We show that spatially structured radiation generates a second harmonic even in homogeneous and isotropic media. The effect originates from the nonlocality of the electric response to the structured electromagnetic field. We develop an analytical theory of such a second harmonic generation in conducting two-dimensional systems. For the general type of structured radiation, we calculate the emerging electric currents at the double frequency and the emitted second harmonic radiation. The theory applied to twisted light reveals that the angular momentum of light doubles in the second harmonic emission. Our results pave the way for light second harmonic generation and structuring beyond the constraints imposed by crystal symmetry.

InSe is a promising material for a next-generation of two-dimensional electronic and optical devices, characteristics of which are largely determined by the type of band structure, direct or indirect. In general, different methods can be sensitive to different peculiarities of the electronic structure leading to different results. In this work, we will focus on the luminescent properties of few-layer $\beta$-InSe with a thickness of 6 to 75 monolayers (ML). Low-temperature micro-photoluminescence ($mu$-PL) studies show a sharp increase in PL intensity in the range of thicknesses from 16 to 20 monolayers, where, in addition, there is a singularity in the dependence of the work function on the thickness. Time-resolved photoluminescence spectroscopy (TRPL) reveals three characteristic PL decay times that differ from each other by about an order of magnitude. We associate the processes underlying the two faster decays with the recombination of electrons and holes between the band extrema, either directly or through the interband relaxation of holes. Their contributions to the total PL intensity increase significantly in the same thickness range, 16-20 MLs. On the contrary, the slowest contribution, which we attribute mainly to the defect-assisted recombination, prevails at a smaller number of monolayers and then noticeably decreases. These results indicate the indirect-to-direct bandgap transition near 16-20 MLs, which determines the range of applicability of a few-layer $\beta$-InSe for efficient light emitters.

We study theoretically the Faraday and Kerr rotation of a probe field due to the orbital magnetization of a two-dimensional electron gas induced by a circularly polarized pump. We develop a microscopic theory of these effects in the intraband spectral range based on the analytical solution of the kinetic equation for linear and parabolic energy dispersion of electrons and arbitrary scattering potential. We show that the spectral dependence of rotation angles and accompanying ellipticities experiences a sharp resonance when the probe and pump frequencies are close to each other. At the resonance, the Faraday and Kerr rotation angles are of the order of $0.1^\circ$ per 1~kW/cm$^2$ of the pump intensity in graphene samples, corresponding to a pump-induced synthetic magnetic field of about 0.1~T. We also analyze the influence of the dielectric contrast between dielectric media surrounding the two-dimensional electron gas on the rotation angles.

Edges in two-dimensional structures are the source of nonlinear transport and optical phenomena which are particularly important in small-size flakes. We present a microscopic theory of the edge photogalvanic effect, i.e., the formation of DC electric current flowing along the sample edges in response to AC electric field of the incident terahertz radiation, for two-dimensional Dirac materials including the systems with massive and massless charge carriers. The edge current direction is controlled by the AC field polarization. The spectral dependence of the current is determined by the carrier dispersion and the mechanism of carrier scattering, as shown for single-layer and bilayer graphene as examples.

Advances in manipulating the structure of optical beams enable the study of interaction between structured light and low-dimensional semiconductor systems. We explore the photocurrents in two-dimensional systems excited by such inhomogeneous radiation with structured field. Besides the contribition associated with the intensity gradient, the photocurrent contains contributions driven by the gradients of the Stokes polarization parameters and the phase of the electromagnetic field. We develop a microscopic theory of the photocurrents induced by structured light and derive analytical expressions for all the photocurrent contributions at intraband transport of electrons. The theory is applied to analyze the radial and azimuthal photocurrents excited by twisted light beams carrying orbital angular momentum, and possible experiments to detect the photocurrents are discussed.

We develop a microscopic theory of the fine structure of Dirac states in (0lh)-grown HgTe/CdHgTe quantum wells (QWs), where l and h are the Miller indices. It is shown that bulk, interface, and structure inversion asymmetry causes the anticrossing of levels even at zero in-plane wave vector and lifts the Dirac state degeneracy. In the QWs of critical thickness, the two-fold degenerate Dirac cone gets split into non-degenerate Weyl cones. The splitting and the Weyl point positions dramatically depend on the QW crystallographic orientation. We calculate the splitting parameters related to bulk, interface, and structure inversion asymmetry and derive the effective Hamiltonian of the Dirac states. Further, we obtain an analytical expression for the energy spectrum and discuss the spectrum for (001)-, (013)-, and (011)-grown QWs.

