Possible Jahn-Teller effect in Si-inverse layers

Jahn-Teller effect in bivalley Si(100) MOSFET under conditions of quantum Hall effect at integer filling factors nu=1,2,3 is studied. This system is described by SU(4) hidden symmetry. At nu=2 static and dynamic lattice deformation creates an easy-plane anisotropy and antiferromagnetic exchange and lifts the valley degeneracy. At nu=1,3 Coulomb interaction is essential to produce weak easy-plane anisotropy. Three phases: ferromagnetic, canted antiferromagnetic and spin-singlet, have been found. Anisotropy energy of charged skyrmion excitation in every phase is found.Comment: 8 pages, 4 figure

Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure