Microscopic linear response theory of spin relaxation and relativistic transport phenomena in graphene

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

Coupled Charge-Spin Transport and Spin–Orbit Phenomena in 2D Dirac Materials

The advent of 2D layered materials, boasting high-crystal quality and rich electronic properties, has provided a unique arena for exploring exotic condensed-matter phenomena, including the emergence of ultra-relativistic Dirac fermions in graphene, topological insulating phases in WS_{2}, long-lived excitons in group-VI dichalcogenides and unconventional superconductivity in twisted bilayer graphene. The enhancement of spin-orbit effects in heterointerfaces, built from the vertical stacking of different 2D layers, is recently attracting much attention. A series of crucial experiments have demonstrated the induction of strong spin-orbit effects in graphene sheets proximity-coupled to group-VI dichalcogenides. Owing to a combination of room-temperature spin transport over long distances and gate-tunable spin orbit interactions, such systems hold great promise for all-electrical generation and manipulation of spin currents, which is key to the realisation of the next generation of spintronics devices. To fully unlock the potential of 2D Dirac materials for spintronics, these recent experimental findings call for the formulation of a solid theoretical framework which can underpin them, but also—and more importantly—predict novel phenomena. This thesis aims to develop the foundations of such a framework, with a focus on spin dynamics and coupled charge-spin transport in 2D Dirac materials with strong proximity-induced interactions. A number of key results are established. We show that charge-to-spin interconversion in 2D Dirac materials can be understood in terms of exact symmetry relations (Ward identities). Depending on the specific spin-orbit interactions present in a 2D Dirac system, the symmetry relations dictate the relative contributions of the so-called spin-Hall effect (SHE) and inverse spin Galvanic effect (ISGE). In particular, for materials with interfacial breaking of mirror symmetry and unbroken (broken) sublattice symmetry, the SHE contribution is suppressed (sizable), whereas the ISGE contribution stays typically large and robust in both scenarios. The extrinsic SHE has its origin in a peculiar skew scattering mechanism—emerging from the non-coplanar spin texture of spin–orbit-coupled Dirac bands—and can be tuned by a gate voltage. We propose a diagrammatic approach to obtain the coupled charge/spin diffusion equations, as well as the spin relaxation times and the charge-to-spin interconversion rates. We supplement this study with a density matrix-based approach, allowing one to gain more insight into the delicate competition of the various energy scales present in realistic systems, and to calculate the spin relaxation time anisotropy of experimental relevance. Finally, we examine ferromagnetic 2D Dirac materials, through a unified theory of charge carrier transport combining semiclassical and fully-quantum mechanical approaches. We identify an experimental signature that characterises the crossover from the nonquantised anomalous Hall effect to the topologically-nontrivial quantum anomalous Hall effect, which can help future experimental efforts to unlock this fascinating quantum state of matter with Dirac fermions

Optimal Charge-to-Spin Conversion in Graphene on Transition-Metal Dichalcogenides

When graphene is placed on a monolayer of semiconducting transition metal dichalcogenide (TMD) its band structure develops rich spin textures due to proximity spin-orbital effects with interfacial breaking of inversion symmetry. In this work, we show that the characteristic spin winding of low-energy states in graphene on a TMD monolayer enables current-driven spin polarization, a phenomenon known as the inverse spin galvanic effect (ISGE). By introducing a proper figure of merit, we quantify the efficiency of charge-to-spin conversion and show it is close to unity when the Fermi level approaches the spin minority band. Remarkably, at high electronic density, even though subbands with opposite spin helicities are occupied, the efficiency decays only algebraically. The giant ISGE predicted for graphene on TMD monolayers is robust against disorder and remains large at room temperature

Covariant Conservation Laws and the Spin Hall Effect in Dirac-Rashba Systems

We present a theoretical analysis of two-dimensional Dirac-Rashba systems in the presence of disorder and external perturbations. We unveil a set of exact symmetry relations (Ward identities) that impose strong constraints on the spin dynamics of Dirac fermions subject to proximity-induced interactions. This allows us to demonstrate that an arbitrary dilute concentration of scalar impurities results in the total suppression of nonequilibrium spin Hall currents when only Rashba spin-orbit coupling is present. Remarkably, a finite spin Hall conductivity is restored when the minimal Dirac-Rashba model is supplemented with a spin–valley interaction. The Ward identities provide a systematic way to predict the emergence of the spin Hall effect in a wider class of Dirac-Rashba systems of experimental relevance and represent an important benchmark for testing the validity of numerical methodologies

Anomalous Hall Effect in 2D Dirac Materials

We present a unified theory of charge carrier transport in 2D Dirac systems with broken mirror inversion and time-reversal symmetries (e.g., as realized in ferromagnetic graphene). We find that the entanglement between spin and pseudospin SU(2) degrees of freedom stemming from spin-orbit effects leads to a distinctive gate voltage dependence (change of sign) of the anomalous Hall conductivity approaching the topological gap, which remains robust against impurity scattering and thus is a smoking gun for magnetized 2D Dirac fermions. Furthermore, we unveil a robust skew scattering mechanism, modulated by the spin texture of the energy bands, which causes a net spin accumulation at the sample boundaries even for spin-transparent disorder. The newly unveiled extrinsic spin Hall effect is readily tunable by a gate voltage and opens novel opportunities for the control of spin currents in 2D ferromagnetic materials

Proposal for Unambiguous Electrical Detection of Spin-Charge Conversion in Lateral Spin Valves

Efficient detection of spin-charge conversion is crucial for advancing our understanding of emergent phenomena in spin-orbit-coupled nanostructures. Here, we provide a proof of principle of an electrical detection scheme of spin-charge conversion that enables full disentanglement of competing spin-orbit coupling (SOC) transport phenomena in diffusive lateral channels, i.e., the inverse spin Hall effect and the spin galvanic effect. A suitable geometry in an applied oblique magnetic field is shown to provide direct access to SOC transport coefficients through a symmetry analysis of the output nonlocal resistance. The scheme is robust against tilting of the spin-injector magnetization, disorder, and spurious non-spin-related contributions to the nonlocal signal and can be used to probe spin-charge conversion effects in both spin- valve and hybrid optospintronic devices

Theory of Spin Injection in Two-dimensional Metals with Proximity-Induced Spin-Orbit Coupling

Spin injection is a powerful experimental probe into a wealth of nonequilibrium spin-dependent phenomena displayed by materials with spin-orbit coupling (SOC). Here, we develop a theory of coupled spin-charge diffusive transport in two-dimensional spin-valve devices. The theory describes a realistic proximity-induced SOC with both spatially uniform and random components of the SOC due to adatoms and imperfections, and applies to the two dimensional electron gases found in two-dimensional materials and van der Walls heterostructures. The various charge-to-spin conversion mechanisms known to be present in diffusive metals, including the spin Hall effect and several mechanisms contributing current-induced spin polarization are accounted for. Our analysis shows that the dominant conversion mechanisms can be discerned by analyzing the nonlocal resistance of the spin-valve for different polarizations of the injected spins and as a function of the applied in-plane magnetic field

Datasets

Datasets used to generate all figures in main text and supplemental material. All data can be generated using the Mathematica notebook provided in this collection. <br