Nicolas Tancogne-Dejean

Impact of the Electronic Band Structure in High-Harmonic Generation Spectra of Solids

An accurate analytic model describing the microscopic mechanism of high-harmonic generation (HHG) in solids is derived. Extensive first-principles simulations within a time-dependent density-functional framework corroborate the conclusions of the model. Our results reveal that (i)xa0the emitted HHG spectra are highly anisotropic and laser-polarization dependent even for cubic crystals; (ii)xa0the harmonic emission is enhanced by the inhomogeneity of the electron-nuclei potential; the yield is increased for heavier atoms; and (iii)xa0the cutoff photon energy is driver-wavelength independent. Moreover, we show that it is possible to predict the laser polarization for optimal HHG in bulk crystals solely from the knowledge of their electronic band structure. Our results pave the way to better control and optimize HHG in solids by engineering their band structure.

Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

The strong ellipticity dependence of high-harmonic generationxa0(HHG) in gases enables numerous experimental techniques that are nowadays routinely used, for instance, to create isolated attosecond pulses. Extending such techniques to solids requires a fundamental understanding of the microscopic mechanism of HHG. Here we use first-principles simulations within a time-dependent density-functional framework and show how intraband and interband mechanisms are strongly and differently affected by the ellipticity of the driving laser field. The complex interplay between intraband and interband effects can be used to tune and improve harmonic emission in solids. In particular, we show that the high-harmonic plateau can be extended by as much as 30% using a finite ellipticity of the driving field. We furthermore demonstrate the possibility to generate, from single circularly polarized drivers, circularly polarized harmonics. Our work shows that ellipticity provides an additional knob to experimentally optimize HHG in solids.The mechanisms of high-order harmonic generation in bulk system and dilute gas are different. Here the authors use first-principle methods to explore the ellipticity dependence and control of the HHG in periodic solids by involving the interband and intraband dynamics in Si and MgO.

Atomic-like high-harmonic generation from two-dimensional materials

Two-dimensional materials offer a unique platform where both bulk and atomic HHG can be investigated. The generation of high-order harmonics from atomic and molecular gases enables the production of high-energy photons and ultrashort isolated pulses. Obtaining efficiently similar photon energy from solid-state systems could lead, for instance, to more compact extreme ultraviolet and soft x-ray sources. We demonstrate from ab initio simulations that it is possible to generate high-order harmonics from free-standing monolayer materials, with an energy cutoff similar to that of atomic and molecular gases. In the limit in which electrons are driven by the pump laser perpendicularly to the monolayer, they behave qualitatively the same as the electrons responsible for high-harmonic generation (HHG) in atoms, where their trajectories are described by the widely used semiclassical model, and exhibit real-space trajectories similar to those of the atomic case. Despite the similarities, the first and last steps of the well-established three-step model for atomic HHG are remarkably different in the two-dimensional materials from gases. Moreover, we show that the electron-electron interaction plays an important role in harmonic generation from monolayer materials because of strong local-field effects, which modify how the material is ionized. The recombination of the accelerated electron wave packet is also found to be modified because of the infinite extension of the material in the monolayer plane, thus leading to a more favorable wavelength scaling of the harmonic yield than in atomic HHG. Our results establish a novel and efficient way of generating high-order harmonics based on a solid-state device, with an energy cutoff and a more favorable wavelength scaling of the harmonic yield similar to those of atomic and molecular gases. Two-dimensional materials offer a unique platform where both bulk and atomic HHG can be investigated, depending on the angle of incidence. Devices based on two-dimensional materials can extend the limit of existing sources.

Self-consistent DFT plus U method for real-space time-dependent density functional theory calculations

We implemented various DFT+U schemes, including the ACBN0 self-consistent density-functional version of the DFT+U method [Phys. Rev. X 5, 011006 (2015)] within the massively parallel real-space time-dependent density functional theory (TDDFT) code Octopus. We further extended the method to the case of the calculation of response functions with real-time TDDFT+U and to the description of non-collinear spin systems. The implementation is tested by investigating the ground-state and optical properties of various transition metal oxides, bulk topological insulators, and molecules. Our results are found to be in good agreement with previously published results for both the electronic band structure and structural properties. The self consistent calculated values of U and J are also in good agreement with the values commonly used in the literature. We found that the time-dependent extension of the self-consistent DFT+U method yields improved optical properties when compared to the empirical TDDFT+U scheme. This work thus opens a different theoretical framework to address the non equilibrium properties of correlated systems.

