Frequency Dependence Of Optical Conductivity Research Articles

Interband optical conductivity in electromagnetic field modulated strained black phosphorene

Black phosphorene (BP) has been widely investigated for its anisotropic and unique photoelectric properties. Strain, voltage and so on are commonly used to modulate the energy band structure and accordingly its photoelectric characteristics. In this study, we consider the energy band structure of BP in the vertical magnetic field, electric field, and in-plane/out-of-plane strains by using the tight-binding approximate Hamiltonian. The anisotropic frequency-dependent interband optical conductivity (IOC) of BP is investigated by using the Kubo formula in these modulation factors. Inherent asymmetry in band dispersion along the armchair (AC) direction and the zigzag (ZZ) direction leads to anisotropic IOC. The introduction of a vertical magnetic field induces band splitting, thereby generating multiple interband transition channels. In this case, the IOC along both the AC direction and the ZZ direction exhibits three peaks around the original peak position, and the magnitudes of the peaks are also modulated. With the increase of in-plane strain (from –20% to 20%), the band gap increases monotonically, and both the position and magnitude of the peaks vary with band gap changing. However, the band gap of BP undergoes a non-monotonic change under out-of-plane strain (from –20% to 20%), which is different from the change under in-plane strain. The band gap reaches a minimum value when a tensile strain of 12% is applied. Along the AC direction, the modulation of the IOC by in-plane strain is opposite to the modulation of out-of-plane strain (<i>ε</i><sub><i>z</i></sub> < 12%), indicating a competitive effect when triaxial strains are applied. Along the ZZ direction, in-plane strain primarily modulates the peak magnitude, while out-of-plane strain effectively modulates not only the peak position but also the peak magnitude obviously. The modulation of the IOC by forward and reverse electric fields are symmetrical. The coefficient for the peak position shift due to the vertical electric field is 1/2 in the AC direction and 1/10 in the ZZ direction. By integrating various modulation factors, we achieve versatile control over the energy band and IOC of BP, providing theoretical support for the application of BP in optoelectronic devices.

Transport Properties of Strongly Correlated Fermi Systems

Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high—Tc superconductors. Their transport properties are defined by strong inter-particle interactions, forming flat bands in these compounds. These properties do not coincide with those of conventional metals. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit linear temperature resistivity ρ(T)∝T. We analyze the magnetoresistance and show that under the application of the magnetic field, it becomes negative. It is shown that near a quantum phase transition, when the density of the electronic states diverges, semiclassical physics remains applicable to describe the resistivity ρ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when T exceeds the extremely low Debye temperature TD, the resistivity ρ(T) changes linearly with T since the mechanism of formation of the T-dependence ρ(T) is a similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of T-linear resistance, electron-phonon scattering leads to a lifetime of τ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant ℏ to the Boltzmann constant kB, Tτ∼ℏ/kB. We explain that due to the non-Fermi-liquid behavior, the real part of the frequency-dependent optical conductivity σoptR(ω) exhibits a scaling behavior and demonstrates the unusual power law behavior σoptR(ω)∝ω−1, rather than the well-known one shown by conventional metals, σoptR(ω)∝ω−2. All our theoretical considerations are illustrated and compared with the corresponding experimental facts. Our results are in a good agreement with experimental observations.

The effects of spin–orbit coupling on optical properties of electronic Lieb lattice in the presence of magnetic field

In this paper, the optical conductivity of a two-dimensional Lieb lattice that is a line-centered square lattice is investigated in the presence of magnetic field and spin–orbit coupling. Specially, we address the frequency dependence of optical conductivity due to spin–orbit interaction. Using Green’s function approach, the behavior of optical conductivity has been obtained in the context of Kane–Mele model Hamiltonian. In the presence of magnetic field at low spin–orbit coupling strength, optical conductivity includes only Drude weight at zero frequency limit while interband transitions of electrons have no contribution to optical conductivity for each gap parameter below normalized value 0.6. However the increase of spin–orbit coupling strength causes to appear finite frequency peak in optical conductivity. Moreover our results show that optical conductivity increases with temperature for each value of spin–orbit coupling and magnetic field. Also we have studied the effects of magnetic field, electron doping and spin–orbit coupling on temperature dependence of optical conductivity of Lieb monolayer.

