Orbital Quantization Research Articles

Quantized density wave ordering induced by a magnetic field in quasi one-dimensional conductors in the weak coupling limit

A theoretical description of the Density Wave ordered phases induced by a magnetic field in quasi-1D conductors is given in the weak coupling limit. Within each phase, labelled by a quantum number, the wave vector is quantized. Density wave ordering and orbital quantization open a series of gaps in the quasi particle spectrum. Specific heat jump at the metal-Density Wave critical line, behaviour of the electronic gaps and of the order parameter, first order transitions between different Density Wave Phases are studied. Departures from BCS theory are discussed.

Oscillatory Magnetoresistance Caused by Field-Dependent Matrix Element for Scattering in Bechgaard Salts

The transverse magnetoresistance of quasi 10 conductors is shown to have a new effect of the title not originating in the orbital quantization like the Shubnikov-de Haas effect. The model band energy is a symplified version of Gor'kov-Leded's model. The eigen energy and wave function in the transverse magnetic field are obtained in the normal state and also in a SDW state. By a variational method the magnetoresistance is calculated for typical processes including the electron-phonon and Umklapp Coulomb scatterings in the normal and SDW states. The matrix elements for these processes are oscillatory due to interference of the incoming and outgoing electron waves modified by the field. The small-period oscillation observed in the magnetoresistance of the Bechgaard salts is ascribed to this new mechanism working with the electron-phonon interaction in the SDW state.

Quantum Cascade of Field-Induced SDW Phases in Quasi-1D Conductors

The metallic open Fermi surface of quasi-1D conductors, such as the (TMTSF)2X family, is destabilized in moderate magnetic fields inducing a semi-metallic SDW phase. The origin of this phenomenon is a quantum interference effect: Because of phase coherence between the SDW and the electron-hole wave function, the susceptibility diverges at low T for a set of quantized wavevector, leading to a metal SDW critical line made of a succession of segments, each of them labelled by a quantum number. Below this line, we expect, in increasing field, a cascade of first-order transitions between SDW phases corresponding to different quantum numbers, as observed recently in salts of the (TMTSF)2X family. Within each phase, SDW ordering and orbital quantization open an infinite series of gaps in the quasi-particle spectrum. The wave vector is quantized so that the Fermi level lies in the middle of a Landau gap. Significant departures from BCS behaviour are predicted.

AN INTRODUCTION TO SUBQUANTUM KINETICS: II. An Open Systems Description of Particles and Fields

Abstract A nonlinear reaction-diffusion system, designated as Model G, is described. This system is similar to the Brusselator with the exception that it includes a third reaction intermediate, variable G. It is shown that a reaction-diffusion substrate of the kind specified by Model G is able to give rise to localized steady state concentration inhomogeneities which are autonomous and self-stabilizing and which exhibit many of the properties of subatomic particles. These “dissipative structures” generate substrate concentration gradients (fields) about themselves which serve as physically realistic analogs of gravitational and electrostatic potential fields. Test particles placed in these 1/r fields are found to experience a 1/r2 accelerating force. Thus action-at-a-distance is elucidated, The same field giving rise to “electrostatic” effects is capable of causing closely spaced particles to undergo nuclear binding. Atom formation with electron orbital quantization is also predicted to occur. The fieid/s...

Semiconductor electrons in electric and magnetic fields

Optical properties of semiconductors in the simultaneous presence of electric and magnetic fields are reviewed, with particular emphasis on the possibilities of modulation techniques. First, the problem of an electron in crossed and parallel fields is solved in the one-level effective mass approximation (EMA), and the results are used to interpret the experimental interband transitions in Ge, with due account of the degenerate character of the valence band in this material. The limitations of the one-level EMA are discussed, and the two-level model is introduced, which correctly describes the experimentally observed transition from a magnetic type to an electric type of motion in increasing transverse electric field. Possibilities to observe electric field effects in cyclotron resonance transitions are discussed in this approximation. Finally, the three-level model is used to describe properly both orbital and spin properties of conduction electrons. It is demonstrated that in a small-gap semiconductor with large spin-orbit interaction a sufficiently strong transverse electric field destroys the Landau orbital quantization but not the Pauli spin quantization. Possible experimental consequences of this situation are discussed. Influence of finite dimensions of the sample on the character of the electron motion in crossed and parallel fields is examined. A possibility to achieve the semiconductor-semimetal transition in a symmetryinduced zero-gap semiconductor in crossed field configuration is predicted and described, taking into account the Luttinger effects in the magnetic level structure.

