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Theory of the Linear photogalvanic effect is developed for direct optical transitions between surface states of three-dimensional topological insulators. The photocurrent governed by the orientation of the polarization plane of light and caused by the warping of the energy dispersion of two-dimensional carriers is calculated. It is shown that both the shift contribution caused by coordinate shifts of the particle wavepackets during the optical transitions and the ballistic contribution caused by interference of the optical absorption and scattering by disorder have generally the same order of magnitude. The ballistic contribution is present owing to electron-hole asymmetry of topological surface states and has a frequency dependence in contrast to the shift photocurrent. In the nonlinear in the light intensity regime appearing due to saturation of the direct optical transitions the ballistic contribution dominates. The nontrivial dependence of the photocurrent on the polarization plane orientation in the nonlinear regime appears solely due to the ballistic contribution. Our findings allow separating the ballistic and shift contributions to the Linear photogalvanic current in experiments., Main paper of 5 pages and 3 figures. Supplementary material of 13 pages and 2 figures

We report on a tunable - by magnetic field and gate voltage - conversion of terahertz radiation into a dc current in spatially modulated bilayer graphene. We experimentally demonstrate that the underlying physics is related to the so-called ratchet effect. Our key findings are the direct observation of a sharp cyclotron resonance in the photocurrent and the demonstration of two effects caused by electron-electron interaction: the plasmonic splitting of the resonance due to long-range Coulomb coupling and the partial suppression of its second harmonic due to fast interparticle collisions. We develop a theory which perfectly fits our data. We argue that the ratchet current is generated in the hydrodynamic regime of non-ideal electron liquid., 13 pages, 10 figures

We report on the observation of the ratchet effect -- generation of direct electric current in response to external terahertz (THz) radiation -- in bilayer graphene, where inversion symmetry is broken by an asymmetric dual-grating gate potential. As a central result, we demonstrate that at high temperature, $T = 150~\textrm{K}$, the ratchet current decreases at high frequencies as $ \propto 1/\omega^2$, while at low temperature, $T = 4.2~\textrm{K}$, the frequency dependence becomes much stronger $\propto 1/\omega^6$. The developed theory shows that the frequency dependence of the ratchet current is very sensitive to the ratio of the electron-impurity and electron-electron scattering rates. The theory predicts that the dependence $1/\omega^6$ is realized in the hydrodynamic regime, when electron-electron scattering dominates, while $1/\omega^2$ is specific for the drift-diffusion approximation. Therefore, our experimental observation of a very strong frequency dependence reveals the emergence of the hydrodynamic regime., Comment: 21 pages, 12 figures

Theory of weak localization is developed for two-dimensional holes in the presence of in-plane magnetic field. The Zeeman splitting even in the hole momentum results in the spin-dependent phase changing the quantum interference. The negative correction to the conductivity is shown to decrease by a factor of two by the in-plane magnetic field. The positive magnetoconductivity in a classically weak perpendicular field caused by the weak localization is calculated for both quadratic and quartic in momentum Zeeman hole splittings. Calculations show that the conductivity corrections are very close to each other in these two cases of low and high hole density., Comment: 6 pages, 3 figures. Paper for Special issue of JETP celebrating the 95-th anniversary of E. I. Rashba

We develop the theory of the spin and valley Hall effects in two-dimensional systems caused by asymmetric -- skew -- scattering of the quasiparticles. The collision integral is derived in the third order in the particle-particle interaction with account for the spin-orbit coupling both for bosons and fermions. It is shown that the scattering asymmetry appears only in the processes where the interaction between the particles in the initial and intermediate state is present. We show that for degenerate electrons or nondegenerate particles the spin and valley currents induced by interparticle collisions are suppressed with their steady-state values being proportional to the squared temperature or density, respectively. Our results imply non-Fermi liquid properties of electrons in the presence of electron-electron skew scattering. Strong deviations from conventional picture of interparticle scattering are also demonstrated for the skew scattering of two-dimensional degenerate bosons, e.g. excitons or exciton polaritons: The spin or valley current of degenerate bosons contains the enhancement factor exponentially growing with increase in the particle density., Comment: 7+6 pages, 2 figures. For the Physical Review B special issue "Spin-Coherent Phenomena in Semiconductors" in honor of E. I. Rashba

We show theoretically that electromagnetic waves propagating in the transparency region of a non-centrosymmetric medium can induce a dc electric current. The origin of the effect is the Raman scattering of light by free carriers in the system. Due to the photon scattering, electrons undergo real quantum transitions resulting in the formation of their anisotropic momentum distribution and in shifts of electronic wavepackets giving rise to a steady state photocurrent. We present microscopic theory of the Raman Photogalvanic effect (RPGE) focusing on two specific situations: (i) generic case of a bulk gyrotropic semiconductor and (ii) a quantum well structure where the light is scattered by intersubband excitations. We uncover the relation of the predicted RPGE and the traditional photogalvanic effect at the light absorption., Comment: 4+2 pages, 3 figures + SI

Theory of optical absorption of linearly and circularly polarized light in surface and edge states in topological insulators is developed for a nonlinear in light intensity regime. The absorbance for surface states and the absorption width for the edge states both decease as $1/\sqrt{I}$ at high light intensity $I$. Elastic scattering of the photoexcited electrons and holes is taken into account. The absorption bleaching at high intensity is shown to be strongly suppressed by the elastic scattering. The linear-circular dichroism of one- and two-photon absorption in surface states, emerging in the nonlinear in intensity regime, decreases due to the elastic scattering of photocarriers. Absorption in the edge states of two-dimensional topological insulators also depends on the elastic scattering rate being suppressed when it is stronger that the energy relaxation rate. The linear dichroism - a dependence of the absorption length on the polarization plane orientation - is studied at arbitrary light intensities. We show that a degree of the linear dichroism is governed by the ratio of the elastic and inelastic relaxation times. The photocurrents generated in the edge states by both linearly and circularly polarized light change their intensity dependencies from the linear one at low $I$ to the $\propto \sqrt{I}$ at high intensities. The variation of the photocurrents with both polarization and intensity are strongly dependent on the elastic scattering rate. The considered effects can be observed in THz frequency range at laser intensities used in modern experiments., Comment: 11 pages, 7 figures

We report on the observation of photogalvanic effects in epitaxially grown Sb2Te3 and Bi2Te3 three-dimensional (3D) topological insulators (TI). We show that asymmetric scattering of Dirac fermions driven back and forth by the terahertz electric field results in a dc electric current. Because of the "symmetry filtration" the dc current is generated by the surface electrons only and provides an optoelectronic access to probe the electron transport in TI, surface domains orientation, and details of electron scattering in 3D TI even at room temperature.