# Thermoelectric unipolar spin battery in a suspended carbon nanotube

## TL;DR

This paper predicts a thermoelectric unipolar spin battery using a suspended carbon nanotube quantum dot, which generates pure spin current driven by temperature differences and influenced by spin-vibration interactions.

## Contribution

It introduces a novel mechanism for pure spin current generation in a carbon nanotube quantum dot via spin-vibration coupling and thermoelectric effects, with detailed analysis of parameter dependencies.

## Key findings

- Pure spin current magnitude depends on spin-vibration interaction strength.
- The spin current direction can be controlled by system parameters.
- Maximum kinetic coefficient occurs when thermal energy matches phonon energy.

## Abstract

A quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. The built-in spin flip mechanism is a consequence of the spin-vibration interaction resulting from the interplay between the intrinsic spin-orbit coupling and the vibrational modes of the suspended carbon nanotube. On the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. We find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin-vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. Moreover, in the linear response regime, the kinetic coefficient is non-monotonic in the temperature $T$ and it reaches its maximum when $k_BT$ is about one phonon energy. The existence of a strong intradot Coulomb interaction is irrelevant for our spin battery, provided that high-order cotunneling processes are suppressed.