Improved ab initio calculation of surface second-harmonic generation from Si(111)(1×1):H

Surface second-harmonic generation (SSHG) has been shown to be an effective, nondestructive and noninvasive probe to study surface and interface properties. SSHG spectroscopy is now very cost-effective and popular because it is an efficient method for characterizing the properties of buried interfaces and nanostructures. The high surface sensitivity of SSHG spectroscopy is due to the fact that within the dipole approximation, the bulk second-harmonic generation (SHG) in centrosymmetric materials is identically zero. The SHG process can occur only at the surface where the inversion symmetry is broken. SSHG is particularly useful for studying the surfaces of centrosymmetric materials. From the theoretical point of view, the calculation of the nonlinear surface susceptibility tensor, χ(−2ω;ω, ω), proceeds as follows. To mimic the semi-infinite system, one constructs a supercell consisting of a finite slab of material plus a vacuum region. Both the size of the slab and the vacuum region should be such that the value of χ(−2ω;ω, ω) is well converged. One has to include a cut function to decouple the two halves of the supercell in order to obtain the value of χ(−2ω;ω, ω) for either half. If the supercell itself is centrosymmetric, the value χ(−2ω;ω, ω) is identically zero, thus the cut function is of paramount importance. The cut function can be generalized to one that is capable of obtaining the value of χ(−2ω;ω, ω) for any part of the slab. The depth within the slab for which χ(−2ω;ω, ω) is nonzero can thus be obtained. One can also study how χ(−2ω;ω, ω) goes to zero towards the middle of the slab where the centrosymmetry of the material is restored. Therefore, for the surface of any centrosymmetric material we can find the thickness of the layer where χ(−2ω;ω, ω) 6= 0. In this article, based on the above approach for the calculation of χ(−2ω;ω, ω), we develop a model for the SH radiation from the surface of a centrosymmetric material. We call this model the three layer model, which considers that the SH conversion takes place in a thin layer just below the surface of the material that lies under the vacuum region and above the bulk of the material. Of course, one can replace the vacuum region with any medium as long as it is not SH active. However, most of the experimental setups for measuring the SH radiation take place in vacuum or air. We develop the model and derive general expressions for the SH radiation for the commonly used polarization combinations of the incoming and outgoing electric fields. We particularize the results for the (111), (110), and (100) crystalline surfaces of centrosymmetric materials. This paper is organized as follows. In Sec. II, we present the relevant equations and theory that describe the SHG yield. In Sec. III, we present the explicit expressions for each combination of input and output polarizations for the (111), (110), and (100) surfaces. Finally, we list our conclusions and final remarks in Sec. IV.

Author Correction: From a quantum-electrodynamical light–matter description to novel spectroscopies

Equation 1 in the original version of the article should read:

All-optical nonequilibrium pathway to stabilising magnetic Weyl semimetals in pyrochlore iridates

Nonequilibrium many-body dynamics is becoming a central topic in condensed matter physics. Floquet topological states were suggested to emerge in photodressed bands under periodic laser driving. Here we propose a viable nonequilibrium route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining ab initio calculations for a time-dependent self-consistent light-reduced Hubbard U and nonequilibrium magnetism simulations for quantum quenches, we find dynamically modified magnetic order giving rise to transiently emerging Weyl cones that can be probed by time- and angle-resolved photoemission spectroscopy. Our work offers a unique and realistic pathway for nonequilibrium materials engineering beyond Floquet physics to create and sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds switching protocols for light-engineered Berry curvature in combination with ultrafast magnetism.Topological states may emerge in nonequilibrium but the mechanisms are much less understood. Here Topp et al. propose a nonequilibrium route to obtain the magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interactions with short laser pulses.

Ellipticity dependence of higher-order harmonics in solids: Unraveling the interplay between intraband and interband dynamics

Recently, we introduced an ab-initio time-dependent density-functional theory (TDDFT) framework that allows us to investigate the coupled interplay between the interband and intraband mechanisms of high-harmonic generation (HHG) from solids [1] without making a-priori model assumptions or strong approximations. Here, using HHG experiments on bulk silicon samples combined with TDDFT simulations, we study the complex physics underlying anisotropic harmonic emission, as reported by You et al. [2] for the strongly anisotropic ellipticity dependence of the 19th harmonic (HH19) generated in bulk MgO. In [2], the observed anisotropy was explained with real-space trajectories in a 2D one-band model including scattering from neighboring atomic sites. Our TDDFT simulations [3] and HHG experiments reveal that the various higher-harmonic orders generated in solids exhibit qualitatively different sensitivity to driver-pulse ellipticity ε (not displayed here), resulting from a different response of intraband and interband dynamics [3], in contradiction with the model proposed in [2]. In fact, band-structure and joint-density-of-states (JDOS) effects become important [1].

Publisher Correction: Ellipticity dependence of high-harmonic generation in solids originating from coupled intraband and interband dynamics

The published version of this Article contained an error in the second sentence of the fourth paragraph of the subheaded section “Ellipticity and helicity of the emitted harmonics”. The final exponent in this sentence should read: inπ/2. This has now been corrected in the PDF and HTML versions of the Article.