Coulomb Drag and Spin Coulomb Drag in the presence of Spin-orbit Coupling

Employing diagrammatic perturbation theory, we calculate the (charge) Coulomb drag resistivity $\rho_D$ and spin Coulomb drag resistivity $\rho_{\uparrow\downarrow}$ in the presence of Rashba spin-orbit coupling. Analytical expressions for $\rho_D$ and $\rho_{\uparrow\downarrow}$ are derived, and it is found that spin-orbit interaction produces a small enhancement to $\rho_D$ and $\rho_{\uparrow\downarrow}$ in the ballistic regime while $\rho_D$ is unchanged in the diffusive regime. This enhancement in the ballistic regime is attributed to the enhancement of the nonlinear susceptibility (i.e. current produced through the rectification of the thermal electric potential fluctuations in the passive layer) while the lack of enhancement in the diffusive regime is due to the suppression by disorder.Comment: 8 pages, 2 figure

Magneto-optical and Magneto-electric Effects of Topological Insulators in Quantizing Magnetic Fields

We develop a theory of the magneto-optical and magneto-electric properties of a topological insulator thin film in the presence of a quantizing external magnetic field. We find that low-frequency magneto-optical properties depend only on the sum of top and bottom surface Dirac-cone filling factors $\nu_{\mathrm{T}}$ and $\nu_{\mathrm{B}}$, whereas the low-frequency magneto-electric response depends only on the difference. The Faraday rotation is quantized in integer multiples of the fine structure constant and the Kerr effect exhibits a $\pi/2$ rotation. Strongly enhanced cyclotron-resonance features appear at higher frequencies that are sensitive to the filling factors of both surfaces. When the product of the bulk conductivity and the film thickness in $e^2/h$ units is small compared to $\alpha$, magneto-optical properties are only weakly dependent on accidental doping in the interior of the film.Comment: 4 page

Giant Magneto-optical Kerr Effect and Universal Faraday Effect in Thin-film Topological Insulators

Topological insulators can exhibit strong magnetoelectric effects when their time-reversal symmetry is broken. In this Letter we consider the magneto-optical Kerr and Faraday effects of a topological insulator thin film weakly exchange-coupled to a ferromagnet. We find that its Faraday rotation has a universal value at low-frequencies, $\theta_{\mathrm{F}} = \mathrm{tan}^{-1}\,\alpha$ where $\alpha$ is the vacuum fine structure constant, and that it has a giant Kerr rotation $\theta_{\mathrm{K}} = \pi/2$. These properties follow from a delicate interplay between thin-film cavity confinement and the surface Hall conductivity of a topological insulator's helical quasiparticles.Comment: 5 pages, 4 figure

Energy Relaxation of Hot Dirac Fermions in Graphene

We develop a theory for the energy relaxation of hot Dirac fermions in graphene. We obtain a generic expression for the energy relaxation rate due to electron-phonon interaction and calculate the power loss due to both optical and acoustic phonon emission as a function of electron temperature $T_{\mathrm{e}}$ and density $n$. We find an intrinsic power loss weakly dependent on carrier density and non-vanishing at the Dirac point $n = 0$, originating from interband electron-optical phonon scattering by the intrinsic electrons in the graphene valence band. We obtain the total power loss per carrier $\sim 10^{-12} - 10^{-7} \mathrm{W}$ within the range of electron temperatures $\sim 20 - 1000 \mathrm{K}$. We find optical (acoustic) phonon emission to dominate the energy loss for $T_{\mathrm{e}} > (<) 200-300 \mathrm{K}$ in the density range $n = 10^{11}-10^{13} \mathrm{cm}^{-2}$.Comment: 5 page

Ballistic Hot Electron Transport in Graphene

We theoretically study the inelastic scattering rate and the carrier mean free path for energetic hot electrons in graphene, including both electron-electron and electron-phonon interactions. Taking account of optical phonon emission and electron-electron scattering, we find that the inelastic scattering time $\tau \sim 10^{-2}-10^{-1} \mathrm{ps}$ and the mean free path $l \sim 10-10^2 \mathrm{nm}$ for electron densities $n = 10^{12}-10^{13} \mathrm{cm}^{-2}$. In particular, we find that the mean free path exhibits a finite jump at the phonon energy $200 \mathrm{meV}$ due to electron-phonon interaction. Our results are directly applicable to device structures where ballistic transport is relevant with inelastic scattering dominating over elastic scattering.Comment: 4 page

Spin Accumulation in the Extrinsic Spin Hall Effect

The drift-diffusion formalism for spin-polarized carrier transport in semiconductors is generalized to include spin-orbit coupling. The theory is applied to treat the extrinsic spin Hall effect using realistic boundary conditions. It is shown that carrier and spin diffusion lengths are modified by the presence of spin-orbit coupling and that spin accumulation due to the extrinsic spin Hall effect is strongly and qualitatively influenced by boundary conditions. Analytical formulas for the spin-dependent carrier recombination rates and inhomogeneous spin densities and currents are presented.Comment: 5 pages, 3 figure