Green’s Function in Magnetic Fields
It is shown that Green’s function for a charged particle in a uniform magnetic field is resolved into a gauge-dependent exponential factor breaking the translational symmetry and the translationally symmetric function which is independent of gauge, but influenced by the magnetic field, even if the system contains periodic potential. In the absence of the periodic potential, the exact Green’s function is derived. This solution is calculated numerically. For the tight-binding approximation, Green’s function is represented by a Fourier transform of the infinite continued fraction. By making use of this Green’s function and the Kirchhoff-Huygens theorem, we can apply the “boundary element method” to analyze the quantum transport of a two-dimensional electron gas confined in an arbitrary structured boundary in the presence of a uniform magnetic field.
KeywordsBoundary Element Method Periodic Potential Uniform Magnetic Field Homogeneous Magnetic Field Bloch Electron
Unable to display preview. Download preview PDF.
- 3.Brebbia CA (1978) The boundary element method for engineers. Pentech, LondonGoogle Scholar
- 5.Gor’kov LP (1959) (in Russian) Soviet Phys JETP 9:1364–1367Google Scholar
- 7.Abramowitz M, Stegun IA (1970) Handbook of mathematical functions. Dover New York, pp 504–510Google Scholar
- 6.Courant R, Hilbert D (1961) Methods of mathematical physics, vol 2. Interscience, New YorkGoogle Scholar