Coupling of Spin and Orbital Motion of Electrons in Carbon Nanotubes

TL;DR

This paper demonstrates that in clean carbon nanotubes, electron spin and orbital motion are coupled, breaking expected degeneracies and enabling new spin control mechanisms for quantum applications.

Contribution

The study provides direct experimental evidence of spin-orbit coupling in carbon nanotubes, revealing symmetry breaking and implications for spin-based quantum devices.

Findings

Observation of splitting of four-fold degeneracy in quantum dots

Spin and orbital moments tend to align parallel for electrons

Implications for electrical control of spins in nanotubes

Abstract

Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes (NTs) are widely believed to be four-fold degenerate, due to independent spin and orbital symmetries, and to also possess electron-hole symmetry. Here we report measurements demonstrating that in clean NTs the spin and orbital motion of electrons are coupled, thereby breaking all of these symmetries. This spin-orbit coupling is directly observed as a splitting of the four-fold degeneracy of a single electron in ultra-clean quantum dots. The coupling favours parallel alignment of the orbital and spin magnetic moments for electrons and anti-parallel alignment for holes. Our measurements are consistent with recent theories that predict the existence of spin-orbit coupling in curved graphene and describe it as a spin-dependent topological phase in NTs. Our findings have important implications for spin-based applications in carbon-based systems, entailing new design principles for the realization of qubits in NTs and providing a mechanism for all-electrical control of spins in NTs.