Neue beiträge zur theorie der elektrischen widerstandsänderung im magnetfeld

Chung, Kyu-Myung; Mrowka, Bernhard

doi:10.1007/bf01392845

Cited by 15 publications

(1 citation statement)

References 18 publications

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“…Schrauben functions describe free electrons in a uniform magnetic field in the symmetric gauge and have been used in the past for magnetoconductance calculations. [26,27] The paper has the following structure: In Section 2 the model is formulated and the projection operator of the M.T.G corresponding to the problem is introduced. In Section 3 we construct a basis of appropriately symmetric Bloch-like wavefunctions as linear combination of Schrauben functions.…”

Section: Introductionmentioning

confidence: 99%

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

Kliros

Divari

2006

Int. J. Mod. Phys. B

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In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.

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Section: Introductionmentioning

confidence: 99%

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

Kliros

Divari

2006

Int. J. Mod. Phys. B

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The Motion of an Electron in One‐Dimensional Periodic Potential under the Influence of Uniform Electric and Magnetic Fields

Jannussis

Papatheou

Tsilimigras

1978

Physica Status Solidi (b)

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a), V. PAPATHEOU (a), and P. TSILIBIIC+RAS (b)The properties are discussed of an electron moving in one-dimensional periodic potential in the presence of homogeneous mutual perpendicular electric and magnetic fields. The perturbation energy is ahown, by two different methods, to be a periodic function of the k, quantum number, as required by Harper's conditions, and also a periodic function of the electric field. Furthermore the partition function is calculated to second order in perturbation. The free energy of the system is evaluated, the magnetic moment as well as the magnetic susceptibility and its dependence on the electric field.Es werden die Eigenschaften eines sich in einem eindimensionalen periodischen Potential bewegenden Elektrons in homogenen, zueinander senkrechten elektrischen und magnetischen Feldern diskutiert. Es wird mit zwei unterschiedlichen Methoden gezeigt, daD die Stkirungsenergie, wie von der Harperschen Bedingung gefordert, eine periodische Funktion der Quantenzahl k, und ebenso eine periodische Funktion des elektrischen Feldes ist. Dariiber hinaus wird die Verteilungsfunktion bis zur zweiten Ordnung der Storung berechnet. Es wird die freie Energie des Systems, das magnetische Moment, die magnetische Suszeptibilitiit sowie ihre Abhiingigkeit vom elektrischen Feld bestimmt.

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Nonlinear Schrödinger‐type field equation for the description of dissipative systems. II. Frictionally damped motion in a magnetic field

Schuch

Chung

Hartmann

1984

Int J of Quantum Chemistry

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With the aid of a method similar to the one we used in an earlier work (part I) a new Schrodinger-type field equation with logarithmic nonlinearity can be derived from a Fokker-Planck equation for a distribution function. This nonlinear field equation describes the frictionally damped motion of a system under the influence of a magnetic field and can be interpreted in the same way as the nonlinear Schrodinger-type equation (NLSE) derived in part I, where no magnetic fields were taken into account. The NLSE for the two-dimensional motion of a charged material system in a homogeneous magnetic field is solved exactly. The solutions are compared with the quantummechanical solutions of the corresponding undamped problem. The method is extended to include also anisotropic conditions; i.e., in the Fokker-Planck equation the diffusion constant has to be replaced by a diffusion matrix, as different diffusion constants may be possible for different space directions. We regard the three-dimensional motion under the combined influence of magnetic and electric fieldsaccording to K = ( q / c ) ( v X B ) + q E -m y v with E , = ( m / q ) o : y , E , = -( m / q ) o : z , B = ( O , O , B ) as an example. This is an approximation of the conditions existing in an ion cyclotron resonance spectrometry cell, neglecting an additional drift motion in the x direction which could be taken into account by Galilean transformation and gauge transformation. The corresponding NLSE for the coupled three-dimensional motion is specified and solved exactly.

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Neue beiträge zur theorie der elektrischen widerstandsänderung im magnetfeld

Cited by 15 publications

References 18 publications

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

The Motion of an Electron in One‐Dimensional Periodic Potential under the Influence of Uniform Electric and Magnetic Fields

Nonlinear Schrödinger‐type field equation for the description of dissipative systems. II. Frictionally damped motion in a magnetic field

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