Quadratic Dispersion Research Articles

Quadratic Frequency Dispersion in the Oscillations of Intermediate-mass Stars

Asteroseismology, the study of stellar vibration, has met with great success, shedding light on stellar interior structure, rotation, and magnetism. Prominently known as δ Scutis, the intermediate-mass main-sequence oscillators that often exhibit rapid rotation and possess complex internal stratification are important targets of asteroseismic study. δ Scuti pulsations are driven by the κ (opacity) mechanism, resulting in a set of acoustic modes that can be challenging to interpret. Here, we apply machine learning to identify new patterns in the pulsation frequencies of δ Scuti stars, discovering resonances spaced according to quadratic functions of integer mode indices. This unusual connection between mode frequencies and indices suggests that rotational influence may play an important role in determining the frequencies of these acoustic oscillations.

Ideal quadratic nodal point in half-Heusler semimetal LaPtBi

The research focus on topological states in electronic systems has recently expanded from traditional linear dispersions to encompass higher-order dispersions. These higher-order dispersions exhibit unique physical properties, including high topological charge, exotic magnetoresponse, and novel transport behaviors. In this study, we employ first-principles calculations to propose the half-Heusler material LaPtBi as an ideal quadratic nodal point semimetal. Our comprehensive analysis of the band structure reveals an ideal nodal point located precisely at the Fermi level, exhibiting quadratic dispersion in all directions. This finding is supported by symmetry analysis and effective model arguments. Moreover, when the spin-orbit coupling effect is considered, the nodal point transitions from triple to quadruple degeneracy, while maintaining its quadratic dispersion. The material also features multiple prominent arc surface states originating from the nodal point, which are distinctly separated from the bulk bands. This separation facilitates experimental verification. Overall, LaPtBi, with its quadratic nodal point and advantageous properties, serves as an ideal platform for further research. The study of this material is expected to enhance our understanding of higher-order topological states in electronic systems, potentially driving future advancements in the field.

Three-dimensional topological crystalline insulator without spin–orbit coupling in nonsymmorphic photonic metacrystal

Abstract By including certain point group symmetry in the classification of band topology, Fu proposed a class of three-dimensional topological crystalline insulators (TCIs) without spin–orbit coupling in 2011. In Fu’s model, surface states (if present) doubly degenerate at Γ ¯ and M ¯ when time-reversal and C 4 symmetries are preserved. The analogs of Fu’s model with surface states quadratically degenerate at M ¯ are widely studied, while surface states with quadratic degeneracy at Γ ¯ are rarely reported. In this study, we propose a three-dimensional TCI without spin–orbit coupling in a judiciously designed nonsymmorphic photonic metacrystal. The surface states of photonic TCIs exhibit quadratic band degeneracy in the (001) surface Brillouin zone (BZ) center ( Γ ¯ point). The gapless surface states and their quadratic dispersion are protected by C 4 and time-reversal symmetries, which correspond to the nontrivial band topology characterized by Z 2 topological invariant. Moreover, the surface states along lines from Γ ¯ to the (001) surface BZ boundary exhibit zigzag feature, which is interpreted from symmetry perspective by building composite operators constructed by the product of glide symmetries with time-reversal symmetry. The metacrystal array surrounded with air possesses high order hinge states with electric fields highly localized at the hinge that may apply to optical sensors. The gapless surface states and hinge states reside in a clean frequency bandgap. The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor (PEC), which provide a pathway for topologically manipulating light propagation in photonic devices.

Experimental observation of parabolic wakes in thin plates

Wakes are medium perturbations created by a moving object, such as wave patterns behind boats, or wingtip vortices following an aircraft. Here, we report about an experimental study of an uncharted form of parabolic wakes occurring in media with the group velocity twice larger than the phase velocity, as opposed to the conventional case of Kelvin wakes. They are formed by moving a laser spot on a thin plate, which excites a unique wake pattern made of confocal parabolas, due to the quadratic dispersion of the zero-order flexural Lamb mode. If the spatial dimensions are rescaled by the perturbation velocity and material constant, we obtain a single universal wake with constant parabolic focal lengths. We demonstrate an evanescent regime above the critical frequency where the wave components oscillate exclusively in the direction parallel to the perturbation path, with an opening angle of 90∘. We define a dimensionless number, analogous to Froude and Mach numbers, which determines whether or not the complete parabolic wake pattern will be excited by the moving source. Finally, we generalize the physics of wake shapes to arbitrary dispersion relations. Published by the American Physical Society 2024

Flat-band and diverse quasi-fermions in Pb10(PO4)6O4

Employing a combination of first-principles calculations and low-energy effective models, we present a comprehensive investigation on the electronic structure of Pb10(PO4)6O4, which exhibits remarkable quasi-one-dimensional topological flat-band around the Fermi level. These flat bands predominantly originate from the px/py orbitals of the oxygen molecules chain at the fully-occupied 4e Wyckoff positions and thus can be well-captured by a minimal four-band tight-binding model. Furthermore, the abundant crystal symmetry inherent in Pb10(PO4)6O4 provides an ideal platform for the emergence of various quasi-fermions characterized by different dispersion, degeneracy, and dimensionality. These include a 0D four-fold degenerate Dirac fermion exhibiting quadratic dispersion, a 1D quadratic/linear nodal-line fermion along symmetric k-paths, a 1D hourglass nodal-line (HNL) fermion associated with the Dirac fermion, and a 2D symmetry-enforced nodal surface located on the kz = π plane. Moreover, when considering the weak ferromagnetic order, Pb10(PO4)6O4 transforms into a rare semi-half-metal, which is characterized by the presence of Dirac fermion and HNL fermion at the Fermi level for a single spin channel exhibiting 100 % spin polarization. Our findings reveal the rarely coexistence of flat bands, diverse topological semimetal states and ferromagnetism in Pb10(PO4)6O4, which may provide valuable insights for further exploring the intriguing interplay between superconductivity and exotic electronic states.

Waveguide modes of exchange spin waves in epitaxial YIG films

It has been shown that exchange spin wave (ESW) waveguide modes can be excited in epitaxial ferrite films. This is facilitated by the presence of a thin transition layer at the interface between the ferrite film and the non-magnetic substrate. A method for calculating the dispersion and energy characteristics of ESW waveguide modes is proposed. It is shown that the propagation of ESW modes is accompanied by the transfer of exchange power in the plane of the film. As the wave numbers increase indefinitely, the dispersion of the ESW modes asymptotically approaches the quadratic dispersion law. At zero wave numbers, the frequencies of the ESW modes coincide with the frequencies of uniform spin wave resonances. The possibility of crossing the dispersion branches of different ESW modes is demonstrated, which indicates the possibility of intermodal magnon-magnon hybridization.

Controllable Andreev Bound States in Bilayer Graphene Josephson Junctions from Short to Long Junction Limits.

We demonstrate that the mode number of Andreev bound states in bilayer graphene Josephson junctions can be modulated by controlling the superconducting coherence length insitu. By exploiting the quadratic band dispersion of bilayer graphene, we control the Fermi velocity and thus the coherence length via the application of electrostatic gating. Tunneling spectroscopy of the Andreev bound states reveals a crossover from short to long Josephson junction regimes as we approach the charge neutral point of the bilayer graphene. Furthermore, analysis of different mode numbers of the Andreev energy spectrum allows us to estimate the phase-dependent Josephson current quantitatively. Our Letter provides a new way for studying multimode Andreev levels by tuning the Fermi velocity.

Magnetic quadratic nodal lines in half-metallic anode material TiF3: A first-principles study

It is anticipated that nodal line materials may demonstrate unique physical phenomena. The traditional nodal line materials have a linear energy distribution surrounding them. A recent prediction is that systems may similarly stabilize nodal lines with a quadratic or cubic energy dispersion. This work focuses on a half-metal anode material, TiF3, which has already been predicted to host stable ferromagnetism and half-metallicity under Li insertion. Using first-principles calculation, we predicted for the first time that TiF3, a ferromagnetic material, has completely spin-polarized quadratic nodal lines along the Γ-X path. The half-metallic state and the spin-polarized quadratic nodal lines are robust to uniform strains (from −3 to +3 %). TiF3 can be regarded as a promising platform for deepening our comprehension of magnetic quadratic nodal lines in half-metals.

Andreev bound states in Josephson junctions of semi-Dirac semimetals

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor–barrier–superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum ɛ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of ɛ on the superconducting phase difference ϕ, we compute the variation of Josephson current as a function of ϕ.

Spatiotemporal dynamics of modulation instability in Kerr nonlinear media with pure-quartic dispersion

We present the analytical and numerical analysis on spatiotemporal dynamics of modulation instability (MI) in Kerr nonlinear media with pure-quartic dispersion. We apply a linear stability method to arrive at a universal expression for pure-quartic instability gain, which can simultaneously describe the temporal, spatial, and spatiotemporal cases. The results show that the condition of such three fundamental instability occurrence in pure-quartic dispersion media (PDM) is the same as that in conventional quadratic dispersion media (QDM). Another interesting observation is that the maximum gain is also the same in both cases. For temporal instability, there exists a critical power below which the instability bandwidth becomes wider than the corresponding case in QDM or otherwise. For spatiotemporal instability, the instability region depending on critical frequencies is found to show some remarkable difference when compared with the latter case. The analytical prediction resulting from linear stability analysis is confirmed by the numerical method.

