Degenerate Points Research Articles

Synergistic boost of catalytic activity in ZrTe topological catalyst via multiple topologically-electronic states

Topological materials feature highly-active topological surface states and high carrier mobility, making them promising catalysts. While ongoing research centers on topological catalysis, most topological semimetal catalysts tend to showcase either a singular topological electronic state or a lone highly catalytic surface, imposing limitations on overall efficiency. Our study highlights ZrTe as a standout catalyst for hydrogen evolution, boasting multiple topological states that excel across various surfaces. ZrTe exhibits a Weyl nodal ring and a triple degenerate nodal point near the Fermi energy, resulting in topological surface states on multiple surfaces. Notably, the (010) and (001) surfaces exhibit remarkable catalytic performance, with Gibbs free energy (ΔGH*) values surpassing that of the Pt metal. Our work establishes a robust and unequivocal link between catalysis and topological properties on the catalytic surfaces, revealing a linear correlation between ΔGH* and topological surface state density. ZrTe emerges as an exceptional topological catalyst, with both of its topological states significantly contributing to the catalytic performance on distinct surfaces. This pioneering discovery offers a valuable platform for advancing catalyst research in the concept of topological catalysts.

Genuine Dirac Half-Metals in Two-Dimensions.

When spin-orbit coupling (SOC) is absent, all proposed half-metals with twofold degenerate nodal points at the K (or K') point in 2D materials are classified as "Dirac half-metals" owing to the way graphene is utilized in the earliest studies. Actually, each band crossing point at the K or K' point is described by a 2D Weyl Hamiltonian with definite chirality; hence, it should be a Weyl point. To the best of its knowledge, there have not yet been any reports of a genuine (i.e., fourfold degenerate) 2D Dirac point half-metal. In this work, using first-principles calculations, it proposes for the first time that the 2D d0 -type ferromagnet Mg4 N4 is a genuine 2D Dirac half-metal candidate with a fourfold degenerate Dirac point at the S high-symmetry point, intrinsic magnetism, a high Curie temperature, 100% spin polarization, topology robust under the SOC and uniaxial and biaxial strains, and spin-polarized edge states. This work can serve as a starting point for future predictions of intrinsically magnetic materials with genuine 2D Dirac points, which will aid the frontier of topo-spintronics research in 2Dsystems.

Transmission properties of time-dependent one-dimensional metamaterials

We solve the wave equation with periodically time-modulated material parameters in a one-dimensional high-contrast resonator structure in the subwavelength regime exactly, for which we compute the subwavelength quasifrequencies numerically using Muller’s method. We prove a formula in the form of an ODE using a capacitance matrix approximation. Comparison of the exact results with the approximations reveals that the method of capacitance matrix approximation is accurate and significantly more efficient. We prove various transmission properties in the aforementioned structure and illustrate them with numerical simulations. In particular, we investigate the effect of time-modulated material parameters on the formation of degenerate points, band gaps and k-gaps.

Time modulation to manage and increase the power harvested from external vibrations

We investigate how a single resonator with a time-modulated component extracts power from an external ambient source. The collected power is largely dependent on the precise modulation signal frequency choice. We focus on the power absorbed from external vibration using a mechanical resonator and how time modulation of the damper can make a significant difference in the amount of harvested power, leading to more than 10 times enhancement compared to an analogous system without time modulation. We also find that a narrow band pair of peak and dip in the spectrum of the absorbed power occurs because of the presence of an exceptional point of degeneracy (EPD). In this narrow frequency range, the delay between the damper modulating signal and the external vibrating signal largely affects the collected power. The high frequency-selectivity of EPD-induced power management could potentially be used in sensing and spectrometer applications.

Chirality reversal of resonant modes in GdFe ferrimagnets

Chirality of antiferromagnetic spin waves as an intrinsic degree of freedom has been attracting considerable attention due to its potential applications for magnonic devices. In this paper, atomistic-scale dynamics simulations were conducted to investigate the chirality of spin wave resonant modes in ferrimagnetic alloy GdxFe1−x (0 < x <1) under different proportion x and external magnetic fields near the angular momentum compensation point. Simulation results reveal that as the proportion of Gd increases, the resonance mode of spin waves undergoes two distinct handedness flipping at magnetization compensation point and angular momentum compensation point. When the proportion x deviates from the magnetization compensation point, a frequency degeneracy point emerges at a non-zero magnetic field, indicating that the chirality of spin waves can also be switched by an external magnetic field. A theoretical analysis is developed to explain the observed phenomena. These findings provide valuable insights into the control and manipulation of spin wave chirality in ferrimagnetic alloys, with potential implications for the development of spin-based devices and technologies.

