Abstract
A triple of quantum numbers of conventional zone theory, namely the quasi-momentum,described in terms of Bloch functions, the lattice coordinate, described in terms of Wannierfunctions, and the associated energy band index, are modified to describe the space ofstates of a charged particle in magnetic field, in a translation covariant manner.A quartet of Bloch functions that belong to an invariant subspace, and definean irreducible representation of an anticommutative subgroup of the magnetictranslation group, lead to Wannier function sets at a single Landau level thatsatisfy the exponential localization criterion. The degrees of freedom within theinvariant subspace of this physically irreducible representation match those of spin1/2. With a view to possible experimental studies, it is shown how a set of four regular arraysof connected wires or a similar quantum device may be used to access the pseudo-spindegree of freedom described, by observation of the effects of a controlled doubly periodicalelectric potential applied to a 2DEG in a strong and commensurate magnetic field.
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