Abstract
To date, spin generation in three-dimensional topological insulators is primarily modelled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface. In this article, we propose a mechanism of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a three-dimensional topological insulator, which transports spins between the top and bottom surfaces. Under sufficiently high surface disorder, the spin relaxation time can be extended via the Dyakonov–Perel mechanism. Consequently, both the spin generation efficiency and surface conductivity are largely enhanced. Numerical simulation confirms that this spin generation mechanism originates from the unique topological connection of the top and bottom surfaces and is absent in other two-dimensional systems such as graphene, even though they possess a similar Dirac cone-type dispersion.
Highlights
To date, spin generation in three-dimensional topological insulators is primarily modelled as a single-surface phenomenon, attributed to the momentum-spin locking on each individual surface
Topological insulators (TIs) are considered as efficient spin generators[5], yet the spin generation is generally regarded as a pure surface phenomenon
We demonstrate that the unique topological connection of the surface bands in a 3D TI demands a pure spin current through the insulating bulk
Summary
Owing to the even symmetry of spin current js under time reversal J , the resultant expression for the spin Hall conductivity is different from that for the electrical conductivity (Kubo–Greenwood formula), but contains a term which involves all states below the Fermi level This term has been thoroughly reviewed in ref. During this process, it is essential that the Fermi level lies within the gap, because there exists another pair of merging points near the conduction band edge. Combined with the fact that velocity operator is proportional to spin on the surface, it is not difficult to understand the anomalous increase of conductivity as well
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