confinement. This confinement can be further enhanced when a polaritonic mode couples to its mirror image in a metallic substrate, giving rise to acoustic hyperbolic polaritons (AHPs). While most previous studies have focused on volume‐confined AHPs (v‐AHPs), edge‐confined AHPs (e‐AHPs) remain experimentally elusive. Here, we provide the first near‐field observation of e‐AHPs by launching and imaging them in the prototypical sample of hexagonal boron nitride (hBN) on a gold substrate. Unlike v‐AHPs propagating inside hBN, these e‐AHPs are guided along the hBN edges and exhibit shorter polariton wavelengths, as revealed by both near‐field imaging and extracted dispersion relations. Enhanced vibrational strong coupling in e‐AHPs, experimentally verified by monitoring molecular‐induced near‐field responses, demonstrates their suitability for high‐sensitivity molecule detection. These distinctive properties establish e‐AHPs as a promising platform for optical sensing and on‐chip nanophotonic devices. This work demonstrates a new type of light wave—edge‐confined acoustic hyperbolic polaritons—in hexagonal boron nitride on gold. These waves travel along crystal edges with nanoscale confinement and strongly interact with molecular vibrations, enabling highly sensitive detection of tiny molecular layers. The findings open pathways toward compact mid‐infrared sensors and integrated nanophotonic devices.

We analyze the quantum phases, correlation functions and edge modes for a class of spin-1/2 and fermionic models related to the one-dimensional Ising chain in the presence of a transverse field. These models are the Ising chain with anti-ferromagnetic long-range interactions that decay with distance r as , as well as a related class of fermionic Hamiltonians that generalize the Kitaev chain, where both the hopping and pairing terms are long-range and their relative strength can be varied. For these models, we provide the phase diagram for all exponents , based on an analysis of the entanglement entropy, the decay of correlation functions, and the edge modes in the case of open chains. We demonstrate that violations of the area law can occur for , while connected correlation functions can decay with a hybrid exponential and power-law behavior, with a power that is -dependent. Interestingly, for the fermionic models we provide an exact analytical derivation for the decay of the correlation functions at every . Along the critical lines, for all models breaking of conformal symmetry is argued at low enough . For the fermionic models we show that the edge modes, massless for , can acquire a mass for . The mass of these modes can be tuned by varying the relative strength of the kinetic and pairing terms in the Hamiltonian. Interestingly, for the Ising chain a similar edge localization appears for the first and second excited states on the paramagnetic side of the phase diagram, where edge modes are not expected. We argue that, at least for the fermionic chains, these massive states correspond to the appearance of new phases, notably approached via quantum phase transitions without mass gap closure. Finally, we discuss the possibility to detect some of these effects in experiments with cold trapped ions.

We investigate the appearance of new types of insulators and superconductors in long-range (LR) fermionic quantum systems. These phases are not included in the famous 'ten-fold way classification' (TWC), valid in the short-range (SR) limit. This conclusion is obtained analysing at first specific one-dimensional models, in particular their phase diagrams and entanglement properties. The LR phases are signalled, for instance, by the violation of the area-law for the von Neumann entropy and by a corresponding peculiar entanglement spectrum (ES). Later on, the origin of the deviations from the TWC is investigated from a more general point of view and in any dimension, showing that it is related with the presence of divergences occurring in the spectrum, due to the LR couplings. A satisfying characterization for the LR phases can be achieved, at least for one-dimensional quantum systems, as well as the definition of a nontrivial topology for them, resulting in the presence of massive edge states, provided a careful evaluation of the LR contributions. Our results allows to infer, at least for one-dimensional models, the weakening of the bulk-boundary correspondence, due to the important correlations between bulk and edges, and consequently to clarify the nature of the massive edge states. The emergence of this peculiar edge structure is signalled again by the bulk ES. The stability of the LR phases against local disorder is also discussed, showing notably that this ingredient can even strengthen the effect of the LR couplings. Finally, we analyse the entanglement content of the paradigmatic LR Ising chain, inferring again important deviations from the SR regime, as well as the limitations of bulk-boundary (tensor-network based) approaches to classify LR spin models.

