Nonlinear Optical Conductivity Research Articles

Microscopic analysis of relaxation behavior in nonlinear optical conductivity of graphene

We produce a general formalism to study the interband dynamical optical conductivity in the nonlinear regime of graphene in the presence of a quantum bath comprising phonons and electrons. When a quantum solid of graphene is subjected to an intense electric field in the optical frequency range, the observation of a nonlinear response is facilitated by formulating a quantum master equation of the density operator associated with the Hamiltonian encapsulated in a spin-boson model of dissipative quantum statistical mechanics. Our results reveal the nonlinear steady-state regime’s population inversion and decoherence. The present method enables us to investigate further the nonlinear interband optical conductivity of pristine and gapped graphene characterized by a single dimensionless parameter at finite temperatures. Different bath spectra’ effects on phonons and electrons are examined in detail. The temperature dependence of conductivity reveals that changing temperature can enable us to make a transition from the linear to the nonlinear regime for fixed optical field parameters. Interestingly, a fascinating switching-like behavior is observed for the low-temperature optical conductivity of the gapped graphene while we vary the energy gap as well as the frequency of the externally applied field. Although our general formulation can address a variety of nonequilibrium responses of the two-band system, it also facilitates a connection with the phenomenological modeling of nonlinear optical conductivity.

Improving the optical properties of magnesium spinel chromites through Ni and Cu substitutions for optoelectronic applications.

In this study, we investigated the optoelectronic performance of magnesium spinel chromites with nickel (Ni) and copper (Cu) substitutions. Using the sol-gel method, we synthesized two spinel chromites: Mg0.6Ni0.4Cr2O4 (MNCO) and Mg0.6Cu0.4Cr2O4 (MCCO). We extensively characterized these samples to analyze their thermal, structural, elastic, and optical properties. Structural analysis reveals good agreement between the calculated and refined structural parameters, which supports the proposed cation distributions for the samples. By calculating stiffness constants from force constants, we derived elastic moduli such as bulk modulus, longitudinal modulus, and rigidity modulus. MCCO exhibited lower values for these moduli, as well as the Debye temperature, compared to MNCO. Both samples displayed a brittle mechanical nature according to the Pugh ratio, while the Poisson ratio remained constant at 0.25, indicating isotropic elasticity. UV-vis-NIR spectroscopy revealed that MNCO has higher band-gap (E g) and Urbach (E u) energies than MCCO. Further analysis of refractive index, penetration depth, extinction coefficients, nonlinear optical parameters, optical conductivity, and optical dielectric constants highlighted the promising optoelectronic applications of the synthesized materials. Our study found that the band-gap energy values of the as-synthesized samples were smaller than reported values for MgCr2O4 spinel chromites, indicating that Ni and Cu substitutions offer an opportunity to extend the sunlight absorption range of magnesium chromites.

Disorder-Induced Singularity of the Quantum Metric

The quantum weight is a new concept to describe gap electronic states of matter. This quantity is obtained by integrating the quantum metric (the real part of the quantum metric tensor) in the same way as the Berry phase is obtained by integrating the Berry curvature (the imaginary part of the quantum metric tensor). The quantum weight determines a number of kinetic quantities such as the nonlinear anomalous Hall effect, optical conductivity, and photovoltaic effect. In this work, it is shown that nonmagnetic disorder in topological insulators can induce a singularity in the quantum metric and quantum weight.

Symmetry transformation of nonlinear optical current of tilted Weyl nodes and application to ferromagnetic MnBi2Te4

A Weyl node is characterized by its chirality and tilt. We develop a theory of how nth-order nonlinear optical conductivity behaves under transformations of anisotropic tensor and tilt, which clarifies how chirality-dependent and -independent parts of optical conductivity transform under the reversal of tilt and chirality. Built on this theory, we propose ferromagnetic MnBi2Te4 as a magnetoelectrically regulated, terahertz optical device, by magnetoelectrically switching the chirality-dependent and -independent DC photocurrents. These results are useful for creating nonlinear optical devices based on the topological Weyl semimetals.

Regularized lattice theory for spatially dispersive nonlinear optical conductivities

Regularized lattice theory for spatially dispersive nonlinear optical conductivities

Phase Stability of Hexagonal/Cubic Boron Nitride Nanocomposites.

