Tunnel transport of interacting spin-polarized electrons through a single-level vibrating quantum dot in external magnetic field is studied. By using density matrix method, the current-voltage characteristics and the dependence of conductance on temperature of a single-electron transistor were calculated. We found that a lifting of Coulomb blockade in external magnetic field happens in stages. The Franck-Condon steps associated with inelastic electron tunneling in our case are doubled due to contribution of two Zeeman-split levels in electron transport. The doubling of steps can be also observed in the presence of Coulomb interaction. For strong electron-vibron interaction the temperature dependence of conductance is shown to be non-monotonic and anomalous growth of conductance maximum weakly depends both on the Coulomb strength and the external magnetic field.

A thermally driven single-electron transistor with magnetic leads and a movable central island (a quantum dot) subject to an external magnetic field is considered. The possibility of a mechanical instability caused by magnetic exchange interactions between spin-polarized electrons in this system was studied by the density matrix method. We proved analytically that for noninteracting electrons in the dot there is no such mechanical instability. However, for finite strengths of the Coulomb correlations in the dot we numerically found critical magnetic fields separating regimes of mechanical instability and electron shuttling on the one hand and damped mechanical oscillations on the other. It was shown that thermally induced magnetic shuttling of spin-polarized electrons is a threshold phenomenon, and the dependence of the threshold bias temperature on model parameters was calculated.

Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from the analogous current through a resonant (BreitWigner) level.