Magnetoresistance in quantum wires: Boundary-roughness scattering

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Abstract
A quantum-mechanical calculation of the magnetoresistance of quantum wires is performed in the presence of boundary-roughness scattering. The roughness is described by two parameters—the root-mean-square deviation and the correlation length—and the Boltzmann transport equation is used. The roughness scattering gives rise to a strong positive magnetoresistance when the wire width is larger and the correlation length smaller than the Fermi wavelength. When the confining potential is varied from hard wall to parabolic, the magnetoresistance is shown to have a sharper peak for softer confinement. A numerical study based on Landauer’s formula is also performed. The localization effect present in weak magnetic fields tends to suppress the positive magnetoresistance in narrow wires but becomes less important with the increase of the wire width.