Boron nitride (BN) is an exceptional material, and among its polymorphs, two-dimensional (2D) hexagonal and three-dimensional (3D) cubic BN (h-BN and c-BN) phases are most common. The phase stability regimes of these BN phases are still under debate, and phase transformations of h-BN/c-BN remain a topic of interest. Here, we investigate the phase stability of 2D/3D h-BN/c-BN nanocomposites and show that the coexistence of two phases can lead to strong nonlinear optical properties and low thermal conductivity at room temperature. Furthermore, spark-plasma sintering of the nanocomposite shows complete phase transformation to 2D h-BN with improved crystalline quality, where 3D c-BN possibly governs the nucleation and growth kinetics. Our demonstration might be insightful in phase engineering of BN polymorph-based nanocomposites with desirable properties for optoelectronics and thermal energy management applications.

Resolving old problems with layered polytungstates related to hexagonal tungsten bronze: phase formation, structures, crystal chemistry and some properties.

A 60-year-old problem with the atomic arrangements and exact compositions of alkali polytungstates related to hexagonal tungsten bronze (HTB) was solved. The systems A2WO4-WO3 (A = K, Rb) were restudied and the average monoclinic layered structures of stoichiometric polytungstates A4W11O35 (A = K, Rb, Cs, Tl) and A2W7O22 (A = K, Rb, Cs) were first successfully determined. The structures resemble those of "MoW11O36" and "MoW14O45" (J. Graham and A. D. Wadsley, Acta Crystallogr., 1961, 14, 379-383) and are derived from HTB by breaking into slabs parallel to (100) due to the ordered omission of some [WO]∞ chains along the hexagonal tunnels. The slabs in A4W11O35 (A = Cs, Tl) and A2W7O22 (A = Rb, Cs) are mutually shifted by the a/2 HTB unit cell axis. These data mainly confirmed our preliminary structural models of HTB-like alkali polytungstates (S. F. Solodovnikov, N. V. Ivannikova, Z. A. Solodovnikova and E. S. Zolotova, Inorg. Mater., 1998, 34, 845-853) and revealed a new similar thallium polytungstate. The structures of the HTB-like polytungstates and related compounds form a homologous series of layered complex oxides or fluorides An+2-xM3n+2X9n+8 where n = 2, 3 and 4 are equal to the numbers of HTB hexagonal tunnels across the polytungstate slab width for Tl2W4O13, A4W11O35 and A2W7O22 (A = K, Rb, Cs or Tl), respectively. The structures of the HTB-like polytungstates seem to intergrow with HTB-type AxWO3 to form, in particular, higher homologues of the series. Our group-supergroup analysis, measurements of nonlinear optical activity and electrical conductivity, and calculations of the bond-valence site energy barriers indicate possible ferroelectric/ferroelastic properties and moderate 2D oxide-ion mobility within the HTB-type slabs of the studied polytungstates.

Correlated Insulators, Density Wave States, and Their Nonlinear Optical Response in Magic-Angle Twisted Bilayer Graphene.

The correlated insulator (CI) states and the recently discovered density wave (DW) states in magic-angle twisted bilayer graphene (TBG) have stimulated intense research interest. However, to date, the nature of these "featureless" correlated states with zero Chern numbers are still elusive and lack a characteristic experimental signature. Thus, an experimental probe to identify the characters of these featureless CI and DW states is urgently needed. In this Letter, we theoretically study the correlated insulators and density wave states at different integer and fractional fillings of the flat bands in magic-angle TBG based on extended unrestricted Hartree-Fock calculations including the Coulomb screening effects from the remote bands. We further investigate the nonlinear optical response of the various correlated states and find that the nonlinear optical conductivities can be used to identify the nature of these CI and DW states at most of the fillings. Therefore, we propose that a nonlinear optical response can serve as a promising experimental probe for unveiling the nature of the CI and DW states observed in magic-angle TBG.

