Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles

TL;DR

This paper demonstrates that quantum spin Hall insulator nanostructures can exhibit robust orbital edge magnetization, which scales linearly with size and surpasses spin magnetization in small islands, due to topologically protected Dirac edge states.

Contribution

It reveals that orbital edge magnetism in quantum spin Hall insulator nanostructures is robust, size-dependent, and distinct from conventional electrons, highlighting a new topological magnetic phenomenon.

Findings

Orbital magnetization scales linearly with island size.

Orbital magnetization exceeds spin contribution in small islands.

Magnetization is robust against disorder, temperature, and shape variations.

Abstract

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. Modelling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island and crystallographic direction of the edges, reflecting its topological protection.