Nonlinear Response Of Electrons Research Articles

Ultrafast Opto-Electronic and Thermal Tuning of Third-Harmonic Generation in a Graphene Field Effect Transistor.

Graphene is a unique platform for tunable opto-electronic applications thanks to its linear band dispersion, which allows electrical control of resonant light-matter interactions. Tuning the nonlinear optical response of graphene is possible both electrically and in an all-optical fashion, but each approach involves a trade-off between speed and modulation depth. Here, lattice temperature, electron doping, and all-optical tuning of third-harmonic generation are combined in a hexagonal boron nitride-encapsulated graphene opto-electronic device and demonstrate up to 85% modulation depth along with gate-tunable ultrafast dynamics. These results arise from the dynamic changes in the transient electronic temperature combined with Pauli blocking induced by the out-of-equilibrium chemical potential. The work provides a detailed description of the transient nonlinear optical and electronic response of graphene, which is crucial for the design of nanoscale and ultrafast optical modulators, detectors, and frequency converters.

Plasmon dispersion and Landau damping in the nonlinear quantum regime.

We study the dispersion properties of electron plasma waves, or plasmons, which can be excited in quantum plasmas in the nonlinear regime. In order to describe nonlinear electron response to finite amplitude plasmons, we apply the Volkov approach to nonrelativistic electrons. For that purpose, we use the Schrödinger equationand describe the electron population of a quantum plasma as a mixture of quantum states. Within the kinetic framework that we are able to derive from the Volkov solutions, we discuss the role of the wave amplitude on the nonlinear plasma response. Finally, we focus on the quantum properties of nonlinear Landau damping and study the contributions of multiplasmon absorption and emission processes.

Spatial Frequency Manipulation of a Quartz Crystal for Phase‐Matched Second‐Harmonic Vacuum Ultraviolet Generation

AbstractSecond harmonic generation (SHG) is the nonlinear response of electrons to high‐intensity light and has been successfully applied in basic scientific research and modern optoelectronics. However, constrained by stringent but essential phase‐matching conditions, efficient vacuum ultraviolet (VUV) SHG is still a challenge in solid‐state lasers. Here, this work employs a spatial frequency manipulation strategy to realize artificially structured phase‐matching conditions in ordinary quartz crystals for efficient frequency doubling in the VUV range. Phase‐matched VUV SHG at wavelengths of 177.3 and 167.8 nm is realized with unprecedented output power and conversion efficiency. The design strategy releases the phase‐matching condition for nonlinear optics and provides a way to study light–matter nonlinear interactions, and the present sources should be helpful for the development of VUV photonics, including high‐resolution angle‐resolved photoemission spectroscopy and Al+ optical clocks.

Theory of coherent optical nonlinearities of intersubband transitions in semiconductor quantum wells

We theoretically study the coherent nonlinear response of electrons confined in semiconductor quantum wells under the effect of an electromagnetic radiation close to resonance with an intersubband transition. Our approach is based on the time-dependent Schr\"odinger-Poisson equation stemming from a Hartree description of Coulomb-interacting electrons. This equation is solved by standard numerical tools and the results are interpreted in terms of approximated analytical formulas. For growing intensity, we observe a redshift of the effective resonance frequency due to the reduction of the electric dipole moment and the corresponding suppression of the depolarization shift. The competition between coherent nonlinearities and incoherent saturation effects is discussed. The strength of the resulting optical nonlinearity is estimated across different frequency ranges from mid-IR to THz with an eye to ongoing experiments on Bose-Einstein condensation of intersubband polaritons and to the speculative exploration of quantum optical phenomena such as single-photon emission in the mid-IR and THz windows.

Probing the Gold/Water Interface with Surface-Specific Spectroscopy.