Stability, electronic, optical and thermoelectric properties of site-substituted [formula omitted

To unravel the structural and chemical stability, electronic, transport, and optical properties of pristine and site substituted lanthanum vanadate, LaVO3, we employed the density functional theory (DFT) and the dynamical mean field theory (DMFT). The generalized gradient approximation (GGA) and the DMFT with continuous time quantum Monte Carlo (CT-QMC) approach is used for the impurity solver. The variation of the spectral density are studied with different values of the onsite Coulomb interaction (U) and exchange interaction (J), as well as the thermodynamic parameter (β), to investigate the metal insulator transition (MIT) for these materials, which are useful for designing Mottronics, neuromorphic computing devices. The predicted values of U and β for the Mott–Hubbard MIT in La0.40Ca0.60V O3 are consistent with current experimental data. The studied sample’s a characteristic sharp quasi-particle peak is found to be at U = 5 eV and β = 6 (eV)−1. The Mott quantum critical point (QCP) is also computed for an elevated temperatures and it is found at U = 2.95 eV and β = 23.58 (eV)−1. With U = 5.0 eV, β = 10.0 (eV)−1, the clear Mott gaps for La0.40Ca0.60V O3 and La0.60Ca0.40V O3 are estimated as 0.74 eV and 1.64 eV, respectively. The electrical and thermal conductivities are calculated at room temperature using the BoltzTraP code, and they are found to be 2.11 (Ωms)−1 and 1.51 W/(mKs), respectively, for a given chemical potential μ = −0.14 eV of the system. The figure of merit (ZT) is estimated to be 1.78 at μ = −1.44 eV. Larger values of the Seebeck coefficient (S), ZT, and thermoelectric power factor (TPF) indicate that La0.40Ca0.60V O3 system is a good candidate of thermoelectric material. The calculated frequency dependent optical conductivity (Drude weight) on the dependency of U and β for the metal insulator transition supports the other calculations.

First-principles approach to the structural, physical, electronic, magnetic and optical properties of honeycomb ordered antimonates Na3Fe2SbO6

The search for new magnetic materials, electrochemical sensors and storage devices has ignited the study of layered honeycomb oxides in the past few years. We have performed a first-principles density functional theory (DFT) based investigation on the structural, elastic and associated thermophysical, mechanical, electronic, and optical properties of Na3Fe2SbO6 honeycomb ordered antimonates. The obtained lattice parameters as well as volume of the geometrically optimized structure were consistent with the available experimental data in the circumstance of ferromagnetic ordering. A comprehensive study of elastic constants implies a low to intermediate level of structure anisotropy, good machinability, mechanically brittle and hard. A large Debye temperature of 442.567 K and melting temperature of 2061.88 ± 300K implies high temperature application. The density of states suggests that the compound possesses a metallic character with a high magnetic moment. Furthermore, Na3Fe2SbO6 possesses excellent absorption characteristics in the spectral range in ultraviolet regions. It has low reflectivity and a high refractive index in the visible range of photon energy, and the plasmon peak found at 17.65 eV. The frequency-dependent optical conductivity confirms a metallic feature and agrees with the electronic density of states observations.

The effects of spin-orbit coupling on optical properties of monolayer text {MoS}_{2} due to mechanical strains

We have studied the optical conductivity of a quasi two-dimensional text {MoS}_{2} in the presence of external magnetic field and spin-orbit coupling. Specially, we address the frequency dependence of optical conductivity due to spin-orbit interaction. Using linear response theory the behavior of optical conductivity has been obtained within Green’s function method. We have also considered the effects of uniaxial and biaxial in-plane strain on the optical absorption of text {MoS}_{2} layer. In the absence of external magnetic field with negative uniaxial strain parameter, optical conductivity includes Drude weight at zero frequency limit while Drude weight vanishes for text {MoS}_{2} layer under positive uniaxial strain. Our results show that the increase of uniaxial positive strain parameter causes to move the position peak to the higher frequencies. In contrast to uniaxial strain case, the Drude weight in optical conductivity appears at positive biaxial strain value 0.15. Also we have studied the effects of magnetic field, electron doping, hole doping in the presence of spin-orbit coupling on frequency dependence of optical conductivity of text {MoS}_{2} in details. The magnetic field dependence of optical absorption shows a monotonic decreasing behavior for each value of temperature in the absence of strain parameter.

Size effect on optical conductivity of Bi2Te3 nanoparticles due to softening of phonon frequencies

The frequency-dependent optical conductivity σ(w) strongly depends on the particle size in nanostructures. Phonon frequencies are believed to be decrease on a decrease in particle size due to the softening of phonon frequencies around grain boundaries in nanomaterials. The optical conductivity of Bi2Te3 nanoparticles is studied using the two components model: First is the coherent motion of Drude electrons within the Bi2Te3 nanoparticles, and second is the incoherent hopping of charge carriers from one Bi2Te3 nanoparticle to another. The model has the phonon frequency and relaxation rates as the independent free parameters, which depend on nanoparticle size. The relaxation rates that are a function of frequency are incorporated in optical conductivity through memory functions. The coherent motion of Drude carriers exhibited a peak in intensity near zero frequency regime and decreased to a minimum value in the far-infrared region. The incoherent hopping of electrons from one Bi2Te3 nanoparticle to another produces a broad peak in the frequency-dependent optical conductivity at around the mid-infrared region. On decreases in nanoparticle size, softening of phonon frequencies occurs at interfaces due to an increase in interface volume ratio; as a result, the peak in optical conductivity at the mid-infrared region shifts towards lower frequencies.

