Fabry-Perot interference and spin filtering in carbon nanotubes

摘要

We study the two-terminal transport properties of a metallic single-walledcarbon nanotube with good contacts to electrodes, which have recently beenshown [W. Liang et al, Nature 441, 665-669 (2001)] to conduct ballisticallywith weak backscattering occurring mainly at the two contacts. The measuredconductance, as a function of bias and gate voltages, shows an oscillatingpattern of quantum interference. We show how such patterns can be understoodand calculated, taking into account Luttinger liquid effects resulting fromstrong Coulomb interactions in the nanotube. We treat back-scattering in thecontacts perturbatively and use the Keldysh formalism to treat non-equilibriumeffects due to the non-zero bias voltage. Going beyond current experiments, weinclude the effects of possible ferromagnetic polarization of the leads todescribe spin transport in carbon nanotubes. We thereby describe bothincoherent spin injection and coherent resonant spin transport between the twoleads. Spin currents can be produced in both ways, but only the latter allowthis spin current to be controlled using an external gate. In all cases, thespin currents, charge currents, and magnetization of the nanotube exhibitcomponents varying quasiperiodically with bias voltage, approximately as asuperposition of periodic interference oscillations of spin- andcharge-carrying ``quasiparticles'' in the nanotube, each with its own period.The amplitude of the higher-period signal is largest in single-mode quantumwires, and is somewhat suppressed in metallic nanotubes due to their sub-banddegeneracy.