We present an experimental and theoretical study of the longitudinal electron spin relaxation (T-1) of shallow donors in the direct band-gap semiconductor ZnO. T-1 is measured via resonant excitation of the Ga donor-bound exciton. T-1 exhibits an inverse-power dependence on magnetic field T-1 proportional to B-n, with 4 <= n <= 5, over a field range of 1.75 T to 7 T. We derive an analytic expression for the donor spin-relaxation rate due to spin-orbit (admixture mechanism) and electron-phonon (piezoelectric) coupling for the wurtzite crystal symmetry. Excellent quantitative agreement is found between experiment and theory suggesting the admixture spin-orbit mechanism is the dominant contribution to T-1 in the measured magnetic field range. Temperature and excitation-energy dependent measurements indicate a donor density dependent interaction may contribute to small deviations between experiment and theory. The longest T-1 measured is 480 ms at 1.75 T with increasing T-1 at smaller fields theoretically expected. This work highlights the extremely long longitudinal spin-relaxation time for ZnO donors due to their small spin-orbit coupling.

We show that driving a two-dimensional electron gas by an in-plane electric field oscillating at the frequency ω gives rise to an electric current at 2 ω flowing near the edge of the system. This current has both parallel and perpendicular to the edge components, which emit electromagnetic waves at 2 ω with different polarizations. We develop a microscopic theory of such an edge second harmonic generation and calculate the edge current at 2 ω in different regimes of electron transport and electric field screening. We also show that at high frequencies the spatial profile of the edge current contains oscillations caused by excitation of plasma waves.

Hole spins in semiconductors are a potential qubit alternative to electron spins. In nuclear-spin-rich host crystals like GaAs, the hyperfine interaction of hole spins with nuclei is considerably weaker than that for electrons, leading to potentially longer dephasing times. Here we demonstrate optical pumping and coherent population trapping for acceptor-bound holes in a strained GaAs epitaxial layer. We find mu s-scale longitudinal spin relaxation time T-1 and an inhomogeneous dephasing time T-2* 2 of similar to 7 ns. We attribute the spin relaxation mechanism to the combined effect of a hole-phonon interaction through the deformation potentials, and heavy-hole-light-hole mixing in an in-plane magnetic field. We attribute the short T-2* to g-factor broadening due to strain inhomogeneity. T-1 and T-2* are calculated based on these mechanisms and compared with the experimental results. While the hyperfine-mediated decoherence is mitigated, our results highlight the important contribution of strain to relaxation and dephasing of acceptor-bound hole spins.

We study theoretically transverse photoconductivity induced by circularly polarized radiation, i.e. the photovoltaic Hall effect, and linearly polarized radiation causing intraband optical transitions in two-dimensional electron gas (2DEG). We develop a microscopic theory of these effects based on analytical solution of the Boltzmann equation for arbitrary electron spectrum and scattering mechanism. We calculate the transverse photoconductivity of 2DEG with parabolic and linear dispersion for short-range and Coulomb scatterers at different temperatures. We show that the transverse electric current is significantly enhanced at frequencies comparable to the inverse energy relaxation time, whereas at higher frequencies the excitation spectrum and the direction of current depend on the scattering mechanism. We also analyse the effect of thermalization processes caused by electron-electron collisions on the photoconductivity.

We report the observation of the resonant excitation of edge photocurrents in bilayer graphene subjected to terahertz radiation and a magnetic field. The resonantly excited edge photocurrent is observed for both inter-band (at low carrier densities) and intra-band (at high densities) transitions between Landau levels (LL). While the intra-band LL transitions can be traced to the classical cyclotron resonance (CR) and produce strong resonant features, the inter-band-LL resonances have quantum nature and lead to the weaker features in the measured photocurrent spectra. The magnitude and polarization properties of the observed features agree with the semiclassical theory of the intra-band edge photogalvanic effect, including its Shubnikov-de-Haas oscillations at low temperatures.