We present a model of a mechanical system with a vibrational mode spectrum identical to the spectrum of electronic excitations in a tight-binding model of graphene. The model consists of point masses connected by elastic couplings, called 'tri-bonds', that implement certain three-body interactions, which can be tuned by varying parameters that correspond to the relative hopping amplitudes on the different bond directions in graphene. In the mechanical model, this is accomplished by varying the location of a pivot point that determines the allowed rigid rotations of a single tri-bond. The infinite system constitutes a Maxwell lattice, with the number of degrees of freedom equal to the number of constraints imposed by the tri-bonds. We construct the equilibrium and compatibility matrices and analyze the model's phase diagram, which includes spectra with Weyl points for some placements of the pivot and topologically polarized phases for others. We then discuss the edge modes and associated states of self stress for strips cut from the periodic lattice. Finally, we suggest a physical realization of the tri-bond, which allows access to parameter regimes not available to experiments on (strained) graphene and may be used to create other two-dimensional mechanical metamaterials with different spectral features.

Recent explorations of topology in physical systems have led to a new paradigm of condensed matters characterized by topologically protected states and phase transition, for example, topologically protected photonic crystals enabled by magneto-optical effects. However, in other wave systems such as acoustics, topological states cannot be simply reproduced due to the absence of similar magnetics-related sound-matter interactions in naturally available materials. Here, we propose an acoustic topological structure by creating an effective gauge magnetic field for sound using circularly flowing air in the designed acoustic ring resonators. The created gauge magnetic field breaks the time-reversal symmetry, and therefore topological properties can be designed to be nontrivial with non-zero Chern numbers and thus to enable a topological sonic crystal, in which the topologically protected acoustic edge-state transport is observed, featuring robust one-way propagation characteristics against a variety of topological defects and impurities. Our results open a new venue to non-magnetic topological structures and promise a unique approach to effective manipulation of acoustic interfacial transport at will.

We present a new high-efficiency splitter waveguide design based on photonic topological insulators. The system’s robust edge states allow electromagnetic waves to propagate in the 2D waveguide without backscattering, resulting in almost 100% transmission in the outputs. We also study resonating modes in the structure and show that introducing specific defects can create such modes. We consider four domains with rods of varying magneto-optical properties to provide edge modes in the system. By eliminating rows and columns of rods, we calculate the transmission at the outputs, revealing resonating modes in the middle of the structure with spatial symmetry. Our calculations indicate that the most promising resonating mode occurs when two rods and two columns are eliminated, with a quality factor Q = 1.02 × 10 6 at frequency f = 8.23 GHz and almost zero transmission at this frequency to the outputs. We further confirm our results using the transmission line resonator model as a semi-analytical model, which agrees well with our findings.

Majorana-based quantum gates are not complete for performing universal topological quantum computation while Fibonacci-based gates are difficult to be realized electronically and hardly coincide with the conventional quantum circuit models. In reference Hu and Kane (2018 Phys. Rev. Lett. 120 066801), it has been shown that a strongly correlated Majorana edge mode in a chiral topological superconductor can be decomposed into a Fibonacci anyon τ and a thermal operator anyon ɛ in the tricritical Ising model. The deconfinement of τ and ɛ via the interaction between the fermion modes yields the anyon collisions and gives the braiding of either τ or ɛ . With these braidings, the complete members of a set of universal gates, the Pauli gates, the Hadamard gate and extra phase gates for one-qubit as well as controlled-NOT (CNOT) gate for two-qubits, are topologically assembled. Encoding quantum information and reading out the computation results can be carried out through electric signals. With the sparse-dense mixed encodings, we set up the quantum circuit where the CNOT gate turns out to be a probabilistic gate and design the corresponding devices with thin films of the chiral topological superconductor. As an example of the universal topological quantum computing, we show the application to Shor’s integer factorization algorithm.