We generate experimentally a honeycomb refractive index pattern in an atomic vapor cell using electromagnetically-induced transparency. We study experimentally and theoretically the propagation of polarized light beams in such photonic graphene. We demonstrate that an effective spin-orbit coupling appears as a correction to the paraxial beam equations because of the strong spatial gradients of the permittivity. It leads to the coupling of spin and angular momentum at the Dirac points of the graphene lattice. Our results suggest that the polarization degree plays an important role in many configurations where it has been previously neglected.
The concept of gauge fields plays a significant role in many areas of physics from particle physics and cosmology to condensed matter systems, where gauge potentials are a natural consequence of electromagnetic fields acting on charged particles and are of central importance in topological states of matter. Here, we report on the experimental realization of a synthetic non-Abelian gauge field for photons in a honeycomb microcavity lattice. We show that the effective magnetic field associated with TE-TM splitting has the symmetry of Dresselhaus spin-orbit interaction around Dirac points in the dispersion, and can be regarded as an SU(2) gauge field. The symmetry of the field is revealed in the optical spin Hall effect (OSHE), where under resonant excitation of the Dirac points precession of the photon pseudospin around the field direction leads to the formation of two spin domains. Furthermore, we observe that the Dresselhaus field changes its sign in the same Dirac valley on switching from s to p bands in good agreement with the tight binding modelling. Our work demonstrating a non-Abelian gauge field for light on the microscale paves the way towards manipulation of photons via spin on a chip.
We analyze the couplings between spins and phonons in graphene. We present a complete analysis of the possible couplings between spins and flexural, out of plane, vibrations. From tight-binding models we obtain analytical and numerical estimates of their strength. We show that dynamical effects, induced by quantum and thermal fluctuations, significantly enhance the spin-orbit gap.
Within an effective Dirac theory the low-energy dispersions of monolayer graphene in the presence of Rashba spin-orbit coupling and spin-degenerate bilayer graphene are described by formally identical expressions. We explore implications of this correspondence for transport by choosing chiral tunneling through pn and pnp junctions as a concrete example. A real-space Greens function formalism based on a tight-binding model is adopted to perform the ballistic transport calculations, which cover and confirm previous theoretical results based on the Dirac theory. Chiral tunneling in monolayer graphene in the presence of Rashba coupling is shown to indeed behave like in bilayer graphene. Combined effects of a forbidden normal transmission and spin separation are observed within the single-band n to p transmission regime. The former comes from real-spin conservation, in analogy with pseudospin conservation in bilayer graphene, while the latter arises from the intrinsic spin-Hall mechanism of the Rashba coupling.
We study the effect of anisotropy of the Rashba coupling on the extrinsic spin Hall effect due to spin-orbit active adatoms on graphene. In addition to the intrinsic spin-orbit coupling, a generalized anisotropic Rashba coupling arising from the breakdown of both mirror and hexagonal symmetries of pristine graphene is considered. We find that Rashba anisotropy can strongly modify the dependence of the spin Hall angle on carrier concentration. Our model provides a simple and general description of the skew scattering mechanism due to the spin-orbit coupling that is induced by proximity to large adatom clusters.
We consider theoretically the influence of crystalline fields on the electronic structure of graphene placed on a layered material with reduced symmetry and large spin-orbit coupling (SOC). We use a perturbative procedure combined with the Slater-Koster method to derive the low-energy effective Hamiltonian around the $K$ points and estimate the magnitude of the effective couplings. Two simple models for the envisaged graphene-substrate hybrid bilayer are considered, in which the relevant atomic orbitals hybridize with either top or hollow sites of the graphene honeycomb lattice. In both cases, the interlayer coupling to a crystal-field-split substrate is found to generate highly anisotropic proximity spin-orbit interactions, including in-plane spin-valley coupling. Interestingly, when an anisotropic intrinsic-type SOC becomes sizeable, the bilayer system is effectively a quantum spin Hall insulator characterized by in-plane helical edge states robust against Bychkov-Rashba effect. Finally, we discuss the type of substrate required to achieve anisotropic proximity-induced SOC and suggest possible candidates to further explore crystal field effects in graphene-based heterostructures.