Driving a 2D electron gas by AC electric field leads to a DC electric current flowing along the edge of the system. The effect is caused by the local breaking of space inversion symmetry at the edge. The current is generated in a narrow stripe determined by the screening length of the AC electric field and the mean free path of carriers. The developed microscopic theory of the effect shows that the excitation spectrum of the edge current and even the current direction depend on the mechanism of electron scattering. In an external magnetic field, the excitation spectrum of the current features the cyclotron resonance.

We show that the inter-band absorption of radiation in a 2D Dirac material leads to a direct electric current flowing at sample edges. The photocurrent originates from the momentum alignment of electrons and holes and is controlled by the radiation polarization. We develop a microscopic theory of such an edge photogalvanic effect and calculate the photocurrent for gapped and gapless 2D Dirac materials, also in the presence of a static magnetic field which introduces additional imbalance between the electron and hole currents. Further, we show that the photocurrent can be considerably multiplied in a ratchet-like structure with an array of narrow strips.

Control of defects in bulk semiconductors such as GaAs is essential to realize novel excitonic phases for emerging quantum devices. In these systems, stacking fault (SF) defects are common, leading to local variations in optical properties, but the exact configuration of such defects and their interaction with excitons are not fully understood. Here we describe the use of aberration-corrected scanning transmission electron microscopy (STEM) imaging to directly examine SF defects in the GaAs system. In particular, we quantify the structure and properties of several SF configurations through multislice image simulations based on ab initio calculations. We show that this approach can reveal significant differences in exciton trapping behavior and suggest ways to control quantum systems.

Two-dimensional stacking fault defects embedded in a bulk crystal can provide a homogeneous trapping potential for carriers and excitons. Here we utilize state-of-the-art structural imaging coupled with density-functional and effective-mass theory to build a microscopic model of the stacking-fault exciton. The diamagnetic shift and exciton dipole moment at different magnetic fields are calculated and compared with the experimental photoluminescence of excitons bound to a single stacking fault in GaAs. The model is used to further provide insight into the properties of excitons bound to the double-well potential formed by stacking fault pairs. This microscopic exciton model can be used as an input into models which include exciton-exciton interactions to determine the excitonic phases accessible in this system.

We report on the observation of edge electric currents excited in bi-layer graphene by terahertz laser radiation. We show that the current generation belongs to the class of second order in electric field phenomena and is controlled by the orientation of the THz electric field polarization plane. Additionally, applying a small magnetic field normal to the graphene plane leads to a phase shift in the polarization dependence. Increasing the magnetic field strength, the current starts to exhibit 1/B-magnetooscillations with a period consistent with that of the Shubnikov-de-Haas effect and amplitude by an order of magnitude larger as compared to the current at zero magnetic field measured under the same conditions. The microscopic theory developed shows that the current is formed in the edges vicinity limited by the mean-free path of carriers and the screening length of the high-frequency electric field. The current originates from the alignment of the free carrier momenta and dynamic accumulation of charge at the edges, where the P-symmetry is naturally broken. The observed magnetooscillations of the photocurrent are attributed to the formation of Landau levels.

We study the effects of electron-hole asymmetry on the electronic structure of helical edge states in HgTe/HgCdTe quantum wells. In the framework of the four-band kp -model, which takes into account the absence of a spatial inversion centre, we obtain analytical expressions for the energy spectrum and wave functions of edge states, as well as the effective g -factor tensor and matrix elements of electro-dipole optical transitions between the spin branches of the edge electrons. We show that when two conditions are simultaneously satisfied—electron-hole asymmetry and the absence of an inversion centre—the spectrum of edge electrons deviates from the linear one, in that case we obtain corrections to the linear spectrum.

We develop a theory of electron-photon interaction for helical edge channels in two-dimensional topological insulators based on zinc-blende-type quantum wells. It is shown that the lack of space inversion symmetry in such structures enables the electro-dipole optical transitions between the spin branches of the topological edge states. Further, we demonstrate the linear and circular dichroism associated with the edge states and the generation of edge photocurrents controlled by radiation polarization.

We observe that the illumination of unbiased graphene in the quantum Hall regime with polarized terahertz laser radiation results in a direct edge current. This photocurrent is caused by an imbalance of persistent edge currents, which are driven out of thermal equilibrium by indirect transitions within the chiral edge channel. The direction of the edge photocurrent is determined by the polarity of the external magnetic field, while its magnitude depends on the radiation polarization. The microscopic theory developed in this paper describes well the experimental data.