Microscopic Linear Response Theory of Spin Relaxation and Relativistic Transport Phenomena in Graphene

Abstract

Abstract:We present a unified theoretical framework for the study of spin dynamics and relativistic transport phenomena in disordered two-dimensional Dirac systems with pseudospin-spin coupling. The formalism is applied to the paradigmatic case of graphene with uniform Bychkov-Rashba interaction and shown to capture spin relaxation processes and associated charge-to-spin interconversion phenomena in response to generic external perturbations, including spin density fluctuations and electric fields. A controlled diagrammatic evaluation of the generalized spin susceptibility in the diffusive regime of weak spin-orbit interaction allows us to show that the spin and momentum lifetimes satisfy the standard Dyakonov-Perel relation for both weak (Gaussian) and resonant (unitary) nonmagnetic disorder. Finally, we demonstrate that the spin relaxation rate can be derived in the zero-frequency limit by exploiting the SU(2) covariant conservation laws for the spin observables. Our results set the stage for a fully quantum-mechanical description of spin relaxation in both pristine graphene samples with weak spin-orbit fields and in graphene heterostructures with enhanced spin-orbital effects currently attracting much attention.

Theory of spin-charge-coupled transport in proximitized graphene: An SO(5) algebraic approach

“…The existence of such a mapping reflects the same basic spin-relaxation (Dyakonov-Perel) mechanism at work. Indeed, our findings put on a firm ground previous heuristic arguments [34,35] for the equivalence of two models in the weak SOC regime. The remaining 16 − 4 = 12 modes in the Dirac-Rashba model are characterized by very large gaps (∆ + s 1/2 ∆ s ), and as such play no role in the diffusive regime.…”

“…Here, we are primarily interested in diffusive coupled spin-charge dynamics which occur in graphene flakes with weak proximity-induced SOC at moderate-high charge carrier densities (ετ 1 λτ ) [35]. The condition ε λ implies that the BR-slit bands with opposite spin helicities are occupied at the Fermi level.…”

“…Their gaps at q = 0 are ∆ s ≡ ∆ (λ/η) 2 for S x,y -and ∆ ⊥ 2∆ for S z -modes. The twice faster dephasing of out-of-plane spin fluctuations is a fingerprint of BR SOC, a feature which is known to survive even in the strong (unitary) scattering regime [35].…”

“…[33]. Moreover, a controlled diagrammatic approach to calculating linear response functions in the presence of disorder and generic proximity effects was developed in a recent series of works [24,34,35,36,37]. An electrical detection scheme that enables full disentanglement of competing SOC transport effects in diffusive lateral spin-valve devices was proposed also recently in Ref.…”

Microscopic theory of spin relaxation anisotropy in graphene with proximity-induced spin-orbit coupling

“…(13)] is the assumption of Gaussian disorder. The latter is equivalent to the first Born approximation [53] and thus it neglects any effects from skew scattering (allowed in the C 3v model [28]) and modifications to the energy dependence of the collision integral due to scattering resonances. Nevertheless, the relation between spin lifetime and momentum scattering time is expected to be preserved at all orders in perturbation theory, as shown explicitly in the minimal Dirac-Rashba model (λ sv = 0) with λ SOC τ 1 [53].…”