Quadratic Dispersion Law Research Articles

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.

Quantum dispersion properties of eigenmodes in semiconductor nanotubes with dielectric filling in dc magnetic field

Dispersion properties of electromagnetic eigenmodes in a semiconductor nanotube (with quadratic electron dispersion law) filled by a nonmagnetic dielectric and placed in a coaxial dc magnetic field are studied theoretically. A new quantum electrodynamical phenomenon is predicted. Namely, it is shown that increase in the electron density n02D in the nanotube results in the appearance of new branches in the eigenmodes spectrum. These branches arise in a bifurcation manner at some critical values of n02D, when a new electron energy subzone starts to fill in. The number of branches monotonously increases with growth n02D and oscillates with increase in the number of magnetic flux quanta through the nanotube (i.e., a peculiar Aharonov–Bohm effect takes place). We also found that the dispersion curves have parts with anomalous dispersion. The analytical expression for electron energy loss due to the excitation of eigenmodes under the Cherenkov resonance condition is derived and numerically analyzed.

On the group velocity of whistling atmospherics

The dynamic spectrum of a whistling atmospheric is a signal of falling tone, and the group delay time of the signal as a function of frequency is formed as a result of propagation of a broadband pulse in a medium (magnetospheric plasma) with a quadratic dispersion law. In this paper, we show that for quadratic dispersion the group velocity is invariant under Galilean transformations. This means that, contrary to expectations, the group velocity is paradoxically independent of the velocity of the medium relative to the observer. A general invariance condition is found in the form of a differential equation. To explain the paradox, we introduce the concept of the dynamic spectrum of Green’s function of the path of propagation of electromagnetic waves from a pulse source (lightning discharge in the case of a whistling atmospheric) in a dispersive medium. We emphasize the importance of taking into account the motion of plasma in the experimental and theoretical study of electromagnetic wave phenomena in near-Earth space.

О групповой скорости свистящих атмосфериков

The dynamic spectrum of a whistling atmospheric is a signal of falling tone, and the group delay time of the signal as a function of frequency is formed as a result of propagation of a broadband pulse in a medium (magnetospheric plasma) with a quadratic dispersion law. In this paper, we show that for quadratic dispersion the group velocity is invariant under Galilean transformations. This means that, contrary to expectations, the group velocity is paradoxically independent of the velocity of the medium relative to the observer. A general invariance condition is found in the form of a differential equation. To explain the paradox, we introduce the concept of the dynamic spectrum of Green’s function of the path of propagation of electromagnetic waves from a pulse source (lightning discharge in the case of a whistling atmospheric) in a dispersive medium. We emphasize the importance of taking into account the motion of plasma in the experimental and theoretical study of electromagnetic wave phenomena in near-Earth space.

ВЫЧИСЛЕНИЕ ТЕМПЕРАТУРНОЙ ЗАВИСИМОСТИ ЭНЕРГЕТИЧЕСКОГО СПЕКТРА НОСИТЕЛЕЙ ЗАРЯДОВ В ПОЛУПРОВОДНИКАХ ПРИ ВОЗДЕЙСТВИИ СИЛЬНОГО МАГНИТНОГО ПОЛЯ

The energy spectrum of free holes in a st rong magnetic field is calculated for a non- quadratic dispersion law. The temperature dependen ce of the broadening of the Landau levels of holes in crystals with the Kane dispersion law has been studied. A new method for calculating the discrete energy spectrum in a quantizing magnetic field is proposed