Water is an integral component in electrochemistry, in the generation of the electric double layer, and in the propagation of the interfacial electric fields into the solution; however, probing the molecular-level structure of interfacial water near functioning electrode surfaces remains challenging. Due to the surface-specificity, sum-frequency-generation (SFG) spectroscopy offers an opportunity to investigate the structure of water near working electrochemical interfaces but probing the hydrogen-bonded structure of water at this buried electrode-electrolyte interface was thought to be impossible. Propagating the laser beams through the solvent leads to a large attenuation of the infrared light due to the absorption of water, and interrogating the interface by sending the laser beams through the electrode normally obscures the SFG spectra due to the large nonlinear response of conduction band electrons. Here, we show that the latter limitation is removed when the gold layer is thin. To demonstrate this, we prepared Au gradient films on CaF2 with a thickness between 0 and 8 nm. SFG spectra of the Au gradient films in contact with H2O and D2O demonstrate that resonant water SFG spectra can be obtained using Au films with a thickness of ∼2 nm or less. The measured spectra are distinctively different from the frequency-dependent Fresnel factors of the interface, suggesting that the features we observe in the OH stretching region indeed do not arise from the nonresonant response of the Au films. With the newfound ability to probe interfacial solvent structure at electrode/aqueous interfaces, we hope to provide insights into more efficient electrolyte composition and electrode design.

Theory for all-optical responses in topological materials: The velocity gauge picture

High Harmonic Generation (HHG), which has been widely used in atomic gas, has recently expanded to solids as a means to study highly nonlinear electronic response in condensed matter and produce coherent high frequency radiation with new properties. Most recently, attention has turned to Topological Materials (TMs) and the use of HHG to characterize topological bands and invariants. Theoretical interpretation of nonlinear electronic response in TMs, however, presents many challenges. In particular, the Bloch wavefunction phase of TMs has undefined points in the Brillouin Zone. This leads to singularities in calculating the inter-band and intra-band transition dipole matrix elements of Semiconductor Bloch Equations (SBEs). Here, we use the laser-electromagnetic velocity gauge ${\boldsymbol p}\cdot {\bf A}(t)$ to numerically integrate the SBEs and treat the singularity in the production of the electrical currents and HHG spectra. We use a prototype of Chern Insulators (CIs), the Haldane model, to demonstrate our approach. We find good qualitative agreement of the velocity gauge compared to the length gauge and the Time-Dependent Density Functional theory in the case of topologically trivial materials such as MoS$_2$. For velocity gauge and length gauge, our two-band Haldane model reproduces key HHG spectra features: ($\textit i$) The selection rules for linear and circular light drivers, ($\textit ii$) The linear cut-off law scaling and ($\textit iii$) The anomalous circular dichroism. We conclude that the velocity-gauge approach captures experimental observations and provides theoretical tools to investigate topological materials.

Density Functional Theory Perspective on the Nonlinear Response of Correlated Electrons across Temperature Regimes.

We explore a new formalism to study the nonlinear electronic density response based on Kohn–Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wavenumbers q < 2qF, with qF being the Fermi wavenumber. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the nonlinear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods.

Free electron harmonic generation in heavily doped semiconductors: the role of the materials properties

Heavily doped semiconductors have emerged as low-loss and tunable materials for plasmonics at mid-infrared frequencies. We analyze the nonlinear optical response of free electrons and show how nonlinear optical phenomena associated with high electron concentration are influenced by the intrinsic properties of semiconductors, namely background permittivity and effective mass. We apply our recently developed hydrodynamic description that takes into account nonlinear contributions up to the third order, usually negligible for noble metals, to compare third-harmonic generation from InP, Ge, GaAs, Si, ITO and InSb. We show how free electron nonlinearities may be enhanced with a proper choice of the semiconductor.

