FisMat2017 - Submission - View

Abstract's title: Covariant conservation laws, spin-Hall and spin-Galvanic effect in the Dirac-Rashba model
Submitting author: Manuel Offidani
Affiliation: University of York
Affiliation Address: University of York, Department of Physics, Heslington, YO105DD, York, United Kingdom
Country: United Kingdom
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Mirco Milletarì (Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR), Singapore 138671, Singapore), Aires Ferreira(Department of Physics, University of York, York YO10 5DD, United Kingdom), Roberto Raimondi (Università Roma Tre, Dipartimento di Matematica e Fisica Via della Vasca Navale 84, 00146 Roma)
Abstract

We consider the Rashba model of graphene and its related spin Hall conductivity away from half filling. The model, in analogy with its two-dimensional electron gas counterpart, possesses an exact symmetry relation, which has the form of a covariant conservation law for the spin density. By exploiting such symmetry relation, we derive a Ward identity relating vertex and propagators of the field theoretical formulation of the model. Since the Ward identity is valid also in the presence of disorder scattering, we immediately can draw a number of conclusions, which are later confirmed by explicit diagrammatic perturbative calculations. First, we find that despite the presence of pseudospin and valley structure, disorder effects lead to a zero spin Hall conductivity in a way that resembles what happens in the two dimensional electron gas. Second, the Ward identity allows to find the exact expression of the spin current vertex, which because of disorder couples to the in-plane spin-density vertex, leading to the inverse spin galvanic effect. Third, guided by the insights provided by the Ward identity, the underlying structure of the disorder-induced vertex corrections (Bethe- Salpeter equation) is revealed, showing how it can be analytically controlled in an expansion around the weak disorder limit. Four, the existence of the Ward identities, together with its extensions in the presence of additional spin-dependent terms in the Hamiltonian, provides a systematic way to investigate the emergence of the spin Hall effect in Dirac-Rashba models. As an example we discuss a valley- spin coupling. Finally, as a side benefit, our work may provide an important benchmark to test the validity of numerical procedures to study spin transport phenomena.