Nonlinear dopplerons in semimetals

The possibility of the nonlinear wave propagation occurring in semimetals in the geometry where a constant magnetic field H is directed along the trigonal axis of the crystal has been investigated theoretically. In the linear regime in this geometry, there is a strong magnetic Landau damping without the wave propagation. It has been shown that the electron trapping by the magnetic field of a large-amplitude radio-frequency wave decreases the efficiency of this damping. As a result, nonlinear dopplerons can propagate in arsenic and, possibly, in antimony.     

Nonlinear skin effect in semimetals

The influence of nonlinearity on propagation of radio waves into semimetals in the geometry where the constant magnetic field H is directed along the trigonal axis of the crystal has been investigated. Strong magnetic Landau damping occurs in the linear mode in this geometry. It is shown that the electron capture by the magnetic field of a radio frequency wave of large amplitude decreases this absorption. As a result, the depth of the skin layer in the semimetal becomes the function of the amplitude of the exciting radio frequency field and can increase many times.     

On the theory of nonlinear dopplerons in metals

The possibility of the nonlinear wave propagation occurring in metals, such as cadmium, in the geometry where a constant magnetic field H is directed at an angle with respect to the hexagonal axis of the crystal has been investigated theoretically. In the linear regime in this geometry, there is a significant magnetic Landau damping, which prevents propagation of waves. It has been shown that the electron trapping by the magnetic field of a wave can substantially decrease the efficiency of this damping. As a result, the propagation of a doppleron, i.e., the mode related to the Doppler-shifted cyclotron resonance of electrons, becomes possible. It has been noted that a similar “bleaching” effect should also take place in some other metals.     

Nonlinear waves in bismuth

The propagation of short radio waves in a bismuth crystal in a constant magnetic field H aligned parallel to the bisecting axis oriented normally to the surface of the crystal plate is investigated theoretically. In this geometry, spatial inhomogeneity of the wave field has a weak effect on electrons and a strong effect on holes. It is demonstrated that, in a certain range of magnetic field strengths H, the bismuth crystal is characterized by two modes, namely, a helicon and a doppleron, whose damping is governed by cyclotron absorption of holes. For small amplitudes of the wave field in a linear regime, the damping lengths of both modes are relatively short due to cyclotron absorption. In a nonlinear regime, the magnetic field of the radio wave captures holes responsible for cyclotron absorption. As a result, the absorption is suppressed and the damping lengths of the helicon and the doppleron increase drastically. The excitation of these modes in the bismuth plate results in the fact that the dependence of the impedance of the plate on the magnetic field strength H exhibits resonance behavior and the transmittance of the plate increases by more than two orders of magnitude. It is shown that this effect should manifest itself at frequencies of the order of a few megahertzes in relatively weak magnetic fields (of the order of a few tens of oersteds).     

Doppler-shifted cyclotron resonance in tungsten plates with atomic pure surface

The surface resistance of thin monocrystalline W plates as a function of the constant magnetic field H directed along the normal to the sample surface is studied in the r.f. spectrum region. The sample surface was cleaned in high vaccum (10^-11 torr) or coated with the monomolecular impurity film. The oscillating with the magnetic field part R_osc due to the Doppler-shifted cyclotron resonance is studied. The doppleron oscillation amplitude is found to depend on the surface state and increases with the crystal cleaning. The observed changes are caused by the increase of the specular reflection coefficient for resonance electrons. With the deviation of the magnetic field from the normal to the plate surface, the doppleron wave undergoes a collisionless magnetic Landau damping and the signal amplitude decreases down to values comparable with that of Gantmakher-Kaner oscillations. Cleaning of the surface (and related increase of specularity) gives rise to a further decrease of the doppleron amplitude and appearance of additional interference maxima induced by the Gantmakher-Kaner effect.     

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ_xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.     

