Self-Isospectrality, Special Supersymmetry, and their Effect on the Band Structure

Francisco Correa, Vít Jakubský, Luis-Miguel Nieto, and Mikhail S. Plyushchay
Phys. Rev. Lett. 101, 030403 – Published 15 July 2008

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.

  • Figure
  • Figure
  • Received 16 January 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.030403

©2008 American Physical Society

Authors & Affiliations

Francisco Correa1, Vít Jakubský1, Luis-Miguel Nieto2, and Mikhail S. Plyushchay1

  • 1Departamento de Física, Universidad de Santiago de Chile, Casilla 307, Santiago 2, Chile
  • 2Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47071, Valladolid, Spain

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 101, Iss. 3 — 18 July 2008

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×