Statistic properties of Fermi gas in a strong magnetic field

Based on the thermodynamic potential function of Fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of Fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.     

Definition and measurement of global thermodynamic variables for laser-cooled trapped gas

We have used the definition of global thermodynamic variables like pressure and volume for atoms trapped in a nonuniform potential to measure the state equation for a sample of cold Na atoms kept trapped in a quadrupole magnetic field. The results show that, for low atomic density, the system behaves like an ideal gas where pressure and volume are inversely proportional. At high density values (compressed system), the deviation from an ideal gas is clear. A model based on virial expansion shows that the measured deviation is larger than the expected first-order correction. Employing the concept of global variables may be an important procedure to describe the thermodynamic of gases in the ultracold regime eventually crossing the values where critical phenomena like Bose condensation, among others, take place.     

Detection of gravitational waves by electromagnetic radiation

A statistical theory of the ionization — recombination equilibrium of a non-degenerate plasma in a homogeneous magnetic field is given. It is shown that the magnetic field changes the reactive composition if the quanta of the oscillatory electron motion in the magnetic field — which corresponds classically to the electron gyration — are of the order of or larger than the thermal energy,?ω?kT. The ionization may be enhanced or depressed depending on whether the background gas of the plasma is diamagnetic or paramagnetic. Some low temperature experiments, where such an anomalous “magnetic ionization” might be observable, are discussed briefly.     

The dependence of the quantum oscillation amplitude on spin splitting

The electron density of states of a semiconductor in magnetic field exhibits an oscillatory behaviour. The amplitude of these oscillations is studied theoretically as a function of the electron spin splitting. The amplitude is shown to be strongly reduced when the spin splitting is equal to the half of the orbital splitting ?ω, provided that the collision broadening of the electronic levels is large enough. This fact should be reflected in a similar reduction of the amplitude of various quantum oscillatory phenomena, e.g. Shubnikov-de Haas effect.     

Magnetic surface levels

As is well known, the energy spectrum of conduction electrons in a metal in a magnetic field is split into the Landau levels. These levels give rise to several phenomena whose essence is in the oscillatory dependence of some property of the metal characteristics on the strength of the magnetic field, in the range of strong and medium fields. Of these the most famous are the de Haas-van Alphen effect, and the Shubnikov-de Haas effect. Electronic transitions between the Landau levels give rise to the cyclotron resonance.

In a surface layer of a metal placed in a weak magnetic field another system of levels appears for electrons moving along shallow arcs, with their ends resting upon the surface of the metal. These levels originate from the quantized periodic motion of electrons along such ‘skipping’ trajectories due to a specular reflection at the metal surface. The spectrum of the system of magnetic surface levels manifests itself in an oscillatory dependence of the surface impedance on a weak magnetic field. The oscillations are due to a resonant absorption of microwave radiation in transitions of electrons between the magnetic levels occurring at discrete values of the magnetic field.

This new quantum effect discovered in several metals in both the normal and superconducting states should, in principle, be common to all the conductors. Studies of the effect are being extended rapidly, and one foresees a discovery of some new phenomena due to the surface bound states of charged quasiparticles, arising in a conductor when exposed to a weak magnetic field.     

Thermodynamic properties of a magnetically modulated graphene monolayer

The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in the presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their bandwidth oscillates with magnetic field, leading to Weiss-type oscillations in the thermodynamic properties. The effect of magnetic modulation on the thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensional electron gas (2DEG). We observe Weiss-type and de Haas-van Alphen oscillations at low and high magnetic fields, respectively. There is a definite phase difference in Weiss-type oscillations in thermodynamic quantities of magnetically modulated graphene compared to electrically modulated graphene. On the other hand, the phase remains the same and the amplitude of the oscillation is large when compared with the magnetically modulated two-dimensional electron gas (2DEG). Explicit asymptotic expressions of the density of states and the Helmholtz free energy are provided to understand the phase and amplitude of the Weiss-type oscillations qualitatively. We also study thermodynamic properties when both electric and magnetic modulations are present. The Weiss-type oscillations still exist when the modulations are out-of-phase.     