Nonlinear Density Response and Higher Order Correlation Functions in Warm Dense Matter

In a recent letter [Phys. Rev. Lett. 125, 085001 (2020)], Dornheim et al. have presented the first ab initio path integral Monte Carlo (PIMC) results for the nonlinear electronic density response at warm dense matter (WDM) conditions. In the present work, we extend these considerations by exploring the relation between the nonlinear response and three-/four-body correlation functions from many-body theory. In particular, this connection directly implies a comparably increased sensitivity of the nonlinear response to electronic exchange–correlation (XC) effects, which is indeed confirmed by our analysis over the entire relevant range of densities (\(r_{s} = 0.5, \ldots ,10\)) and temperatures (\(\theta = 0.01, \ldots ,4\)). Finally, our work suggests the possibility of deliberately probing the nonlinear regime to experimentally probe three- and potentially even four-body correlation functions in WDM.

Density response of the warm dense electron gas beyond linear response theory: Excitation of harmonics

In a recent Letter, Dornheim et al. [PRL 125, 085001 (2020)] have investigated the nonlinear density response of the uniform electron gas in the warm dense matter regime. More specifically, they have studied the cubic response function at the first harmonic, which cannot be neglected in many situations of experimental relevance. In this work, we go one step further and study the full spectrum of excitations at the higher harmonics of the original perturbation based on extensive new ab initio path integral Monte Carlo (PIMC) simulations. We find that the dominant contribution to the density response beyond linear response theory is given by the quadratic response function at the second harmonic in the moderately nonlinear regime. Furthermore, we show that the nonlinear density response is highly sensitive to exchange-correlation effects, which makes it a potentially valuable new tool of diagnostics. To this end, we present a new theoretical description of the nonlinear electronic density response based on the recent effective static approximation to the local field correction [PRL 125, 235001 (2020)], which accurately reproduces our PIMC data with negligible computational cost.

Nonlinear electronic density response of the ferromagnetic uniform electron gas at warm dense matter conditions

AbstractIn a recent Letter [T. Dornheim et al., Phys. Rev. Lett. 125, 085001 (2020)], we have presented the first ab initio results for the nonlinear density response of electrons in the warm dense matter (WDM) regime. In the present work, we extend these efforts by carrying out extensive new path integral Monte Carlo simulations of a ferromagnetic electron gas that is subject to an external harmonic perturbation. This allows us to unambiguously quantify the impact of spin‐effects on the nonlinear density response of the warm dense electron gas. In addition to their utility for the description of WDM in an external magnetic field, our results further advance our current understanding of the uniform electron gas as a fundamental model system, which is important in its own right.

Linear and Nonlinear Phenomena in a Flow of Surface Plasmon–Polaritons

The excitation and propagation of plasmon–polariton modes are considered at a single interface of a dielectric medium and metal in linear and nonlinear regimes. Physical mechanisms of the emergence of a nonlinear response of free electrons in the metal based on the quantum hydrodynamic model are described. It is shown that the period and profile of the envelope of a cnoidal wave of surface plasmon–polaritons in the nonlinear regime change, depending on the conditions of excitation and the energy density of the exciting electromagnetic wave.

Nonlinear Work Function Tuning of Lead‐Halide Perovskites by MXenes with Mixed Terminations

AbstractMXenes are a recent family of 2D materials with very interesting electronic properties for device applications. One very appealing feature is the wide range of work functions shown by these materials, depending on their composition and surface terminations, that can be exploited to adjust band alignments between different material layers. In this work, based on density functional theory calculations, how mixed terminations of F, OH, and/or O affect the work function of Ti3C2 MXene is analyzed in detail, covering the whole phase‐space of mixtures. The Ti3C2/CH3NH3PbI3 (MAPbI3) perovskite coupled system for solar cell applications is also analyzed. A strong nonlinear behavior is found when varying the relative concentrations of OH, O, and F terminations, with the strongest effect of the OH groups in lowering the work function, already at a relative amount of 25%. A surprising minimum work function is found for relative OH:O fraction of 75:25, explained in terms of the nonlinear electronic response in screening the surface dipoles.

