The intrinsic charge and spin conductivities of doped graphene in the Fermi-Liquid regime

The experimental availability of ultra-high-mobility samples of graphene opens the possibility to realize and study experimentally the "hydrodynamic" regime of the electron liquid. In this regime the rate of electron-electron collisions is extremely high and dominates over the electron-impurity and electron-phonon scattering rates, which are therefore neglected. The system is brought to a local quasi-equilibrium described by a set of smoothly varying (in space and time) functions, {\it i.e.} the density, the velocity field and the local temperature. In this paper we calculate the charge and spin conductivities of doped graphene due solely to electron-electron interactions. We show that, in spite of the linear low-energy band dispersion, graphene behaves in a wide range of temperatures as an effectively Galilean invariant system: the charge conductivity diverges in the limit $T \to 0$, while the spin conductivity remains finite. These results pave the way to the description of charge transport in graphene in terms of Navier-Stokes equations.Comment: 19 pages, 7 figures. arXiv admin note: text overlap with arXiv:1406.294

A Bipartite Kronig-Penney Model with Dirac Potential Scatterers

Here we present a simple extension to the age-old Kronig-Penney model, which is made to be bipartite by varying either the scatterer separations or the potential heights. In doing so, chiral (sublattice) symmetry can be introduced. When such a symmetry is present, topologically protected edge states are seen to exist. The solution proceeds through the conventional scattering formalism used to study the Kronig-Penney model, which does not require further tight-binding approximations or mapping into a Su-Schrieffer-Heeger model. The topological invariant for this specific system is found to be the winding of the reflection coefficient, ultimately linked to the system wavefunction. The solution of such a simple and illustrative 1D problem, whose topological content is extracted without requiring further tight-binding approximations, represents the novel aspect of our paper. The cases in which chiral symmetry is absent are then seen to not host topologically protected edge states, as verified by the behaviour of the reflection coefficient and the absence of winding.Comment: 15 pages, 16 figures. Noticed crucial typos in equations 8 and 9 leading to a change of figures 5 and 11. The analysis is unchanged however. Change of abstract to better present novel aspects of pape

Hall viscosity and electromagnetic response of electrons in graphene

We derive an analytic expression for the geometric Hall viscosity of non-interacting electrons in a single graphene layer in the presence of a perpendicular magnetic field. We show that a recently-derived formula in [C. Hoyos and D. T. Son, Phys. Rev. Lett. {\bf 108}, 066805 (2012)], which connects the coefficient of $q^2$ in the wave vector expansion of the Hall conductivity $\sigma_{xy}(q)$ of the two-dimensional electron gas (2DEG) to the Hall viscosity and the orbital diamagnetic susceptibility of that system, continues to hold for graphene -- in spite of the lack of Galilean invariance -- with a suitable definition of the effective mass. We also show that, for a sufficiently large number of occupied Landau levels in the positive energy sector, the Hall conductivity of electrons in graphene reduces to that of a Galilean-invariant 2DEG with an effective mass given by $\hbar k_F/v_F$ (cyclotron mass). Even in the most demanding case, i.e. when the chemical potential falls between the zero-th and the first Landau level, the cyclotron mass formula gives results accurate to better than 1$\%$. The connection between the Hall conductivity and the viscosity provides a possible avenue to measure the Hall viscosity in graphene.Comment: 10 pages including one Appendix, one figure. As main modifications, in this version the result for the Hall viscosity and Hall conductivity of graphene reflect the expected electron-hole symmetry and a detailed discussion section has been added to compare our results with those obtained earlier in the literatur

Kondo effect and non-Fermi-liquid behavior in Dirac and Weyl semimetals

We study the Kondo effect in three-dimensional (3D) Dirac materials and Weyl semimetals. We find the scaling of the Kondo temperature with respect to the doping n and the coupling J between the moment of the magnetic impurity and the carriers of the semimetal. We consider the interplay of long-range scalar disorder and Kondo screening and find that it causes the Kondo effect to be characterized not by a Kondo temperature, but by a distribution of Kondo temperatures with features that cause the appearance of strong non-Fermi-liquid behavior. We then consider the effect of Kondo screening, and of the interplay of Kondo screening and long-range scalar disorder, on the transport properties of Weyl semimetals. Finally, we compare the properties of the Kondo effect in 3D and 2D Dirac materials such as graphene and topological insulators

Edge modes and Fabry-Perot Plasmonic Resonances in anomalous-Hall Thin Films

We study plasmon propagation on a metallic two-dimensional surface partially coated with a thin film of anomalous-Hall material. The resulting three regions, separated by two sharp interfaces, are characterised by different Hall conductivities but identical normal conductivities. A single bound mode is found, which can localise to either interface and has an asymmetric potential profile across the region. For propagating modes, we calculate the reflection and transmission coefficients through the magnetic region. We find Airy transmission patterns with sharp maxima and minima as a function of the plasmon incidence angle. The system therefore behaves as a high-quality filter.Comment: 11 pages, 7 figures. Upon revision, the basic content and analysis of the paper is unchanged but the emphasis on topological insulators has been removed. The title and abstract has been changed to reflect this. Damping of the bound mode has been include

Pseudo-Euler equations from nonlinear optics: plasmon-assisted photodetection beyond hydrodynamics

A great deal of theoretical and experimental efforts have been devoted in the last decades to the study of long-wavelength photodetection mechanisms in field-effect transistors hosting two-dimensional (2D) electron systems. A particularly interesting subclass of these mechanisms is intrinsic and based on the conversion of the incoming electromagnetic radiation into plasmons, which resonantly enhance the photoresponse, and subsequent rectification via hydrodynamic nonlinearities. In this Article we show that such conversion and subsequent rectification occur well beyond the frequency regime in which hydrodynamic theory applies. We consider the nonlinear optical response of generic 2D electron systems and derive pseudo-Euler equations of motion for suitable collective variables. These are solved in one- and two-dimensional geometries for the case of graphene and the results are compared with those of hydrodynamic theory. Significant qualitative differences are found, which are amenable to experimental studies. Our theory expands the knowledge of the fundamental physics behind long-wavelength photodetection.Comment: 15 pages, 4 figure