Magnetic field dependence of the thermoelectric power of n - type gallium arsenide in the extreme quantum limit

The effect of the quantization of the electron energy levels in a strong transverse magnetic field H on the low-temperature thermoelectric power (TEP) S of a high-purity isotropic semiconductor ($\text{n}$ - type gallium arsenide GaAs) is investigated theoretically. The “electron-diffusion” (S_e) and “phonon-drag” (S_p) components of S( = S_e + S_p) are calculated in the extreme quantum limit, when all the electrons in the conduction band are concentrated in the lowest Landau level. The transition to nondegeneracy, which takes place when the bottom of the lowest Landau level is driven through the Fermi level, has a large effect on the variations of S_e and S_p with magnetic field. The results are illustrated with numerical calculations for $\text{n}$ - type GaAs at 4.2 K with 1.2 × 10¹⁶ cm^-3 electrons.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Landau quantization of a two-dimensional electron with the nonparabolic dispersion law, pseudospin components and chirality terms

The Landau quantization of a two-dimensional electron in a perpendicular magnetic field on the basis of a Hamiltonian with two pseudospin components is considered. The diagonal elements of the Hamiltonian have non-parabolic but circular symmetric dispersion laws, whereas the off diagonal elements contain the chirality terms of different degrees. The solution of the matrix form Schrödinger equation was found following the method proposed by Rashba in his theory of spin-orbit coupling, taking into account different degrees of chirality and deviations on the parabolic dispersion law. The Landau quantization Hamiltonians were obtained by substituting the canonical momentum operators by the kinetic momentum operators. Two concrete examples were discussed. One of them concerns the Mexican hatlike dispersion law in the biased bilayer graphene with second order chirality, when the Landau quantization levels except two are characterized by two quantum numbers (n−2) and n for n≥2, corresponding to different pseudospin projections. They differ by 2 as the degree of chirality is. There are two energy levels E^±(n−2,n) with the same numbers (n−2) and n. The lower energy levels E⁻(n−2,n) have a linear decreasing behavior with dependence on the magnetic field strength H with different slopes and minima for different values of n≥2. At the intersection point H_th, two energy levels E⁻(1,3) and E⁻(0,2) have the same energy forming two degenerate LLLs. Touching the minima at different values of H, the energy branches gradually transform in the increasing quadratic dependences proportional to (2n+1)²H². The similar results were obtained in the case of cosine-type dispersion law in the frame of one-band model.     

Quantum waves in noble metals

A theoretical study is presented of the effect of hole energy quantization in a dc magnetic field on microwave penetration through a noble-metal plate. It is shown that quantization results in strong oscillations of cyclotron absorption. Between the absorption peaks, the damping decreases sufficiently to enable propagation of unique quantum waves. Excitation of such waves in a metallic plate gives rise to sharp oscillations of its surface resistance with magnetic field. The shape of these oscillations is also very unusual. Fiz. Tverd. Tela (St. Petersburg) 41, 1354–1360 (August 1999)     

Magnetic-impurity states of electron in two-dimensional semiconductor structures

Electron states on an attractive center of small-radius r _c ? l (l = $\sqrt {\frac{{c\hbar }}{{eH}}} $ is the magnetic length) located in a two-dimensional structure are investigated in a uniform magnetic field H applied perpendicularly to the structure surface. The spectrum of magnetic-impurity (MI) particle states with an arbitrary moment projection on the direction H for Landau bands 0 ≤ N < l ²/r _c ² is derived in the approximation that mixing of Landau levels is weak. The dependence of the electron energy states on magnetic field, the layer thickness, and the impurity position are studied. It is shown that dimension lowering leads to a qualitatively different spectrum of MI states compared to the three-dimensional case [1]. A comparison of the obtained binding energy of the D ^? center with experimental data is performed.     