2D electrons floating on a suspended atomically thin dielectric

The 2D electrons trapped in vacuum near the atomically thin dielectric (ATD, mono- or N-layer film of h-BN or transition metal dichalcogenide) are considered. ATD is suspended above the back gate and forms the capacitor, which is controlled by the biased voltage determining 2D concentration, n2D. It is found that the leakage current through ATD is negligible, and the effect of the polarizability of ATD is weak if N≤5. At temperatures T=0.1–15 K and n2D=5×108–1010cm−2, one deals with the Boltzmann liquid having a macroscopic thickness of ∼100 A. Due to the bending of ATD, the quadratic dispersion law of the flexural vibrations is transformed into the linear one at small wave vectors. The scattering processes of the electrons caused by these phonons or the monolayer islands on ATD are examined and the momentum and energy relaxation rates are analyzed based on the corresponding balance equations. The momentum relaxation times vary over orders of magnitude in the above region (T, n2D) and N. The response may change from the polaron transport, for a perfect single-layer ATD at low T and high n2D, to the high-mobility (≥107cm2/Vs) regime at high T and low n2D. The quasi-elastic energy relaxation due to phonon-induced scattering is considered, and the conditions for the heating of electrons by a weak in-plane electric field are found.

Effect of deviation from stoichiometry on transport and mechanical properties of Bi2Se3 polycrystals

The dependences of electrical conductivity, the Hall coefficient, the Seebeck coefficient, thermoelectric power factor and microhardness of Bi2Se3 polycrystals on the degree of deviation from stoichiometry 59.9–60.0 at. % Se and temperature (77–300 K) were obtained. The samples exhibited n-type conductivity in the studied ranges of compositions and temperatures. The boundaries of the Bi2Se3 homogeneity region were estimated. A non-monotonic behavior of the concentration dependences of the properties in the studied composition range, associated with a change in the phase composition and defect structure under the deviation from stoichiometry, was observed. The calculation of the power coefficient in the temperature dependence of electron mobility showed that in a stoichiometric Bi2Se3, electrons are predominantly scattered by acoustic phonons, and under the deviation from stoichiometry the contribution of impurity scattering increases. Based on the experimental data, the Fermi energy EF was calculated in the approximation of the relaxation time and within the framework of the single-band model with a quadratic dispersion law. The obtained values of EF showed that both in stoichiometric and non- stoichiometric Bi2Se3, the conduction is mainly due to electrons in the lower conduction subband.

Temperature Dependence of Autowave Characteristics of Localized Plasticity

The behavior of localized plastic flow autowaves in a Fe–Ni–Cr alloy at temperatures 143 K ≤ T ≤ 420 K is considered. The temperature variation of the autowave propagation velocity is studied. It is found that, for the region of low temperatures, the autowave velocity is inversely proportional to the work hardening coefficient and the quadratic dispersion law takes place. The elastoplastic strain invariant does not depend on temperature.

Температурная зависимость автоволновых характеристик локализованной пластичности

The behavior of autowaves of localized plastic flow in the Fe-Ni-Cr alloy at temperatures of 143≤ T≤ 420 K is considered. The temperature dependence of the propagation velocity of the autowave is studied. It was found that for the region of low temperatures the inverse proportionality of the autowave velocity to the strain hardening coefficient and the quadratic dispersion law are fulfilled. The temperature independence of the elastoplastic deformation invariant is established.

Collective Modes in BCS-Like Models

The Hamiltonian of the gapped modes in the BCS model of superconductivity is derived using the nilpotency expansion. It has the form of the Bogoliubov Hamiltonian of a boson superfluid. The gapped modes have a quadratic dispersion law. The smallest energy gap is smaller than twice the fermionic energy gap. The nilpotency expansion respects all the symmetries and it has been previously applied to nuclear physics and relativistic field theories including QCD. In particular, it reproduces exactly the bosonization occurring in a relativistic 4-fermion interaction model.

Magnetic-field-driven surface electromagnetic states in the graphene-antiferromagnetic photonic crystal system

The surface electromagnetic states (SEMSs) on graphene, which has a linear carrier dispersion law and is placed in an antiferromagnetic photonic crystal, are theoretically studied in the terahertz frequency range. The unit cell of such a crystal consists of layers of a nonmagnetic insulator and a uniaxial antiferromagnet, the easy axis of which is parallel to the crystal layers. A dc magnetic field is parallel to the easy axis of the antiferromagnet. An expression that relates the SEMS frequencies to the structure parameters is obtained. The problem of SEMS excitation by an external TE-polarized electromagnetic wave is solved, and the dependences of the transmission coefficient on the dc magnetic field and the carrier concentration are constructed. These dependences are shown to differ substantially from the case of a conventional two-dimensional electron gas with a quadratic electron dispersion law. Thus, the positions of the transmission coefficient peaks related to resonance SEMS excitation can be used to determine the character of carrier dispersion law in a two-dimensional electron gas.