Nonlinear optical Hall effect of few-layered NbSe2

${\mathrm{NbSe}}_{2}$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered ${\mathrm{NbSe}}_{2}$, but absent for even-number-layered ${\mathrm{NbSe}}_{2}$ with the inversion symmetry. In this paper we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered ${\mathrm{NbSe}}_{2}$ based on an effective tight-binding model which includes ${d}_{{z}^{2}}$, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$, and ${d}_{xy}$ orbitals of Nb atoms. We show that the nonlinear optical Hall conductivity for the second harmonic generation (SHG) process has a nonvanishing value in odd-number-layered ${\mathrm{NbSe}}_{2}$. Also, we provide a nonlinear optical selection rule in few-layered ${\mathrm{NbSe}}_{2}$ and their polarization dependencies. Furthermore, for the even-number-layered case, the nonlinear optical Hall currents can be generated by applying electric fields which break inversion symmetry. We also discuss that the nonlinear optical Hall effect is expected to occur in TMDC materials in general. Thus, our results will serve to design potential opt-spintronics devices based on 2D materials to generate the spin Hall current by SHG.

Effect of cycle numbers on the structural, linear and nonlinear optical properties in Fe2O3 thin films deposited by SILAR method

Fe2O3 thin films were deposited by Successive Ionic Layer Adsorption and Reaction (SILAR) method onto glass substrates at different cycle numbers to investigate structural, linear and nonlinear optical properties. X-Ray Diffraction (XRD) analysis revealed that the Fe2O3 thin films have a non-crystalline nature. The morphological properties of the films were investigated by Field Emission-Scanning Electron Microscopy (FE-SEM) and the results show that the films’ surfaces are porous. The linear and nonlinear optical parameters were evaluated and analyzed by using transmittance and absorbance measurements. For these measurements, UV–Vis spectroscopy at room temperature was used. The refractive index values were calculated in the range of 1.45–3.23 for visible region (400–700 nm). Obtained results reveal that direct optical band gap changed between 2.62 and 2.68 eV and indirect optical band gap changed between 1.67 and 1.77 eV. Additionally, optical electronegativity, optical dielectric constants, surface and volume energy loss functions, nonlinear refractive index, linear optical susceptibility, third-order nonlinear optical susceptibility, optical and electrical conductivity, and loss tangent values were calculated and discussed in detail. It was found that each parameter studied is dependent on the cycle numbers. Also, it can be stated that Fe2O3 thin films are promising candidate for solar cells and optoelectronic device technology.

Optical response from charge-density waves in Weyl semimetals

The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as ${\text{(TaSe}}_{4}{\text{)}}_{2}\text{I}$. However, the interplay between collective phonon excitations and charge transport in Weyl-CDW systems has not been systematically studied. In this paper, we examine the longitudinal electromagnetic response due to collective modes in a Weyl semimetal gapped by a quasi-one-dimensional CDW order, using both continuum and lattice-regularized models. We systematically compute the contributions of the collective modes to the linear and nonlinear optical conductivity of our models, both with and without tilting of the Weyl cones. We discover that, unlike in a single-band CDW, the gapless CDW collective mode does not contribute to the conductivity unless the Weyl cones are tilted. Going further, we show that the lowest nontrivial collective mode contribution to charge transport with untilted Weyl cones comes in the third-order conductivity for a single collective mode. This third-order process is mediated by the gapped amplitude mode. We show that this leads to a sharply peaked third-harmonic response at frequencies below the single-particle energy gap. We discuss the implications of our findings for transport experiments in Weyl-CDW systems.

Nonlinear optical conductivity of a two-band crystal I

The structure of the electronic nonlinear optical conductivity is elucidated in a detailed study of the time-reversal symmetric two-band model. The nonlinear conductivity is decomposed as a sum of contributions related with different regions of the first Brillouin zone, defined by single or multiphoton resonances. All contributions are written in terms of the same integrals, which contain all information specific to the particular model under study. In this way, ready-to-use formulas are provided that reduce the often tedious calculations of the second and third order optical conductivity to the evaluation of a small set of similar integrals. In the scenario where charge carriers are present prior to optical excitation, Fermi surface contributions must also be considered and are shown to have an universal frequency dependence, tunable by doping. General characteristics are made evident in this type of resonance-based analysis: the existence of step functions that determine the chemical potential dependence of electron–hole symmetric insulators; the determination of the imaginary part by Hilbert transforms, simpler than those of the nonlinear Kramers–Krönig relations; the absence of Drude peaks in the diagonal elements of the second order conductivity, among others. As examples, analytical expressions are derived for the nonlinear conductivities of some simple systems: a very basic model of direct gap semiconductors and the Dirac fermions of monolayer graphene.