Anomalies in the Magnetic Susceptibility in the Second-Order Phase Transitions beyond the Curie Point

Taking into account the inexhaustible interest in studying the peculiarities of physical properties in the neighborhood of phase transitions and the growth of experimental investigations of cobalt fluoride, we have studied the peculiarities of magnetic susceptibility in the vicinity of the critical field H_C at which cobalt fluoride performs the second-order phase transition from the antiferromagnetic phase to the angular phase. It is discovered that in the magnetic field H ‖ C₄, the magnetic susceptibility becomes infinite at H → H_C. It is shown that as the magnetic field direction deviates from the C₄ axis, the magnetic susceptibility in the critical field H_C proves to be finite. It is also shown that the change in the magnetic susceptibility with the change in the magnetic field considerably decreases at extremely insignificant deviations of the field H from the C₄ axis. Since the calculations are performed in terms of the Landau theory of phase transitions, we pay attention to the similarity and difference between the obtained results and those in the vicinity of the Curie point obtained by using the Landau theory of phase transitions.     

Electronic properties of a Weyl semimetal in crossed magnetic and electric fields

The study of Weyl semimetals is one of the most challenging problems of condensed matter physics. These materials exhibit interesting properties in a magnetic field. In this work, we investigate the Landau bands and the density of states (DOS) oscillations in a Weyl semimetal in crossed magnetic and electric fields. An expression is obtained for the energy spectrum of the system using the following three different methods: an algebraic approach, a Lorentz shift-based approach, and a quasi-classical approach. It is interesting that the energy spectrum calculated in terms of the quasi-classical approach coincides with the spectrum obtained using the microscopic approaches. An electric field is shown to change the Landau bands radically. In addition, the classical motion of a three-dimensional Dirac fermion in crossed fields is studied. In the case of a Dirac spectrum, the longitudinal (with respect to magnetic field) component of momentum (p _z ∥ H) is shown to be an oscillating function of the magnetic field. When the electric field is v⊥H/c, the Landau levels collapse and the motion becomes fully linear in an unusual manner. In this case, the wavefunction of bulk states vanishes and only states with p _z = 0 are retained. An electric field affects the character of DOS oscillations. An analytical expression is obtained for the quantum capacitance in crossed fields in the cases of strong and weak electric fields. Thus, an electric field is an additional parameter for adjusting the diamagnetic properties of Weyl semimetals.     

Nonlinear doppler-shifted cyclotron resonance in aluminum

The Doppler-shifted cyclotron resonance in an aluminum plate in the geometry when constant magnetic field H is directed along the [100] crystallographic axis oriented normally to the surface of the plate is studied theoretically. The analysis is performed for a simple model Fermi surface possessing fourth-order symmetry. Capture of holes by the magnetic field of a radio-frequency wave is shown to considerably decrease the effectiveness of cyclotron absorption at large exciting field amplitudes. This suppresses the collisionless damping of dopplerons (propagating modes related to odd cyclotron resonance harmonics). As a result, the sample becomes more transparent to radio-frequency radiation.     

Photon-drag effect in a two-dimensional electron gas in high magnetic fields

We present the first measurements concerning the photon drag effect in a two-dimensional electron gas based on intersubband transitions in high magnetic fields. It is shown that the excitation mechanism of the drag voltage in a magnetic field differs obviously from the case of zero magnetic field. The longitudinal as well as the Hall drag voltage show strong oscillations around zero when the magnetic field is swept. Both consist of a B-symmetrical and an antisymmetrical part with the same periodicity in B as the magnetoresistanceR_xx. The drag voltage oscillations are strongly correlated to the relative position of Fermi energy and Landau levels and are independent of the photon energy in the range of usable laser lines.     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Stress dependence of the domain wall dynamics in the adiabatic regime

In this work, we determine the domain wall velocity in the low field region and study the domain dynamics in as-cast and annealed bi-stable amorphous glass-covered Fe_77.5Si_7.5B₁₅ microwires. In particular, from the relation between the domain wall velocity and magnetic field in the adiabatic regime, the power-law critical exponent β, the critical field H₀ and the domain wall damping η were obtained. It has been verified that the main source of domain wall damping is the eddy current and spin relaxation, both with a strong relation with the magnetoelastic energy. This energy term is changed by the axial applied stress, which, by its time, modifies the damping mechanisms. It was also verified that the domain wall damping terms present different behavior at low (mainly eddy currents) and high applied stress (spin relaxation).     