Perturbation of a piecewise regular-singular Liénard system

In this paper we discuss the perturbation of a generalized Liénard system, defined in two regions. For x≤0 the system is regular, while for x > 0 the system is singularly perturbed. An essential difference with other papers is that a degenerate canard point appears which requires a blow-up analysis.We prove that under generic conditions the perturbed system has at most one small-amplitude limit cycle and at most N canard limit cycles, where N is the number of local extrema of the function F(x) in the singular part of the Liénard system. For critical values of the control parameters the mechanism of a canard explosion is discussed.As an application we prove that the upper bound for the number of limit cycles in a Gause predator-prey system with a general monotonic functional response function with cut-off is two times the number of maxima of the natural prey growth function after the cut-off.

GaAs-chip-based mid-infrared supercontinuum generation

The mid-infrared spectral region opens up new possibilities for applications such as molecular spectroscopy with high spatial and frequency resolution. For example, the mid-infrared light provided by synchrotron sources has helped for early diagnosis of several pathologies. However, alternative light sources at the table-top scale would enable better access to these state-of-the-art characterizations, eventually speeding up research in biology and medicine. Mid-infrared supercontinuum generation in highly nonlinear waveguides pumped by compact fiber lasers represents an appealing alternative to synchrotrons. Here, we introduce orientation-patterned gallium arsenide waveguides as a new versatile platform for mid-infrared supercontinuum generation. Waveguides and fiber-based pump lasers are optimized in tandem to allow for the group velocities of the signal and the idler waves to match near the degeneracy point. This configuration exacerbates supercontinuum generation from 4 to 9 µm when waveguides are pumped at 2750 nm with few-nanojoule energy pulses. The brightness of the novel mid-infrared source exceeds that of the third-generation synchrotron source by a factor of 20. We also show that the nonlinear dynamics is strongly influenced by the choice of waveguide and laser parameters, thus offering an additional degree of freedom in tailoring the spectral profile of the generated light. Such an approach then opens new paths for high-brightness mid-infrared laser sources development for high-resolution spectroscopy and imaging. Furthermore, thanks to the excellent mechanical and thermal properties of the waveguide material, further power scaling seems feasible, allowing for the generation of watt-level ultra-broad frequency combs in the mid-infrared.

A transducer positioning method for transcranial focused ultrasound treatment of brain tumors.

As a non-invasive method for brain diseases, transcranial focused ultrasound (tFUS) offers higher spatial precision and regulation depth. Due to the altered path and intensity of sonication penetrating the skull, the focus and intensity in the skull are difficult to determine, making the use of ultrasound therapy for cancer treatment experimental and not widely available. The deficiency can be effectively addressed by numerical simulation methods, which enable the optimization of sonication modulation parameters and the determination of precise transducer positioning. A 3D skull model was established using binarized brain CT images. The selection of the transducer matrix was performed using the radius positioning (RP) method after identifying the intracranial target region. Simulations were performed, encompassing acoustic pressure (AP), acoustic field, and temperature field, in order to provide compelling evidence of the safety of tFUS in sonication-induced thermal effects. It was found that the angle of sonication path to the coronal plane obtained at all precision and frequency models did not exceed 10° and 15° to the transverse plane. The results of thermal effects illustrated that the peak temperatures of tFUS were 43.73°C, which did not reach the point of tissue degeneration. Once positioned, tFUS effectively delivers a Full Width at Half Maximum (FWHM) stimulation that targets tumors with diameters of up to 3.72 mm in a one-off. The original precision model showed an attenuation of 24.47 ± 6.13 mm in length and 2.40 ± 1.42 mm in width for the FWHM of sonication after penetrating the skull. The vector angles of the sonication path in each direction were determined based on the transducer positioning results. It has been suggested that when time is limited for precise transducer positioning, fixing the transducer on the horizontal surface of the target region can also yield positive results for stimulation. This framework used a new transducer localization method to offer a reliable basis for further research and offered new methods for the use of tFUS in brain tumor-related research.

