Renormalization of impurity scattering in one-dimensional interacting electron systems in magnetic field

Abstract

We study the renormalization of a single impurity potential in one-dimensional interacting electron systems in the presence of magnetic field. Using the bosonization technique and Bethe ansatz solutions, we determine the renormalization group flow diagram for the amplitudes of scattering of up- and down-spin electrons by the impurity in a quantum wire at low electron density and in the Hubbard model at less than half filling. In the absence of magnetic field the repulsive interactions are known to enhance backscattering and make the impurity potential impenetrable in the low-energy limit. On the contrary, we show that in a strong magnetic field the interaction may suppress the backscattering of majority-spin electrons by the impurity potential in the vicinity of the weak-potential fixed point. This implies that in a certain temperature range the impurity becomes almost transparent for the majority-spin electrons while it is impenetrable for the minority-spin ones. The impurity potential can thus have a strong spin-filtering effect.

11 pages, 2 figures; v2: a typo corrected and a reference added; v3: published version, Sec.II revised with an additional explanatory subsection, comments on the case of more than half-filling added, typos corrected, a reference updated

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• Bosonization of strongly interacting electrons
• Spin current and rectification in one-dimensional electronic systems
• Spin current and rectification in Luttinger liquids
• Generation of spin current by Coulomb drag
• Transmission of correlated electrons through sharp domain walls in magnetic nanowires: a renormalization group approach
• Spectral functions of two-band spinless fermion and single-band spin-1/2 fermion models
• Few-Body Route to One-Dimensional Quantum Liquids
• Spin-charge mixing effects on resonant tunneling in a polarized Luttinger Liquid
• Role of a spin-flip scatterer in a magnetized Luttinger liquid
• Spin-filtering by field dependent resonant tunneling
• Effects of a single impurity in a Luttinger liquid with spin-orbit coupling