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Quantum motion of electrons in topologically distorted crystals
Author(s) -
Bausch Richard,
Schmitz Rudi,
Turski Łukasz A.
Publication year - 1999
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/(sici)1521-3889(199903)8:3<181::aid-andp181>3.0.co;2-h
Subject(s) - physics , covariant transformation , electron , bound state , topological defect , quantum , quantum tunnelling , classical mechanics , quantum mechanics , topology (electrical circuits) , mathematics , combinatorics
For the description of the long‐wavelength quantum states of electrons in crystals with topological defects we establish a general framework on the basis of the continuum theory of defects. The resulting one‐particle Schrödinger equation lives on a Riemann‐Cartan manifold, representing the distorted crystal, and consists of two parts. All effects due to the topology of the defects are contained in the first part which has a covariant form and describes the purely geometric particle motion. The second part is non‐covariant and derives from deformation‐dependent tunneling rates of the particle which e.g. are responsible for the existence of bound states to edge dislocations.