The Impact of Tendon Lengthening Following Achilles Tendon Repair on Foot Kinetics, a Finite Element Analysis

Category: Midfoot/Forefoot; Hindfoot Introduction/Purpose: Triceps surae muscle force is transferred through the Achilles tendon to the calcaneus and from the calcaneus to the plantar fascia and then to the metatarsal heads and the toes which exert force on the ground. Achilles tendon ruptures occur in tendons that have reached a critical point of intrasubstance degeneration. The Achilles tendon almost always heals but frequently lengthens during the healing process, leading to an alteration in the triceps surae force production profile. We hypothesized that Achilles tendon overlengthening has implications not only for force generation but likely has many other impacts throughout the foot. The goal of this work was to evaluate the effect of a lengthened Achilles tendon following tendon repair on the kinetics of the foot. Methods: A validated finite element model of the foot was used to compare foot biomechanics between the foot with a functional and non-functional Achilles tendon. The model of the foot constructed from CT scan images of a female cadaveric foot weighing 60 kg included all 28 bones, 72 ligaments, cartilage, and an encapsulating soft tissue. The model was loaded with 0.5 body weight applied at the center of mass and 0.25 body weight applied to the Achilles tendon simulating quiet stance. The tendon forces were applied using force vectors in the direction of their lines of action. The foot with a non-functional Achilles tendon was created by unloading the Achilles tendon since triceps surae muscle shortening due to tendon lengthening significantly decreases force production. The force transmitted through the joints, force in the ligaments, and plantar pressure were determined for both the foot with a functional and non-functional Achilles tendon. Results: We found that the force transmitted through all the joints decreased when the Achilles tendon force was removed (Figure 1a). In addition, removing the Achilles tendon decreased the force within the plantar fascia, long and short plantar ligaments, and deep deltoid ligament, while it increased the force within the spring and superficial deltoid ligaments (Figure 1b). The plantar fascia experienced the greatest reduction in ligament force after unloading of the Achilles tendon (from 93 N to 26 N). Moreover, the maximum plantar pressure in the heel fat pad increased from 164 kPa to 231 kPa when the Achilles tendon was removed. Conclusion: The varying changes in the force in the ligaments and joints due to Achilles lengthening suggest that Achilles tendon rupture with sequent healing with overlengthening can alter the force distribution throughout the entire foot. A major implication of this work is that in treating Achilles ruptures, an extended period of protection with heel wedges beyond the customary six weeks may be needed to prevent over lengthening of the Achilles. Moreover, this study supports the efficiency of surgical lengthening of the Achilles in the treatment of diabetic forefoot foot ulcers by shifting the plantar pressure towards the calcaneus.

Superlinear fractional elliptic problems via the nonlinear Rayleigh quotient with two parameters

AbstractIt is established existence of weak solutions for nonlocal elliptic problems driven by the fractional Laplacian where the nonlinearity is indefinite in sign. More specifically, we shall consider the following nonlocal elliptic problem: where , and . The potentials satisfy some extra assumptions. The main feature is to find sharp parameters and where the Nehari method can be applied. In order to do that, we employ the nonlinear Rayleigh quotient together a fine analysis on the fibering maps associated to the energy functional. It is important to mention also that for each parameters and , there exist degenerate points in the Nehari set that give serious difficulties. Furthermore, we consider nonlinearities that are superlinear at the origin and superlinear at infinity. In order to overcome these difficulties, we apply some estimates together with a carefully analysis on the fibering maps. Here, we also consider the asymptotic behavior of the weak solutions for our main problem when or . Furthermore, we consider a nonexistence result for our main problem under some appropriate conditions on the parameters and .

Gain-loss-induced non-Abelian Bloch braids

Onsite gain-loss-induced topological braiding principle of non-Hermitian energy bands is theoretically formulated in multiband lattice models with Hermitian hopping amplitudes. Braid phase transition occurs when the gain-loss parameter is tuned across exceptional point degeneracy. Laboratory realizable effective-Hamiltonians are proposed to realize braid groups B2 and B3 of two and three bands, respectively. While B2 is trivially Abelian, the group B3 features non-Abelian braiding and energy permutation originating from the collective behavior of multiple exceptional points. Phase diagrams with respect to lattice parameters to realize braid group generators and their non-commutativity are shown. The proposed theory is conducive to synthesizing exceptional materials for applications in topological computation and information processing.

