Crystal electrons in magnetic fields: General reduction of the dimensionality and properties of the wave functions

Hans-Joachim Schellnhuber
Phys. Rev. B 25, 2358 – Published 15 February 1982
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Abstract

The motion of Bloch electrons in homogeneous magnetic fields is reduced without approximations to, at most, two dimensions in the general three-dimensional case, i.e., for arbitrary crystal potential, arbitrary field-lattice geometry, and all rational fields. This is done by fully exploiting a canonical transformation and by constructing with the aid of ray-group projection operators generalized kq functions, which separate off one degree of freedom. Previous ad hoc reductions to one dimension for essentially two-dimensional situations are recovered and explained. The solutions of the resulting lower-dimensional effective Schrödinger equations are functions of generalized coordinates. They are converted into the real-space wave functions by means of a contact transformation; their local and global properties are investigated. The results presented allow first-principles calculations of diamagnetic band structures and wave functions to realistic systems.

  • Received 8 September 1981

DOI:https://doi.org/10.1103/PhysRevB.25.2358

©1982 American Physical Society

Authors & Affiliations

Hans-Joachim Schellnhuber*

  • Fakultät für Physik, Universität Regensburg, D-8400 Regensburg, West Germany
  • Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

  • *Present address.

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Issue

Vol. 25, Iss. 4 — 15 February 1982

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