Quantum Oscillations of Microwave Helicon Dispersion inn-Type InSb and InAs

The effect of orbital quantization on microwave helicon dispersion in $n$-type InSb and InAs is investigated theoretically and experimentally. In the local limit, the leading term describing helicon dispersion is, unlike helicon damping, unaffected by orbital quantization. Quantum effects enter through the scattering-dependent terms involved in the dispersive part of the helicon propagation constant. The main contribution is shown to be associated with the Shubnikovde Haas-like oscillations of the scattering correction to the dissipationless Hall conductivity. Experimental measurements of the transmitted helicon phase observed at quantizing magnetic fields in highly doped $n$-type InSb and InAs at 35 GHz and liquid-helium temperature are compared with the theory. The magnetic field dependence of the observed oscillations in helicon phase agrees reasonably well with the theoretical analysis. While little can be said analytically about the amplitude of these oscillations (of the order of a few percent), our data does provide an empirical measure of the limits within which the usual classical analysis of helicon dispersion is valid. Finally, the effect of quantum oscillations appears to be considerably stronger in the helicon dispersion than in the related dc problem of the Hall coefficient.

Effect of Orbital Quantization on the Critical Field of Type-II Superconductors

We discuss the effect of the discreteness of the Landau levels on the upper critical field of a type-II superconductor. At $T=0\ifmmode^\circ\else\textdegree\fi{}$K an ideal superconductor will remain superconducting in an arbitrarily large magnetic field. However, the high-field state is destroyed by a minute amount of impurity scattering or by a small misalignment of up- and down-spin Landau levels. The residual effects are (a) a small shift in the low-temperature critical field [$\frac{\ensuremath{\Delta}{H}_{c2}}{{H}_{c2}}\ensuremath{\approx}{({k}_{F}{\ensuremath{\xi}}_{0})}^{\ensuremath{-}1}$] and (b) oscillatory structure in the transition temperature ${T}_{c2}(H)$ for temperatures $T\ensuremath{\lesssim}\frac{\ensuremath{\hbar}{\ensuremath{\omega}}_{c}}{2{\ensuremath{\pi}}^{2}k}$.

The role of surface treatment in the field effect anomaly of n-type InSb at high magnetic fields

By applying a magnetic field perpendicular to the surface of n-type InSb during a classical field effect experiment, a decrease in surface conductance was observed as contrasted to the expected field effect increase in conductance. This anomaly in the field effect was found in the case of cleaved {110} as well as etched {111} surfaces at 77 °K both in vacuum or immersed in liquid nitrogen. In the case of the {110} surfaces the anomaly was also observed at 4.2 °K in vacuum but not when they were immersed in liquid helium. The anomaly was not present at 4.2 °K in the case of {111} surfaces either in vacuum or when they were immersed in liquid helium. The results are explained on the basis of cross quantization of the kinetic energy of the electrons by the narrow surface space charge potential barrier normal to the surface and the magnetic orbital quantization on a plane parallel to the surface.

Effect of Current Carrier Scattering on the Complex Dielectric Tensor

AbstractA general expression is derived for the scattering‐dependent complex conductivity tensor σα β(ω, q). The density matrix satisfying the local charge and energy conservation laws in the presence of an electromagnetic field, is calculated in a linear approximation with respect to the carrier‐field interaction. It is shown that the conductivity tensor involves the term Δσαβ which vanishes if either the spatial dispersion or the scattering is not considered. In a high non‐uniform magnetic field at low frequencies the term gives rise to the conductivity current. If the orbital quantization is essential Δσαβ causes the diamagnetic susceptibility to become frequency‐dependent.

Influence of the Electron Interactions on Orbital Quantization

Influence of the Electron Interactions on Orbital Quantization

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Theory of Cyclotron Resonance Absorption by Negative-Mass Holes in Germanium

The effect of orbital quantization on cyclotron resonance absorption by negative-mass heavy holes in germanium is considered. The Landau level system for the heavy holes in the approximation of an axial energy surface is computed with an equation derived by Firsov. A semiclassical technique is used to compute the cyclotron absorption by the holes in negative mass states under thermal equilibrium conditions. It is shown that at low temperatures the absorption is markedly less than that which would be calculated by the usual classical transport theory; at 4.2\ifmmode^\circ\else\textdegree\fi{}K and 30 kMc/sec the absorption resonance essentially disappears. Similar effects are present, in principle, for any nonellipsoidal energy surface. The bearing of these calculations on several recent experiments is discussed.

The Change of Carrier Concentration in the Graphite with Static Magnetic Field

The change of carrier concentration with static magnetic field in a single crystal of graphite is considered and the Hall coefficient R is discussed from this point of view. The Wallace's model of the two dimensional zone and its orbital quantization proposed by McClure are the starting point of the analysis. By comparing with the Kinchin's experiment we propose that the acceptor levels exist at 11×10 -3 eV. above the bottom of the conduction band and their concentration is 1.7×10 18 /c.c.. As to the Wallace's resonance integral γ 0 we estimate its value as 1.43 eV. semiempirically. The ratio of the mobilities of two carriers b =µ p /µ n =0.87 gives the best fit of R at the low temperature under the strong magnetic field. By using these resonable values of the parameters the Hall coefficient R is plotted as the function of temperature and magnetic field. The agreement with experimental data may be good except the low field region. The origins of discrepancy are discussed.