Orthonormal wave functions for periodic fermionic states under an applied magnetic field

Article

关键词: WANNIER FUNCTIONS;    BLOCH ELECTRONS;    ENERGY-LEVELS;    DIAMAGNETISM;   

DOI  :  10.1103/PhysRevB.104.054423

来源: SCIE

【 摘 要 】

We report an infinite number of orthonormal eigenfunction bases for the quantum problem of a free electron in presence of an applied external magnetic field, suitable to describe doubly periodic electronic densities. The completeness of these bases is shown here and so, a single basis, labeled by the number of magnetic fluxons trapped in the unit cell (integer p), expands any function in the unit cell. The present framework unveils for the electronic density an egg-box pattern that displays fractional charge and magnetic flux. In case of electrons confined to the lowest Landau level we obtain an analytic expression for the local magnetic field created by their own motion and find that it yields an attractive magnetic interaction. The well-known de Haas-van Alphen oscillations are retrieved, thus showing the correctness of the present theoretical framework.

【 授权许可】

Free