Energy-loss straggling with higher-order effects and electron correlations taken into account

The approach suggested previously to treat the mean energy loss of charged projectiles in terms of induced currents is extended to describe the energy-loss straggling. It has been shown that, provided the perturbed wave function of electrons is known, the phenomenon can be represented in a form of distributions of densities of energy and energy squared within the target volume. These distributions satisfy respective continuity equations with the source terms defining the local deposition of energy and energy squared. The approach is applied to treat the canonical phenomenon, the stopping in a uniform electron gas, and provides a possibility to account for the spatial correlation of electrons. Two types of approximations for the perturbed state of electrons are considered, the impulse and continuum distorted-wave approximations. Together with the effect of electron correlations, these nonperturbative approaches permit one to evaluate the higher-order correction over the projectile charge. The origin of this correction is similar to the origin of Barkas correction in the stopping power; it can be argued also that there is no place in straggling for the Bloch correction. These properties, i.e., nonlinear electron response and electron correlations, can result in significant effects, both capable of changing dramatically the straggling at small projectile energies. However, in the case of positively charged projectiles, the two effects mainly compensate for one another. For negatively charged projectiles, due to the impossibility of close approaches of the collision partners, both effects are effectively smeared out.

Extraction of higher-order nonlinear electronic response in solids using high harmonic generation

Nonlinear susceptibilities are key to ultrafast lightwave driven optoelectronics, allowing petahertz scaling manipulation of the signal. Recent experiments retrieved a 3rd order nonlinear susceptibility by comparing the nonlinear response induced by a strong laser field to a linear response induced by the otherwise identical weak field. The highly nonlinear nature of high harmonic generation (HHG) has the potential to extract even higher order nonlinear susceptibility terms. However, up till now, such characterization has been elusive due to a lack of direct correspondence between high harmonics and nonlinear susceptibilities. Here, we demonstrate a regime where such correspondence can be clearly made, extracting nonlinear susceptibilities (7th, 9th, and 11th) from sapphire of the same order as the measured high harmonics. The extracted high order susceptibilities show angular-resolved periodicities arising from variation in the band structure with crystal orientation. Our results open a door to multi-channel signal processing, controlled by laser polarization.

Enhancement of valley polarization in graphene with an irradiating charged particle

We use a two-dimensional two-component nonlinear hydrodynamic method to study valley-dependent plasmons in bounded strained graphene in the presence of an irradiating proton, realizing electrostatic control of the valley-dependent plasmons in actual space. We use flux-corrected transport to solve the nonlinear hydrodynamic equations numerically and self-consistently. Our results answer the important question of whether full valley polarization can be obtained in a specific valley at the boundary or inside the graphene sheet in the presence of the injected proton. The electrons experience collective excitations due to the proton interaction and the strain-induced pseudomagnetic field. The electron density fluctuation can be much larger than the equilibrium electron density, leading to a strong nonlinear effect and thus full valley polarization. This demonstrates the nature of the nonlinear response of electrons in graphene to strong interactions, a response that originates from the strong nonperturbative interaction between the irradiating proton and the electrons. Thus, our method opens up the possibility of investigating the nonlinear behavior of valley-dependent plasmons in strong modulations. The effects of the proton on the valley polarization are examined. There is K-polarization inside the surface behind the proton, whereas there is K′-polarization at the edge which decays away from the edge, thereby switching the valley polarization. This work establishes a link between actual-space valley-dependent plasmons in graphene and the irradiating proton and provides an alternative way to realize full valley polarization with tunable polarity. Compared to the case with no proton, the valley polarization is enhanced considerably in the presence of a proton.