Pressure-tuned quantum criticality in the large-D antiferromagnet DTN

Strongly correlated spin systems can be driven to quantum critical points via various routes. In particular, gapped quantum antiferromagnets can undergo phase transitions into a magnetically ordered state with applied pressure or magnetic field, acting as tuning parameters. These transitions are characterized by z = 1 or z = 2 dynamical critical exponents, determined by the linear and quadratic low-energy dispersion of spin excitations, respectively. Employing high-frequency susceptibility and ultrasound techniques, we demonstrate that the tetragonal easy-plane quantum antiferromagnet NiCl2 ⋅ 4SC(NH2)2 (aka DTN) undergoes a spin-gap closure transition at about 4.2 kbar, resulting in a pressure-induced magnetic ordering. The studies are complemented by high-pressure-electron spin-resonance measurements confirming the proposed scenario. Powder neutron diffraction measurements revealed that no lattice distortion occurs at this pressure and the high spin symmetry is preserved, establishing DTN as a perfect platform to investigate z = 1 quantum critical phenomena. The experimental observations are supported by DMRG calculations, allowing us to quantitatively describe the pressure-driven evolution of critical fields and spin-Hamiltonian parameters in DTN.

Raman-assisted Kerr platicon and perfect soliton crystal formation in the cavity

In this paper, we investigate the soliton evolution dynamics influenced by the stimulated Raman scattering effect. The strong Raman gain ensures the breathing platicon and stable platicon formation at the cavity with normal quartic dispersion. The switching waves benefitted from the power transformation between pump mode and Raman gain spectrum could modulate the temporal waveform at the breathing platicon existence region. The oscillated characteristics of the temporal waveform mainly rely on the central frequency of the Raman gain spectrum. Meanwhile, at the anomalous quadratic dispersion regime, the Raman effects could capture the perfect soliton crystal formation which provides one novel method for the implementation of the harmonic mode-locking process. Our findings provide a viable way to demonstrate the cavity soliton dynamics and soliton-based applications.

Hamiltonian birefringence and Born-Infeld limits

Using Hamiltonian methods, we find six relativistic theories of nonlinear electrodynamics for which plane wave perturbations about a constant uniform background are not birefringent. All have the same conformal strong-field limit to Bialynicki-Birula (BB) electrodynamics, but only four avoid superluminal propagation: Born-Infeld (BI), its non-conformal “extreme” limits (electric and magnetic) and the conformal BB limit. The quadratic dispersion relation of BI is shown to degenerate in the extreme limits to a pair of linear relations, which become identical in the BB limit.

Conservation of a Spectral Asymmetry Invariant in Optical Fiber Four‐Wave Mixing

AbstractThe conservation of spectral asymmetry is a fundamental feature of the ideal four‐wave mixing process as it exists in a medium combining quadratic chromatic dispersion and third‐order nonlinearity. The robustness of this invariant in an experimental configuration where the excitation conditions of an optical fiber are sequentially updated, mimicking infinite propagation is tested in this paper. This theoretical and experimental study reveals the high sensitivity of the asymmetry to very slight deviations from the ideal case, and the idealized system behaves as an intermediate case between the ideal case of noncascaded four‐wave mixing and propagation in a system governed by the nonlinear Schrödinger equation is shown.

Chiral Magnons in Altermagnetic RuO_{2}.

Magnons in ferromagnets have one chirality, and typically are in the GHz range and have a quadratic dispersion near the zero wave vector. In contrast, magnons in antiferromagnets are commonly considered to have bands with both chiralities that are degenerate across the entire Brillouin zone, and to be in the THz range and to have a linear dispersion near the center of the Brillouin zone. Here we theoretically demonstrate a new class of magnons on a prototypical d-wave altermagnet RuO_{2} with the compensated antiparallel magnetic order in the ground state. Based on density-functional-theory calculations we observe that the THz-range magnon bands in RuO_{2} have an alternating chirality splitting, similar to the alternating spin splitting of the electronic bands, and a linear magnon dispersion near the zero wave vector. We also show that, overall, the Landau damping of this metallic altermagnet is suppressed due to the spin-split electronic structure, as compared to an artificial antiferromagnetic phase of the same RuO_{2} crystal with spin-degenerate electronic bands and chirality-degenerate magnon bands.

