2005/10/01 by Takafumi Kita, Masao Arai, M. Arai · 12 citations
Physics and Astronomy · #Advanced Chemical Physics Studies #Bloch oscillations #Condensed matter physics #Electron #Feynman diagram #Gauge theory #Magnetic field #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Quasiparticle #Superconductivity #cond-mat.mtrl-sci #cond-mat.str-el
paper · pdf · doi:10.1143/jpsj.74.2813
published in Journal of the Physical Society of Japan 74(10), 2813-2830 (Physical Society of Japan) · 19 pages, 2 figures
openalex publication_date 2005/10/01 · arxiv created 2005/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study interacting electrons in a periodic potential and a uniform magnetic field \bf B taking the spin-orbit interaction into account. We first establish a perturbation expansion for those electrons with respect to the Bloch states in zero field. It is shown that the expansion can be performed with the zero-field Feynman diagrams of satisfying the momentum and energy conservation laws. We thereby clarify the structures of the self-energy and the thermodynamic potential in a finite magnetic field. We also provide a prescription of calculating the electronic structure in a finite magnetic field within the density functional theory starting from the zero-field energy-band structure. On the basis of these formulations, we derive explicit expressions for the magnetic susceptibility of \bf B→\bf 0 at various approximation levels on the interaction, particularly within the density functional theory, which include the result of Roth [J. Phys. Chem. Solids \bf 23 (1962) 433] as the non-interacting limit. We finally study the de Haas-van Alphen oscillation in metals to show that quasiparticles at the Fermi level with the many-body effective mass are directly relevant to the phenomenon. The present argument may be more transparent than that by Luttinger [Phys. Rev. \bf 121 (1961) 1251] of using the gauge invariance and has an advantage that the change of the band structure with the field may be incorporated.