We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation [1]. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice.PACS numbers: 71.23. An,72.15.Rn,71.30.+h One of the most important experimental probes in condensed matter physics is the electrical response to an external electrical field. In addition to the longitudinal conductivity, in specific circumstances, a system can present a transverse conductivity under an electrical perturbation. The Hall effect [2] and the anomalous Hall effect in magnetic materials [3] are two examples of this type of response. Paramagnetic materials with spin-orbit interaction can also present transverse spin currents [4]. There are also the quantized versions of the three phenomena: while the quantum Hall effect (QHE) was observed more than 30 years ago [5], the quantum spin Hall effect (QSHE) and the quantum anomalous Hall effect (QAHE) could only be observed [6, 7] with the recent discovery of topological insulators, a new class of quantum matter [8].In the linear response regime, the conductivity tensor can be calculated using the Kubo formalism [9]. The Hall conductivity can be easily obtained in momentum space in terms of the Berry curvature associated with the bands [10]. The downside of working in momentum space, however, is that the robustness of a topological state in the presence of disorder can only be calculated perturbatively [11]. Real-space implementations of the Kubo formalism for the Hall conductivity, on the other hand, allow the incorporation of different types of disorder in varying degrees, while providing flexibility to treat different geometries. Real-space techniques, however, normally require a large computational effort. This has generally restricted their use to either small systems at any temperature [12,13], or large systems at zero temperature [14].In this Letter, we propose a new efficient numerical approach to calculate the conductivity tensor in solids. We use a real space implementation of the Kubo formalism where both diagonal and off-diagonal conductivities are treated in the same footing. We adopt a formulation of the Kubo theory that is known as Bastin formula [1] and expand the Green's functions involved in terms of Chebyshev polynomials using the kernel polynomial method [16]. There are few numerical methods that use Chebyshev expansions to calculate the longitudinal DC conductivity [17][18][19][20] and transverse conductivity [14,21] at zero temperature. An advantage of our approach is the possibility of obtaining both conductivities for large systems in a single calculation step, independe...

Acoustic graphene plasmons are highly confined electromagnetic modes carrying large momentum and low loss in the mid-infrared and terahertz spectra. However, until now they have been restricted to micrometer-scale areas, reducing their confinement potential by several orders of magnitude. Using a graphene-based magnetic resonator, we realized single, nanometer-scale acoustic graphene plasmon cavities, reaching mode volume confinement factors of ~5 × 10–10. Such a cavity acts as a mid-infrared nanoantenna, which is efficiently excited from the far field and is electrically tunable over an extremely large broadband spectrum. Our approach provides a platform for studying ultrastrong-coupling phenomena, such as chemical manipulation via vibrational strong coupling, as well as a path to efficient detectors and sensors operating in this long-wavelength spectral range.

In this Letter, we have predicted the existence of two different classes of quantum critical points for the Kondo problem in graphene, which was shown to correspond effectively to the problem of a localized spin 1=2 coupled to a fermionic bath with electronic density of states ð!Þ / j!j r , with r ¼ 1 or 3. Here we point out that the mean-field exponent ¼ 1=3 derived within the slave boson approach for the class of orbitals of type II ð r ¼ 3) is incorrect.Above the upper critical scaling dimension of the Anderson model ( r > 1), the intermediate coupling fixed point is noninteracting and describes the level crossing between singlet and doublet states with the trivial exponent ¼ 1 [1]. Albeit fluctuations do not play a role in the critical behavior for r > 1, the critical theory is not of the Ginzburg-Landau type and the validity of the mean-field slave boson equation of state (9) breaks down in the r ¼ 3 class, invalidating Eqs. (10)and (11), and the inset of Fig. 2(b) for the case of type II orbitals.All the other results of the Letter remain valid, including the spin exchange Hamiltonian in Eq. (6) and the prediction of a fast power law for the spatial decay of the RKKY interaction for type II orbitals ( 1=R 7 ).We note that since hyperscaling is not obeyed for r > 1, the scaling prediction for the Kondo temperature with the chemical potential in the quantum critical region T K / jj can be violated [2]. In the situation where the scaling prediction fails, the criticality in the r ¼ 1 and r ¼ 3 classes can be in principle distinguished. That will be verified with numerical renormalization group methods elsewhere.We acknowledge M. Vojta for many helpful discussions.[1] M. Vojta and L. Fritz, Phys. Rev.