Asymptotic expansion of the one-loop Ω-potential of quantum fields with a quadratic dispersion law

Nonextensive contributions of free quantum fields with quadratic dispersion law to the partition function are investigated. Nonextensive corrections are caused by finite sizes of the system. The general procedure of finding such corrections is developed. As an example, a model of the ideal gas of nonrelativistic fermions in a cube is considered. The equations of state are obtained for this system.

Spin relaxation due to deflection coupling in nanotube quantum dots

We consider relaxation of a single-electron spin in a nanotube quantum dot due to its coupling to flexural phonon modes, and identify a new spin-orbit-mediated coupling between the nanotube deflection and the electron spin. This mechanism dominates other spin-relaxation mechanisms in the limit of small energy transfers. Due to the quadratic dispersion law of long-wavelength flexons, $\ensuremath{\omega}\ensuremath{\propto}{q}^{2}$, the density of states $dq/d\ensuremath{\omega}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}1/2}$ diverges as $\ensuremath{\omega}\ensuremath{\rightarrow}0$. Furthermore, because here the spin couples directly to the nanotube deflection, there is an additional enhancement by a factor of $1/q$ compared to the deformation-potential coupling mechanism. We show that the deflection coupling robustly gives rise to a minimum in the magnetic field dependence of the spin lifetime ${T}_{1}$ near an avoided crossing between spin-orbit split levels in both the high- and low-temperature limits. This provides a mechanism that supports the identification of the observed ${T}_{1}$ minimum with an avoided crossing in the single-particle spectrum by Churchill et al. [Phys. Rev. Lett. 102, 166802 (2009)].

Pauli paramagnetism and Landau diamagnetism

The Landau diamagnetism of conduction electrons at sufficiently high temperatures (larger than the Landau level spacing but smaller than the Fermi energy) is considered using the analogy with Pauli paramagnetism. An expression obtained for the diamagnetic susceptibility is identical to the well-known Landau result. While the model describing free particles assumes a quadratic dispersion law, the difference between the effective mass of a carrier and electron mass is taken into account.

Temperature dependence of the hole concentration in the model of a hole metal with negative-U centers

The temperature dependence of the hole concentration is studied within the model of a hole metal with negative-U centers. Different versions of the model with a simplified representation of allowed bands and a quadratic valence-band dispersion law are considered. It is found that the temperature dependence of the hole concentration can acquire different forms, and the regions of the model parameters corresponding to these forms are determined. The results obtained are used in the discussion of the relation between normal to superconducting properties of high-temperature superconductors.

Goldstone bosons in presence of charge density

We investigate spontaneous symmetry breaking in Lorentz-noninvariant theories. Our general discussion includes relativistic systems at finite density as well as intrinsically nonrelativistic systems. The main result of the paper is a direct proof that nonzero density of a non-Abelian charge in the ground state implies the existence of a Goldstone boson with nonlinear (typically, quadratic) dispersion law. We show that the Goldstone boson dispersion relation may in general be extracted from the current transition amplitude and demonstrate on examples from recent literature, how the calculation of the dispersion relation is utilized by this method. After then, we use the general results to analyze the nonrelativistic degenerate Fermi gas of four fermion species. Because of its internal SU(4) symmetry, this system provides an analog to relativistic two-color quantum chromodynamics with two quark flavors. In the end, we extend our results to pseudo-Goldstone bosons of an explicitly broken symmetry.