Transport properties of conduction electrons in n-type inversion layers in (100) surfaces of silicon

The conductivities of n-type inversion layers in (100) surfaces of p-type silicon were measured extensively as functions of electron density in the inversion layer, the ambient temperature and the applied magnetic field. Measurements were made on the carefully fabricated four “classes” of MOS field-effect transistors whose maximum mobilities at 4·2K were 14,000, 8000, 6800 and 1500 cm²/V·sec, respectively. From the temperature dependence of the mobility, dominant momentum scattering was reasonably ascribed to surfon at 100 ～ 300 K. and degenerate or non-degenerate coulomb scattering at lower temperatures as treated by Stern and Howard. From the curves of conductivity vs temperature at low temperatures and low electron concentration for specimens with high mobilities, an activation energy of 1·2 meV, relating to the shallow bound states associated with the lowest electrin sub-band, was observed. The conductivity σ_xx of the inversion layer in a strong transverse magnetic field showed behaviors like those of completely free electrons without effects belonging to its material in its oscillation pattern. That is, the peak value of σ_xx as a function of the gate voltage V_R dependend only on the Landau index. The σ_xx as a function of the magnetic field H at a constant V_R showed a similar Shubnikov-de Haas (SdH) type oscillation to that of three dimensional one. The SdH oscillation gave an “apparent” g-value g* which ranges from 2 to 5 depending on the surface carrier density n_s, due to the change in the ratios of the widths of the Landau levels to the level separation. The “reasonable” g-value of the conduction electrons in the inversion layer has been determined using a modified tilted magnetic field method. The g-value at the fixed magnetic field was independent of surface carrier density n_s and tended to 2 in the extreme strong magnetic field.Discussion is made of the g-value relating to the Landau level width and the energy gaps in the density of states under strong magnetic field.     

Thermoelectric power of semiconductors in the extreme quantum limit—I: The ‘electron-diffusion’ contribution

A study is made of the effect of the quantization of the electron energy levels in a strong magnetic field on the ‘electron-diffusion’ contribution, S_e, of the transverse thermoelectric power of a high-purity isotropic semiconductor (n-type gallium arsenide GaAs) in the extreme quantum limit, when all the carriers in the conduction band are in the lowest Landau level. A theoretical expression for S_e is derived, taking into account of spin splitting. The sign of S_e is either positive or negative, depending on the sign of the conducting carriers. The transition to nondegeneracy, which takes place when the lowest Landau level is driven through the Fermi level, has a large effect on the variation of S_e with magnetic field. This effect is characterized by a large and rapid increase in |S_e|. Spin splitting effects, even with a small effective mass ($\text{m1 = 0·07 m}{}_0$, where m₀ is the free-electron mass) and a very small g-factor (g ≈ 0·32), greatly modify and reduce |S_e| a a function of field. For large fields, |S_e| increases monotonically with H. Calculations are carried out for n-type GaAs at T = 0·5°K with N = 1·2 × 10¹⁶cm^?3 carriers.     

Clear experimental evidence for boundary and impurity scattering related crossover field scales in GaAs/AlGaAs split-gate wires

We study the magnetic field dependence of the correlation field ΔB_cand amplitude δgof the conductance fluctuations, observed in the low temperature magnetoresistance of GaAs/AlGaAs split-gate wires. Near zero field, universality of quantum interference is retained and the magnetoresistance shows universal conductance fluctuations. At high magnetic fields, although the discrete Landau level quantization becomes resolved. ΔB_cand δgare found to increase linearly with magnetic field, with a slope which depends upon the nature of electron scatterings in the wire.