Spin-boson model of quantum dissipation in graphene: Nonlinear electrical response

Dissipation in the quantum solid of graphene is couched in the methodology of nonequilibrium statistical mechanics of an open quantum system. Of specific interest is the absorption accompanied by relaxation of energy because of an external frequency-dependent oscillatory electric field. At optical frequencies and for sizable amplitude of the electric field, the response is nonlinear, the treatment of which is simplified by means of a ``rotating wave approximation'' in which rapidly changing, off-resonance terms are omitted. The characteristic resonant frequency is what quantifies the tunneling between the valence and the conduction bands across the so-called Dirac point in graphene. The valence and the conduction states are mapped into the eigenstates of pseudo Pauli spin operators and the corresponding Hamiltonian, when embedded in a dissipative heat bath comprising the surrounding phonons and other electrons, makes possible a comprehensive analysis in terms of the much-studied spin-boson model of dissipative quantum statistical mechanics. A master equation for the density operator associated with this Hamiltonian yields rate equations for the mean population of the valence and the conduction states as well as the transition (matrix elements) between them. Further approximation of these rate equations allows contact with phenomenological treatments of the nonlinear optical conductivity. The present paper then provides a microscopic framework for investigating the response characteristics of a material of great topical interest using contemporary methods of quantum dissipation.

Terahertz nonlinear optics of chiral semimetals RhSn, HfSn, and PdGa

Topological semimetals have linear band dispersion around the band crossing which is near the Fermi level. Chiral topological semimetals have no spatial inversion symmetry, and they have non-vanishing second-order optical response. The band structure and nonlinear optical conductivity (NOC) of the isostructural chiral semimetals RhSn, HfSn, and PdGa are studied by the first-principles calculation in this work. Our calculation demonstrates that the maximal NOC of chiral semimetals RhSn is about under terahertz optical field with photon energy of 12 meV, while the maximal NOCs of HfSn and PdGa are and , respectively. The relatively large NOC of RhSn can be interpreted by its multiple band crossing on the Fermi level, while multiple band crossings in the band structures of HfSn and PdGa are not on the Fermi level. Our calculations also reveal that the calculated imaginary part of dielectric function decreases with increasing photon energy, while the absorption coefficient increases with increasing photon energy in the terahertz region. The relatively large NOC makes chiral topological semimetal RhSn suitable for terahertz detection.

Nonlinear effects in topological materials.

Materials, where charge carriers have a linear energy dispersion, usually exhibit a strong nonlinear optical response in the absence of disorder scattering. This nonlinear response is particularly interesting in the terahertz frequency region. We present a theoretical and numerical investigation of charge transport and nonlinear effects, such as the high harmonic generation in topological materials including Weyl semimetals (WSMs) and α-T3 systems. The nonlinear optical conductivity is calculated both semi-classically using the velocity operator and quantum mechanically using the density matrix. We show that the nonlinear response is strongly dependent on temperature and topological parameters, such as the Weyl point (WP) separation b and Berry phase ϕB. A finite spectral gap opening can further modify the nonlinear effects. Under certain parameters, universal behaviors of both the linear and nonlinear response can be observed. Coupled with experimentally accessible critical field values of 104-105 V/m, our results provide useful information on developing nonlinear optoelectronic devices based on topological materials.

On the General Properties of Non-linear Optical Conductivities

The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo’s response theory, we study the general properties of the nonlinear optical conductivities of quantum many-body systems both in equilibrium and non-equilibrium. We obtain an expression of the second- and the third-order optical conductivity in terms of correlation functions and present a perturbative proof of the generalized Kohn formula proposed recently. We also discuss a generalization of the f-sum rule to a non-equilibrium setting by focusing on the instantaneous response.

Comparative investigation of linear and nonlinear optical properties of As–70 at% Te thin films: influence of Ga content