Effective mass of the 2-dimensional electron gas in an Al0.6Ga0.4Sb/InAs single quantum well

The 2-dimensional electron gas (2DEG) in an Al_0.6Ga_0.4Sb/InAs single quantum well is studied using cyclotron resonance and Shubnikov - de Haas (SdH) techniques. The effective mass (m^*) of the 2DEG was obtained from the peak positions of the cyclotron resonance transmission spectra. The results exhibit oscillatory behavior as a function of the magnetic field strength (B). The m^* value extracted from the temperature dependence of the SdH oscillations is in good agreement with the average value of m^* obtained from cyclotron resonance measurements. The effective mass is calculated as a function of B using an electron self-energy model based on the Hartree-Fock approximation. The calculated m^* values also show oscillatory behavior similar to that of the measured cyclotron resonance m^*. Both experiment and theory show that m^* maxima are shifted from the integral values (both odd and even) of the filling factors.     

Novel magneto-oscillatory behavior of confined electrons at a twin boundary in ZnSe and at an interface in GaAs/AlGaAs heterostructures

Electronic properties of confined electrons at naturally formed twin boundaries in ZeSe have been investigated by microwave absorption measurements. Cyclotron resonance signal of the confined electrons was observed. On the cyclotron resonance peak, novel oscillation of the absorption intensity was observed. Similar oscillatory behavior was also observed in GaAs/AlGaAs heterostructures near cyclotron resonance filed at which new Shubnikov–de Haas-like oscillation was observed by Zudov. The oscillatory structure has a period not in inverse magnetic field but magnetic field. The origin of the oscillation observed is caused by Rayleigh interference of two-dimensional electron gas.     

On the equation of state for an electron gas in an intense magnetic field

In this paper we derive the equation of state for a relativistic electron gas imbedded in a static homogeneous magnetic field of arbitrary strength. The derivation is based on the evaluation of the energy-momentum tensor and the use of Dirac's equation for such a problem. Contrary to a derivation presented several years ago, the present derivation is completely gauge-invariant. We also show how to recover, in an exact manner, the perfect gas law for the case of weak magnetic fields.     

耦合电磁场对石墨烯量子磁振荡的影响

我们研究了包含自旋轨道耦合与杂质散射在内的石墨烯量子磁振荡对外加电磁场的响应.我们发现,石墨烯中自旋轨道耦合、电磁场以及边界共同修正了朗道能谱,且当电场与磁场比值超过某一临界值时,量子磁振荡会突然消失,这与非相对论二维电子气的情况显著不同.这种现象可以通过朗道量子化轨道由封闭转化为开放的半经典理论来解释.此外,我们还发现杂质散射和温度的共同作用会使得磁振荡振幅衰减.我们的结果可用于分析石墨烯及其类似结构(硅烯、锗烯、锡烯等)的费米能级与朗道能谱的相互作用,进而探测自旋轨道耦合引起的能隙.     

Diffusion of electrons scattered by short-range impurities in a quantizing magnetic field

Formulas for transverse diffusion and conductivity in a semiconductor are obtained for electrons scattered by neutral impurities in a quantizing magnetic field. The formulas are valid for an impurity potential of arbitrary depth. Based on Kubo’s theory [1], calculations are performed using electron wavefunctions of the problem of single-impurity scattering in a magnetic field [2]. The poles of the scattering amplitude correctly determine electron eigenstates and magnetic impurity states. As a result, an exact expression is found for the dependence of transverse diffusion coefficient D _⊥ on longitudinal electron energy ? due to scattering by short-range (neutral) impurities. The behavior of D _⊥(?) is examined over an interval of magnetic field strength for several values of impurity potential depth. The experimental observability of diffusion and conductivity using IR lasers is discussed.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

Oscillatory magnetization and specific heat of electron gas in InSb

Oscillatory magnetization and specific heat of electron gas in InSb-type semiconductors are calculated. It is shown that a nonparabolic shape of the conduction band strongly affects amplitudes of the deHaas-vanAlphen oscillations. An oscillatory character of the electronic specific heat in the presence of a quantizing magnetic field is demonstrated. Intra-subband and inter-subband thermal excitations contribute to a double-peak structure of the specific heat versus magnetic field intensity.     

Two-dimensional electron gas in a strong magnetic field. I

We obtain expressions for the thermodynamic potential, concentration, and magnetic moment of an ideal two-dimensional electron gas in a strong (quantizing the motion) magnetic field at low temperatures. The results are used to explain the integer quantum Hall effect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 101–106, January, 1990.     