Mesons and diquarks in a dense quark medium with color superconductivity

In the framework of the Nambu-Jona-Lasinio model with two quark flavors, we investigate the spectrum of meson and diquark excitations of dense quark matter in the phase with color superconductivity. The color SUc(3) symmetry is spontaneously broken to SUc(2) in this phase. But instead of the expected five Goldstone bosons in the mass spectrum, we observe only three, among which two bosons obey the quadratic dispersion law. We find the doublet of light diquark states with the mass ∼ 15 MeV and also the heavy diquark resonance (SUc(2) singlet) with the mass ∼ 1100 MeV. The π-and σ-mesons have the mass ∼ 330 Mev in the phase with color superconductivity. The π-mesons are then stable particles, while the σ-meson is stable only in the chiral limit in which the current quark mass m0 becomes zero. If m0 ≠ 0, then the σ-meson mixes with diquarks in the phase with color superconductivity and becomes a resonance with the width ∼ 30 MeV.

Superfluidity in a three-flavor Fermi gas withSU(3)symmetry

We investigate the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with SU(3) global symmetry. The s-wave pairing occurs in flavor anti-triplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the SU(3) symmetry to a SU(2) symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law and the mass gap have significant effect on the low temperature thermodynamics of the matter.

Abnormal number of Nambu-Goldstone bosons in the color-asymmetric dense color superconducting phase of a Nambu–Jona-Lasinio–type model

We consider an extended Nambu--Jona-Lasinio model including both (q \bar q)- and (qq)-interactions with two light-quark flavors in the presence of a single (quark density) chemical potential. In the color superconducting phase of the quark matter the color SU(3) symmetry is spontaneously broken down to SU(2). If the usual counting of Goldstone bosons would apply, five Nambu-Goldstone (NG) bosons corresponding to the five broken color generators should appear in the mass spectrum. Unlike that expectation, we find only three gapless diquark excitations of quark matter. One of them is an SU(2)-singlet, the remaining two form an SU(2)-(anti)doublet and have a quadratic dispersion law in the small momentum limit. These results are in agreement with the Nielsen-Chadha theorem, according to which NG-bosons in Lorentz-noninvariant systems, having a quadratic dispersion law, must be counted differently. The origin of the abnormal number of NG-bosons is shown to be related to a nonvanishing expectation value of the color charge operator Q_8 reflecting the lack of color neutrality of the ground state. Finally, by requiring color neutrality, two massive diquarks are argued to become massless, resulting in a normal number of five NG-bosons with usual linear dispersion laws.

Spin-wave resonance and magnetic properties in amorphous Co95-xZr5Mx (M=Zr,Nb,Ti) and Co91-xZr9Ptx thin films.

Amorphous ${\mathrm{Co}}_{95\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zr}}_{5}$${\mathit{M}}_{\mathit{x}}$ (M=Zr,Nb,Ti) and ${\mathrm{Co}}_{91\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zr}}_{9}$${\mathrm{Pt}}_{\mathit{x}}$ thin films were prepared by rf sputtering in a magnetic field applied parallel to the film surface. Here we report their ferromagnetic-resonance and magnetic properties. For the spin-wave resonance spectra corresponding to ${\mathrm{Co}}_{100\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Zr}}_{\mathit{x}}$ thin films, all the resonance fields, including the one corresponding to the uniform mode, follow a quadratic dispersion law with excellent precision. The intensities of the spin-wave mode are very weak. The overall results are fairly well explained by a model where it is shown that the characteristics of the spectra are determined by the random local anisotropy ${\mathit{K}}_{\mathit{l}}$. The value of the deduced ${\mathit{K}}_{\mathit{l}}$ decreases with decreasing ${\mathit{M}}_{\mathit{s}}$ as predicted by the single-ion anisotropy theory. The magnetic properties were studied systematically as a function of the pressure of sputtering gas ${\mathit{P}}_{\mathrm{Ar}}$ and rf input power ${\mathit{W}}_{\mathrm{rf}}$. The in-plane uniaxial anisotropy energy ${\mathit{K}}_{\mathit{u}}$ and the coercive field ${\mathit{H}}_{\mathit{c}}$ along the easy axis were dependent on the deposition parameters. The variations of saturation magnetization 4\ensuremath{\pi}${\mathit{M}}_{\mathit{s}}$ and magnetostriction ${\ensuremath{\lambda}}_{\mathit{s}}$ are also described.