The motion of a conducting electron in a quantum dot, with one or several dislocations in the underlying crystal lattice, was considered in the continuum case; where dislocations were represented by a torsion of space. The possible effects of torsion were investigated at the levels of classical motion, non-relativistic quantum motion and spin-torsion coupling terms in the non-relativistic limit of generalizations of the Dirac equation for a space with torsion. Phenomenological spin torsion couplings which were analogous to Pauli terms were considered in the case of non-relativistic equations. Various choices of classical and non-relativistic quantum motion in a space with torsion were shown to give effects that could, in principle, be observed. Semi-classical arguments were presented which showed that torsion was not relevant to the classical motion of the centre of a wave-packet. The correct semi-classical limit could instead be described as the classical trajectories in a Hamiltonian given by the band energy. In the special case of a spherically symmetrical band, these were reduced to straight line motions, regardless of the local crystal orientations. By means of dimensional analysis, the coupling constants of the possible spin-torsion interactions were deduced to be proportional to a combination of the effective mass of the electron and the lattice constant. The level splitting was then very small, with transition frequencies of the order of 1kHz or less.

Torsion and Electron Motion in Quantum Dots with Crystal Lattice Dislocations. E.Aurell: Journal of Physics A, 1999, 32, 571-84