Self-isospectrality, special supersymmetry, and their effect on the band structure

Details Self-isospectrality, special supersymmetry, and their effect on the band structure Self-isospectrality, special supersymmetry, and their effect on the band structure

2008-01-10

arxiv.org/abs/0801.1671v3

Phys.Rev.Lett.101:030403,2008

Physics

High Energy Physics

High Energy Physics - Theory

Title changed by the Editor of Phys. Rev. Lett., published version

Scientific paper

10.1103/PhysRevLett.101.030403

We study a planar model of a non-relativistic 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 Lame 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.

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