Electronic thermal conductivity of few-layer black phosphorus

The theoretical investigations of anisotropic electronic thermal conductivity of nanoscale black phosphorus along zigzag and armchair directions are presented. Electrons in black phosphorus assumed to be scattered by in-plane linear dispersion phonons and out-of-plane quadratic dispersion phonons via deformation potential couplings. The individual contributions from in-plane phonon and out-of-plane phonon processes to the electronic thermal conductivity show dominant role of in-plane phonon processes. The anisotropic behaviour of electronic thermal conductivity is noticed and found to be sensitive to the carrier density and temperature. Role and relative importance of anisotropic electronic thermal conductivity in the analysis of experimental thermal conductivity data of nanoscale black phosphorus samples is investigated.

Revisiting Schrödinger's fourth-order, real-valued wave equation and the implication from the resulting energy levels.

In his seminal part IV, Annalen der Physik vol. 81, 1926 paper, Schrödinger has developed a clear understanding about the wave equation that produces the correct quadratic dispersion relation for matter-waves and he first presents a real-valued wave equation that is fourth-order in space and second-order in time. In the view of the mathematical difficulties associated with the eigenvalue analysis of a fourth-order, differential equation in association with the structure of the Hamilton-Jacobi equation, Schrödinger splits the fourth-order real operator into the product of two, second-order, conjugate complex operators and retains only one of the two complex operators to construct his iconic second-order, complex-valued wave equation. In this paper, we show that Schrödinger's original fourth-order, real-valued wave equation is a stiffer equation that produces higher energy levels than his second-order, complex-valued wave equation that predicts with remarkable accuracy the energy levels observed in the atomic line spectra of the chemical elements. Accordingly, the fourth-order, real-valued wave equation is too stiff to predict the emitted energy levels from the electrons of the chemical elements; therefore, the paper concludes that quantum mechanics can only be described with the less stiff, second-order, complex-valued wave equation.

Nonlinear evolution of modulational instability under the interaction of Kerr nonlinearity with pure higher, even-order dispersion

We investigate the nonlinear evolutions of modulation instability (MI) under the interaction of Kerr nonlinearity with pure higher, even-order dispersion (HEOD) by using the truncating method of three-wave mixing. For any HEOD, we find the phase-plane topological structure of the MI changes in three frequency regions whose ranges depend on the order of HEOD. And we present the novel types of nonlinear evolutions of the MI, which do not exist in the case of quadratic dispersion. Taking the pure-sextic dispersion as an example, the theoretical predictions of the MI evolutions are confirmed by numerically solving the modified nonlinear Schrödinger equation. Our results not only further deepen the understanding of MI, but also provide a universal guideline for experimental investigation of nonlinear waves, such as breather solitons or rogue waves excitation, in nonlinear Kerr media with pure HEOD.

Fano Resonances for Tilted Linear and Quadratic Band Touching Dispersions in a Harmonically Driven Potential Well

AbstractConsidering models with tilted linear and quadratic band touching dispersions, the effect of the transverse linear tilt on the transmission spectra is analyzed through a harmonically driven potential well oriented longitudinally. Employing the Floquet scattering matrix formalism, Fano resonances are found as an outcome of matching between the Floquet sidebands and quasi‐bound states, where the tilt renormalizes their energies and wave vectors. It is found that the Fano resonance energy decreases (increases) for linear (quadratic) band touchings as the magnitude of the transverse momentum increases, indicating a distinct signature of the underlying band dispersion in the transmission profile. The sign of the product of the transverse momentum and the tilt also determines the relative shift in the Fano resonance energy with respect to the untilted case for both band dispersions, suggesting a possible tunability of the Fano resonance for tilted systems. Importantly, the tilt strength can also be directly determined by measuring the Fano resonance energy as function of the transverse momenta direction. The shot noise spectra and their differential property are further studied where an inflection region and undulation, respectively, is found around the Fano resonance energy. Interestingly, differential shot noise and transmission spectra both qualitatively behave in a similar fashion and might thus serve as important observables for future experiments on driven solid‐state systems.

Acceleration-free propagation of Airy pulses in pure-quartic dispersion media

We investigate the propagation dynamics of Airy pulses in pure-quartic dispersion media both numerically and analytically. For linear propagation, our results show that Airy pulses will keep the acceleration-free propagation behaviors under the action of pure-quartic dispersion, quite different from the case in the presence of only quadratic or cubic dispersion. Another notable observation is that the optical fields will evolve to become a symmetric-shaped pulse and the oscillatory tail is gradually suppressed over long propagation. For nonlinear propagation, the Airy pulse having high powers will be shed into multiple soliton dynamics through the physical balance between anomalous pure-quartic dispersion and the Kerr nonlinear effect.