Anisotropic nonlinear optical response of phosphorene

The pseudorelativistic behaviour of carriers is found in the energy bands of certain class of two dimensional (2D) semi-conducting materials such as phosphorene. In this article, the nonlinear optical response of pseudorelativistic electrons in phosphorene under intense applied electromagnetic field is investigated. Using Floquet theory, we demonstrate the anisotropic behaviour of anomalous Rabi oscillations in phosphorene, which occurs far from the conventional resonance. The role of anisotropy on anomalous Rabi oscillations in phosphorene is also justified numerically. The Bloch-Siegert shift is observed under strong driving field that strongly depends on the anisotropy of the energy bands of phosphorene. A theoretical description of the pump-probe experiment is given to detect the anomalous Rabi oscillations in phosphorene. The differential transmission coefficient shows a sinusoidal behaviour as a function of pump pulse duration whose amplitude exhibits a power law decay, which is quite different from graphene (relativistic fermionic system). So the Floquet theory can be used to characterize the different fermionic systems.

Exploring circular polarization in the CMB due to conventional sources of cosmic birefringence

The circular polarization of the cosmic microwave background (CMB) is usually taken to be zero since it is not generated by Thomson scattering. Here we explore the actual level of circular polarization in the CMB generated by conventional cosmological sources of birefringence. We consider two classes of mechanisms for birefringence. One is alignment of the matter to produce an anisotropic susceptibility tensor: the hydrogen spins can be aligned either by density perturbations or CMB anisotropies themselves. The other is anisotropy of the radiation field coupled to the non-linear response of the medium to electromagnetic fields: this can occur either via photon-photon scattering (non-linear response of the vacuum); atomic hyperpolarizability (non-linear response of neutral atoms); or plasma delay (non-linear response of free electrons). The strongest effect comes from photon-photon scattering from recombination at a level of ∼ 10−14 K. Our results are consistent with a negligible circular polarization of the CMB in comparison with the linear polarization or the sensitivity of current and near-term experiments.

Terawatt-scale optical half-cycle attosecond pulses

Extreme-ultravoilet (XUV) attosecond pulses with durations of a few tens of attosecond have been successfully applied for exploring ultrafast electron dynamics at the atomic scale. But their weak intensities limit the further application in demonstrating nonlinear responses of inner-shell electrons. Optical attosecond pulses will provide sufficient photon flux to initiate strong-field processes. Here we proposed a novel method to generate an ultra-intense isolated optical attosecond pulse through relativistic multi-cycle laser pulse interacting with a designed gas-foil target. The underdense gas target sharpens the multi-cycle laser pulse, producing a dense layer of relativistic electrons with a thickness of a few hundred nanometers. When the dense electron layer passes through an oblique foil, it emits single ultra-intense half-cycle attosecond pulse in the visible and ultraviolet spectral range. The emitted pulse has a peak intensity exceeding 1018 W/cm2 and full-width-half-maximum duration of 200 as. The peak power of this attosecond light source reaches 2 terawatt. The proposed method relaxes the single-cycle requirement on the driving pulse for isolated attosecond pulse generation and significantly boosts the peak power, thus it may open up the route to new experiments tracking the nonlinear response of inner-shell electrons as well as nonlinear attosecond phenomena investigation.

The non-linear terahertz response of hot electrons in low-dimensional semiconductor superlattices: Suppression of the polar-optical phonon scattering

We study the response of low-dimensional semiconductor superlattices to strong terahertz fields on condition of a strong suppression of inelastic scattering processes of electrons caused by the polar-optical phonons. For our study, we employ a balance equations approach, which allows investigating the response of the superlattices to strong terahertz fields taking account of both the inelastic and the strongly pronounced elastic scattering of electrons. Our approach provides a way to analyze the influence of the Bloch dynamics of electrons in a superlattice miniband side by side with the effects of the electron heating on the magnitude and the frequency dependence of a superlattice current responsivity in the terahertz frequency band. Our study shows that the suppression of the inelastic scattering caused either by a reduction of the superlattice dimensionality by lateral quantization or by a strong magnetic field application can give rise to a huge enhancement of the current responsivity. This enhancement can be interpreted in terms of the well pronounced electronic bolometric effect occurring due to the efficient electron heating in the low-dimensional superlattices by the incident terahertz fields.