title: Self-isospectrality, special supersymmetry, and their effect on the band structure.
abstract: We study a planar model of a nonrelativistic electron in periodic magnetic and electric fields that produce a 1D crystal for two spin components separated by a half-period spacing. We fit the fields to create a self-isospectral pair of finite-gap associated Lamé equations shifted for a half-period, and show that the system obtained is characterized by a new type of supersymmetry. It is a special nonlinear supersymmetry generated by three commuting integrals of motion, related to the parity-odd operator of the associated Lax pair, that coherently reflects the band structure and all its peculiarities. In the infinite-period limit it provides an unusual picture of supersymmetry breaking.
authors.affiliation: Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile.
authors.forename: Francisco
authors.initials: F
authors.lastname: Correa
authors.forename: Vít
authors.initials: V
authors.lastname: Jakubský
authors.forename: Luis-Miguel
authors.initials: LM
authors.lastname: Nieto
authors.forename: Mikhail S
authors.initials: MS
authors.lastname: Plyushchay