Electrophysiological properties of layer 2/3 pyramidal neurons in the primary visual cortex of a retinitis pigmentosa mouse model (rd10).

Retinal degeneration is one of the main causes of visual impairment and blindness. One group of retinal degenerative diseases, leading to the loss of photoreceptors, is collectively termed retinitis pigmentosa. In this group of diseases, the remaining retina is largely spared from initial cell death making retinal ganglion cells an interesting target for vision restoration methods. However, it is unknown how downstream brain areas, in particular the visual cortex, are affected by the progression of blindness. Visual deprivation studies have shown dramatic changes in the electrophysiological properties of visual cortex neurons, but changes on a cellular level in retinitis pigmentosa have not been investigated yet. Therefore, we used the rd10 mouse model to perform patch-clamp recordings of pyramidal neurons in layer 2/3 of the primary visual cortex to screen for potential changes in electrophysiological properties resulting from retinal degeneration. Compared to wild-type C57BL/6 mice, we only found an increase in intrinsic excitability around the time point of maximal retinal degeneration. In addition, we saw an increase in the current amplitude of spontaneous putative inhibitory events after a longer progression of retinal degeneration. However, we did not observe a long-lasting shift in excitability after prolonged retinal degeneration. Together, our results provide evidence of an intact visual cortex with promising potential for future therapeutic strategies to restore vision.

Bifurcations and steady states of a predator–prey model with strong Allee and fear effects

In this paper, the predator–prey model with strong Allee and fear effects is considered. The existence of the equilibria and their stability are established. Especially it is found that there is an interesting degenerate point, which is a cusp point with codimension 2 or higher codimension, or an attracting (repelling)-type saddle-node, subject to different conditions. Then the Hopf bifurcation and its direction, the saddle-node bifurcation and the Bogdanov–Tankens bifurcation are further explored. Afterwards, with the help of the energy estimates and the Leray–Schauder degree, the nonexistence and existence of the nonconstant steady states of the model are presented. From the obtained results, we find that strong Allee effect will cause the per capita growth rate of prey species from negative to positive; both the fear and Allee effects could affect the existence of equilibria and bifurcations; meanwhile, the diffusion rates will affect the existence of the nonconstant steady states.

Noise resilient exceptional-point voltmeters enabled by oscillation quenching phenomena

Exceptional point degeneracies (EPD) of linear non-Hermitian systems have been recently utilized for hypersensitive sensing. This proposal exploits the sublinear response that the degenerate frequencies experience once the system is externally perturbed. The enhanced sensitivity, however, might be offset by excess (fundamental and/or technical) noise. Here, we developed a self-oscillating nonlinear platform that supports transitions between two distinct oscillation quenching mechanisms – one having a spatially symmetric steady-state, and the other with an asymmetric steady-state – and displays nonlinear EPDs (NLEPDs) that can be employed for noise-resilient sensing. The experimental setup incorporates a nonlinear electronic dimer with voltage-sensitive coupling and demonstrates two-orders signal-to-noise enhancement of voltage variation measurements near NLEPDs. Our results resolve a long-standing debate on the efficacy of EPD-sensing in active systems above self-oscillating threshold.

Design of a Modified Coupled Resonators Optical Waveguide Supporting a Frozen Mode

We design a three-way silicon optical waveguide with the Bloch dispersion relation supporting a stationary inflection point (SIP). The SIP is a third order exceptional point of degeneracy (EPD) where three Bloch modes coalesce forming the frozen mode with greatly enhanced amplitude. The proposed design consists of a coupled resonators optical waveguide (CROW) coupled to a parallel straight waveguide. At any given frequency, this structure supports three pairs of reciprocal Bloch eigenmodes, propagating and/or evanescent. In addition to full-wave simulations, we also employ a so-called “hybrid model” that uses transfer matrices obtained from full-wave simulations of sub-blocks of the unit cell. This allows us to account for radiation losses and enables a design procedure based on minimizing the eigenmodes’ coalescence parameter. The proposed finite-length CROW displays almost unitary transfer function at the SIP resonance, implying a nearly perfect conversion of the input light into the frozen mode. The group delay and the effective quality factor at the SIP resonance show an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> scaling, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of unit cells in the cavity. The frozen mode in the CROW can be utilized in various applications like sensors, lasers and optical delay lines.

On-chip single-photon chirality encircling exceptional points

Exceptional points (EPs), typically defined as the degeneracy points of a non-Hermitian Hamiltonian, have been investigated in various physical systems such as photonic systems. In particular, the intriguing topological structures around EPs have given rise to novel strategies for manipulating photons and the underlying mechanism is especially useful for on-chip photonic applications. Although some on-chip experiments using lasers have been reported, EP-based photonic chips working in the quantum regime have been largely elusive. Here, we propose a single-photon experiment to dynamically encircle an EP in on-chip photonic waveguides possessing passive anti-parity-time symmetry. Photon coincidences measurement reveals a chiral feature of transporting single photons, which can act as a building block for on-chip quantum devices that require asymmetric transmissions. Our findings pave the way for on-chip experimental study on the physics of EPs as well as inspiring applications for on-chip non-Hermitian quantum devices.

Merged Potts-clock model: Algebraic and conventional multistructured multicritical orderings in two and three dimensions.

A spin system is studied with simultaneous permutation-symmetric Potts and spin-rotation-symmetric clock interactions in spatial dimensions d=2 and 3. The global phase diagram is calculated from the renormalization-group solution with the recently improved (spontaneous first-order detecting) Migdal-Kadanoff approximation or, equivalently, with hierarchical lattices with the inclusion of effective vacancies. Five different ordered phases are found: Conventionally ordered ferromagnetic, quadrupolar, antiferromagnetic phases and algebraically ordered antiferromagnetic, antiquadrupolar phases. These five different ordered phases and the disordered phase are mutually bounded by first- and second-order phase transitions, themselves delimited by multicritical points: Inverted bicritical, zero-temperature bicritical, tricritical, second-order bifurcation, and zero-temperature highly degenerate multicritical points. One rich phase diagram topology exhibits all of these phenomena.

A bulk-edge correspondence between the second Chern number and the spectral flow

A one-parameter family of semi-quantum Hamiltonians admitting the time-reversal symmetry is defined on the product S2(r1)×S2(r2) of two-spheres of respective radii r1 and r2, and a corresponding one-parameter family of quantum Hamiltonians is defined in terms of the angular momentum operators associated with respective spheres. The second Chern number of the eigen-vector bundle associated with a positive eigenvalue of the semi-quantum Hamiltonian is a piecewise constant function of the parameter with jumps at singular parameter values leading to the emergence of total degeneracy points for the eigenvalues. Correspondingly, the quantum Hamiltonian has edge-state eigenvalues which, as functions of the parameter, pass the zero energy level at the singular parameter values and the bulk-state eigenvalues prove to correspond to eigenvalues of the semi-quantum Hamiltonian. It is shown that the second-Chern number c2(T) at a non-singular parameter value T is in one-to-one correspondence with the spectral flow as a function of the end point of the interval (−∞,T). The bulk-edge correspondence is also shown to hold between the linearized semi-quantum and quantum systems, where the semi-quantum Hamiltonian is linearized at each of the degeneracy points of the eigenvalues and quantized to define linear quantum Hamiltonians. On this level, the spectral flow of each linear quantum Hamiltonian with a parameter μ proves to coincide with the index of the linear quantum Hamiltonian with μ=0.

Center conditions to find certain degenerate centers with characteristic directions

We consider the two-dimensional autonomous systems of differential equations where the origin is a monodromic degenerate singular point, i.e., with null linear part. In this work we give two heuristic procedures to obtain some center conditions (perhaps not necessary) for certain degenerate centers at the origin although they have characteristic directions.

Equivalent resolvents of Douglas-Rachford splitting and other operator splitting algorithms: a unified degenerate proximal point analysis

We introduce a generalized proximal point algorithm, and perform a detailed convergence analysis with the focus on the case of degenerate metric. The degeneracy leads to a well-defined resolvent form restricted to a reduced dimensional space. This approach unifies the algorithmic structures of Douglas-Rachford splitting and other related operator splitting schemes. Various aspects of these algorithms, in particular, the convergence of Douglas-Rachford splitting in terms of the solution itself and Chambolle-Pock algorithm under the limit setting, are investigated or revisited by the unified degenerate proximal point analysis.