Sources of negative tunneling magneto-resistance in multilevel quantum   dots with ferromagnetic contacts
  We analyze distinct sources of spin-dependent energy level shifts and their impact on the tunneling magnetoresistance (TMR) of interacting quantum dots coupled to collinearly polarized ferromagnetic leads. Level shifts due to virtual charge fluctuations can be quantitatively evaluated within a diagrammatic representation of our transport theory. The theory is valid for multilevel quantum dot systems and we exemplarily apply it to carbon nanotube quantum dots, where we show that the presence of many levels can qualitatively influence the TMR effect. 
S. Koller, J. Paaske and M. Grifoni
cond-mat.mes-hall quant-ph