Dielectric linear response of magnetized electrons: Drag force on ions

The drag force on ions moving in a magnetized electron plasma is calculated in dielectric linear response. Various representations of the dielectric function ε(k, ω) are investigated for their suitability to display the limits for an infinite and a vanishing magnetic field. While the influence of the magnetic field is negligible in certain regions of k-space, it introduces in other regions a strong oscillatory structure in the dielectric function. This requires a careful treatment of the multidimensional integrations necessary for the drag force. The contributions from oscillatory integrands are treated by the saddle point method. Explicit results are obtained for the dependence of the drag force on the magnetic field, the direction of motion of the ion relative to the magnetic field, the shielding in the electron plasma, its density and the anisotropy of the electron temperature. The importance of the collective response of the electrons is investigated for limiting cases of the magnetic field. The validity of the linearization of the dielectric theory is checked by comparison with results obtained by numerical simulation of the nonlinear Vlasov-Poisson equation. For strong magnetic fields and low ion velocities, the simulations rather agree with the complementary binary collision model than with linear response.     

Wigner function of a two-dimensional electron gas in a magnetic field

The Wigner function of a two-dimensional electron gas in an arbitrary magnetic field perpendicular to the plane in which the electrons are confined is constructed rigorously. The function is useful in taking various statistical averages and illuminates the roles played by the hyperbolic functions of the field which appear in the expressions of the susceptibility and other physical quantities.     

Righi-Leduc effect in a quantizing magnetic field

The Righi-Leduc effect in semiconductors with a Kane dispersion law in the presence of strong, quantizing, magnetic fields is studied theoretically. The explicit form of the dependence on the magnetic field, temperature, and concentration in arbitrary quantizing magnetic fields is established for semiconductors with a nondegenerate electron gas in the approximation of small nonparabolicity. A simple formula that is applicable for all strong magnetic fields, including quantizing fields, is derived for the Righi-Leduc coefficient in the case of strongly degenerate semiconductors with an arbitrary nonparabolic band. It is shown that in order to determine the photon part of the thermal conductivity ,ph directly from experiment it is best to employ samples with a nondegenerate electron gas in strong, but nonquantizing, magnetic fields.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 102–107, July, 1988.     

Inverted satellites of a solitary oscillating pearl vortex in a thin magnetic superconductor film

An electrodynamic equation is derived for the magnetic field of an isolated Pearl vortex moving along an arbitrary trajectory in an ultrathin film of a magnetic superconductor. This equation is valid for any type of magnetic order in the magnetic subsystem. The magnetic structure of an isolated oscillating Pearl vortex is investigated in a thin magnetic superconductor film. Oscillations of the vortex and the presence of the magnetic subsystem are shown to lead to a significant renormalization of the vortex field in comparison with the Pearl solution. New phenomena of inverted satellites are predicted in which an inverted precursor appears in front of the vortex and an inverted wake is formed behind the latter at a distance of the order of 10λ_eff from the vortex center. These phenomena can be observed in magnetooptical experiments.     

Thermodynamic functions of degenerate magnetized electron gas

The Fermi energy, pressure, internal energy, entropy, and heat capacity of completely degenerate relativistic electron gas are calculated by numerical methods. It is shown that the maximum admissible magnetic field on the order of 10⁹ G in white dwarfs increases the pressure by a factor of 1.06 in the central region, where the electron concentration is ∼10³³ cm⁻³, while the equilibrium radius increases by approximately a factor of 1.03, which obviously cannot be observed experimentally. A magnetic field of ∼10⁸ G or lower has no effect on the pressure and other thermodynamic functions. It is also shown that the contribution of degenerate electron gas to the total pressure in neutron stars is negligible compared to that of neutron gas even in magnetic fields with a maximum induction ∼10¹⁷ G possible in neutron stars. The neutron beta-decay forbiddeness conditions in a superstrong magnetic field are formulated. It is assumed that small neutron stars have such magnetic fields and that pulsars with small periods are the most probable objects that can have super-strong magnetic fields.     

Spin waves,vortices, and the structure of equilibrium states in the classicalXY model

We prove that, for spin systems with a continuous symmetry group on lattices of arbitrary dimension, the surface tension vanishes at all temperatures. For the classicalXY model in zero magnetic field, this result is shown to imply absence of interfaces in the thermodynamic limit, at arbitrary temperature. We show that, at values of the temperature at which the free energy of that model is continuously differentiable, i.e. at all except possibly countably many temperatures, there iseither aunique translation-invariant equilibrium state, or all such states are labelled by the elements of the symmetry group, SO(2). Moreover, there areno non-translation-invariant, but periodic equilibrium states. We also reconsider the representation of theXY model as a gas of spin waves and vortices and discuss the possibility that, in four or more dimensions, translation invariance may be broken by imposing boundary conditions which force an (open) vortex sheet through the system. Among our main tools are new correlation inequalities.