Quantum theory of transverse galvano-magnetic phenomena

Adams, Edward N.; Holstein, T.

doi:10.1016/0022-3697(59)90002-2

Cited by 470 publications

(102 citation statements)

References 12 publications

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“…In this case the expression for yx σ in (5) coincides with that for the non-diagonal component of the conductivity tensor of the bulk semiconductor material. For the calculation of the diagonal components of conductivity tensor xx σ when the electric field is perpendicular to the plane of two-dimensional electron gas we will make use of the expressions obtained in [6] and [8], modified so as to allow for 2D character of the electron gas. The scattering mechanisms considered in the present work are the elastic electron scattering on short-range potential.…”

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confidence: 99%

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Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field

Nizametdinova

Hashimzade

Hasanov

et al. 2010

J. Phys.: Conf. Ser.

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Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field Abstract. We developed a quantitative theory of transverse magnetoresistance for the twodimensional electron gas (2DEG) in a quantum well with parabolic confinement potential in the magnetic field in the plane of the free movement of electrons. Our theory is based on the solution of Boltzmann kinetic equation for the components of the tensors of kinetic coefficients, when the perturbing force is directed along the plane of the free movement of electrons, and Titeike's formula for the diagonal component of the conductivity along the direction of confinement, based on the idea of the drift of the centres of cyclotron orbits in the crossed electric and magnetic fields. Numerical calculations have been performed for the 2D electron gas in GaAs/Al x Ga 1-x As QWs. It is shown, that the magnetoresistance is negative and equal about 50% in the weak magnetic field case, ω c <<ω 0 if the quantum limit 0 0 k T ω > is fulfilled. IntroductionMuch interest has been aroused recently in the behavior of two-dimensional electron systems in the presence of magnetic field parallel to the 2DEG layer. The electrical characteristics of these systems are of interest both for fundamental and applied physics. The study of magnetotransport in these structures makes it possible to understand better the mechanisms and parameters of electron scattering. The theory of the quantum galvanomagnetic effects in size-quantized systems was studied in [1][2][3][4]. In [1,2] the case of a strongly degenerate electronic gas was considered with the focus was on oscillation phenomena. In [3] the conductivity in QW structures has been calculated, and the size dependence of conductivity in the quantum limit for different mechanisms of electronic scattering has been considered. The authors used the kinetic equation method and the density matrix approach. In the latter case, the scattering was entered into the equation of motion for the density matrix through the lifetime of a quantum state. In [5] the magnetoresistance was studied for the case of electron scattering on a deformation potential of a three-dimensional crystal in a transverse magnetic field. It has been shown that for semiconductors with low mobility the magnetoresistance is negative in weak transverse magnetic fields. In the same paper it was noted that the negative magnetoresistance is not directly associated with weak localization.

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confidence: 99%

“…In the case when the current is along the direction of confinement it is necessary to use the density matrix approach obtained in [6][7] for calculation of the diagonal conduction tensor components.…”

Section: Introductionmentioning

confidence: 99%

Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field

Nizametdinova

Hashimzade

Hasanov

et al. 2010

J. Phys.: Conf. Ser.

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“…If the spectrum of electrons is assumed to be isotropic and quadratic, then the eigenvalues of energy have the form [1]:…”

Section: Introductionmentioning

confidence: 99%

Distribution function of electrons and phonons in semiconductors and semimetals in high electric and quantizing magnetic fields

Gassym

2003

Phys. Rev. B

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The distribution function of electrons and phonons interacting with electrons in semiconductors and semimetals in high electric and quantizing magnetic fields as a result of the solution of the coupled system of equations for the density matrixes of electrons and phonons is obtained. The effects of heating of electrons and phonons and their arbitrary mutual drag are taken into account. The dispersion relation of energy of electrons is assumed to be arbitrarily spherically symmetric one. The spectrum of phonons is assumed to be isotropic.The distribution function of electrons, phonons, the amplification coefficient of phonons and the dependence of chemical potential on E, H, n and T e are obtained.The distribution function of phonons is obtained for arbitrary drift velocities of phonons.

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“…The Shubnikov-de Haas oscillation and the Fermi surface were already well known, but I wondered what would happen in the extreme quantum limit if the magnetic field is so strong that only the lowest Landau level is occupied. The theory by Adams & Holstein (12) predicted that the magnetoresistance should be sensitive to the scattering mechanism, which in turn should make phonon scattering, point defects, and ionized impurity scattering distinguishable. These experiments required undoped crystals or at least those with a hole concentration of less than 2 × 10 16 cm −3 , and I was fortunate to have such crystals grown solely for my research.…”

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confidence: 99%

“…I did not include measurements on n-channels in my talk at that conference because such data had in principle already been covered by the pioneering work of Fowler, Fang, Howard, and Stiles (20,21). Today we know that my measurements on n-channels were different and the first to show the quantized resistance h/ie 2 (h = Planck constant, e = elementary charge, and i = 4, 8,12). In this respect the experimental birthday of the QHE was November 28, 1973, when I obtained the results shown in Figure 1, which were never published.…”

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confidence: 99%

Quantum Hall Effect: Discovery and Application

Klitzing

2017

Annu. Rev. Condens. Matter Phys.

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The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed matter science.

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Quantum theory of transverse galvano-magnetic phenomena

Cited by 470 publications

References 12 publications

Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field

Negative transverse magnetoresistance of the two-dimensional electron gas in quantum well with parabolic confinement potential under an in-plane magnetic field

Distribution function of electrons and phonons in semiconductors and semimetals in high electric and quantizing magnetic fields

Quantum Hall Effect: Discovery and Application

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