Thin films (~ 150 nm) of amorphous As30Te70−xGax (where x = 0, 1, 3, 6, and 10 at%) are prepared through thermal evaporation of As30Te70−xGax bulk samples on glass substrates. X-ray powder diffraction (XRD) analysis reveals the amorphous nature of the as-prepared As30Te70−xGax thin films. The influence of Ga content on the As30Te70−xGax thin films’ linear and nonlinear optical properties is determined based on the optical reflectance and transmittance spectra. The estimated (direct or indirect) optical bandgap decreases with an increase in Ga content up to 3 at% and then increases, whereas the Urbach energy exhibits an opposite trend. The linear and nonlinear refractive indices, extension coefficient, optical conductivity, electrical conductivity and nonlinear susceptibility, optical density, inter-band transition strength, etc., are found to be significantly influenced by Ga content and the energy of incident waves. The As30Te67Ga3 composition can be considered as a puzzling compound as most of the investigated parameters in As30Te70−xGax alloys demonstrate opposite behaviors around that composition. Moreover, the optical surface resistance and thermal emission of As30Te70−xGax thin films are estimated from the investigated optical parameters and it was found that they are dependent on Ga content. The obtained results enhanced basic understanding and showed that the As–Te–Ga system qualifies for various optoelectronic applications.

Four-wave mixing in Weyl semimetals

Weyl semimetals (WSMs) have unusual optical response originated from unique topological properties of their bulk and surface electron states. Their third-order optical nonlinearity is expected to be very strong, especially at long wavelengths, due to linear dispersion and high Fermi velocity of three-dimensional Weyl fermions. Here we derive the third-order nonlinear optical conductivity of WSMs in the long-wavelength limit and calculate the intensity of the nonlinear four-wave mixing signal as it is transmitted through the WSM film or propagates away from the surface of the material in the reflection geometry. All results are analytic and show the scaling of the signal intensity with variation of all relevant parameters. The nonlinear generation efficiency turns out to be surprisingly high for a lossy material, of the order of several mW per W$^3$ of the incident pump power. Optimal conditions for maximizing the nonlinear signal are realized in the vicinity of bulk plasma resonance. This indicates that ultrathin WSM films of the order of skin depth in thickness could find applications in compact optoelectronic devices.

Determination and analysis of linear and nonlinear optical properties and electrical conductivity of amorphous PbxGe42−xSe48Te10 thin films

Thin films of amorphous PbxGe42−xSe48Te10 (6 ≤ x ≤ 18) have been synthesized by thermal evaporation method on glass substrate. From XRD analysis, it was found that films have an amorphous nature. Different constants (absorption coefficient, α, refractive index, n, extinction coefficient, k, optical energy band gap, Eg, real and imaginary parts of dielectric constants, er and ei, as well as energy band tail, Eu) depending on composition were determined by spectrophotometric measurements in wavelength range 200 ≤ λ ≤ 2500 nm. It is found that Eg1 and Eg2 increase with increasing Pb content, but Eu decreases with the increase in Pb content. By using Wemple–DiDomenico model, dispersion energy, Ed, energy of effective dispersion oscillator, Eo, dielectric constant at infinite wavelength, e∞, and first and third order of moments, (M−1) and (M−3), can be calculated. In addition, N/m* values increase with the increase in Pb concentration. Moreover, optical (σopt) and electrical (σele) conductivity can be derived from optical measurements. Electrical conductivity, σ, was investigated at room temperature. σ decreases with rising Pb concentration and then rises. Electrical properties can be discussed on the basis of Kolobov’s proposal of modulation in defect states with the addition of Pb.

Optical Kerr effect and third harmonic generation in topological Dirac/Weyl semimetal.

We study the nonlinear optical response generated by the massless Dirac quasiparticles residing around the topologically-protected Dirac/Weyl nodal points in three-dimensional (3D) topological semimetals. Analytical expressions of third-order interband nonlinear optical conductivities are obtained based on a quantum mechanical formalism which couples 3D Dirac fermions with multiple photons. Our results reveal that the massless Dirac fermions in three dimensions retains strong optical nonlinearity in terahertz frequency regime similar to the case of the two-dimensional Dirac fermions in graphene. At room temperature, the Kerr nonlinear refractive index and the harmonic generation susceptibility are found to be n2 = 10-11 ∼ 10-8 m2W-1 and χ(3) = 10-14 ∼ 10-8 m2V-2, respectively, in the few terahertz frequency regimes, which is comparable to graphene and orders of magnitudes stronger than many nonlinear crystals. Importantly, because 3D topological Dirac/Weyl semimetals possess bulk structural advantage not found in the strictly two-dimensional graphene, greater design flexibility and improved ease-of-fabrication in terms of photonic and optoelectronic device applications can be achieved. Our finding reveals the potential of 3D topological semimetals as a viable alternative to graphene for nonlinear optics applications.