Effects of spin-orbit coupling and magnetic field on electronic properties of Germanene structure

In this paper, we present a Kane-Mele model in the presence of magnetic field and next nearest neighbors hopping amplitudes for investigations the electronic and optical properties of monolayer Germanene. Specially, we address the dynamical conductivity of the structure as a function of photon frequency and in the presence of magnetic field and spin-orbit coupling at finite temperature. Using linear response theory and Green’s function approach, the frequency dependence of optical conductivity has been obtained in the context of Kane-Mele model Hamiltonian. Our results show a finite Drude response at low frequency at non zero value for magnetic field in the presence of spin-orbit coupling. However Drude weight gets remarkable amount in the presence of electron doping. The thermal conductivity and specific heat increase with increasing the temperature at low amounts of temperature due to the increasing of thermal energy of charge carriers and excitation of them to the conduction bands. The results for Seebeck coefficient show the sign of thermopower is negative in the presence of spin-orbit coupling. Also we have studied the temperature dependence of electrical conductivity of Germanene monolayer due to both spin orbit coupling and magnetic field factors in details.

Optical properties of biased bilayer graphene due to gap parameter effects

We address the optical conductivity of undoped bilayer graphene in the presence of a finite bias voltage at finite temperature. The effects of gap parameter and stacking type on optical conductivity are discussed in the context of tight binding model Hamiltonian. Green’s function approach has been implemented to find the behavior of optical conductivity of bilayer graphene within linear response theory. We have found the frequency dependence of optical conductivity for different values of gap parameter and bias voltage. Also the dependence of optical conductivity on the temperature has been investigated in details. A peak appears in the plot of optical conductivity versus frequency for different values of temperatures and bias voltage. Furthermore we find the frequency position of broad peak in optical conductivity goes to higher values with increase of gap parameter for both bernal and simple stacked bilayer graphenes.

Unfolding optical transition weights of impurity materials for first-principles LCAO electronic structure calculations

A method to analyze optical transitions is developed by combining the Kubo-Greenwood formula with the unfolding method to construct an unfolded electronic band structure with optical transition weights, which allows us to investigate how optical transitions are perturbed by imperfections such as impurity, vacancy, and structural distortions. Based on the Kubo-Greenwood formula, we first calculate frequency-dependent optical conductivity based on the first-principles electronic structure calculations using the linear combinations of atomic orbitals. Benefiting from the atomic orbital basis sets, the frequency-dependent optical conductivity can be traced back to their individual components before summations over all of $k$ points and bands. As a result, optical transition weights of the material can be put on the unfolded electronic band structure to show contributions at different $k$ points and bands. This method is especially useful to study the effects of broken symmetry in the optical transitions due to presence of impurities in the materials. As a demonstration, decomposed optical transition weights of a monolayer Si-doped graphene are shown in the electronic band structure.

Blue shift in the interband optical transitions of gated monolayer black phosphorus

The anisotropic frequency-dependent optical conductivity of single-layer puckered phosphorene is studied, and also its dependence on the electrostatic gating of the top and bottom sublayers. The effective Hamiltonian within the k→⋅p→ approximation is used to obtain the electronic band structure from which the interband optical transitions are evaluated using the Kubo formula. Inherent asymmetry in the dispersion energy of carriers along the armchair and zigzag edges gives rise to anisotropic optical features. The bandgap increases with gate voltage resulting in absorption at higher optical energies along the armchair edge, which is the so-called blue shift, while along the zigzag edge such a shift is not significant. The temperature and exciton effects on the interband response are concisely discussed. These results provide new insights which render phosphorene attractive for optoelectronic devices.

Quantum-critical conductivity of the Dirac fluid in graphene.

Graphene near charge neutrality is expected to behave like a quantum-critical, relativistic plasma-the "Dirac fluid"-in which massless electrons and holes collide at a rapid rate. We used on-chip terahertz spectroscopy to measure the frequency-dependent optical conductivity of clean, micrometer-scale graphene at electron temperatures between 77 and 300 kelvin. At charge neutrality, we observed the quantum-critical scattering rate characteristic of the Dirac fluid. At higher doping, we detected two distinct current-carrying modes with zero and nonzero total momenta, a manifestation of relativistic hydrodynamics. Our work reveals the quantum criticality and unusual dynamic excitations near charge neutrality in graphene.

Temperature-Driven Topological Phase Transition and Intermediate Dirac Semimetal Phase in ZrTe_{5}.

We present an infrared spectroscopy study of ZrTe_{5}, which confirms a recent theoretical proposal that this material exhibits a temperature-driven topological quantum phase transition from a weak to a strong topological insulating state with an intermediate Dirac semimetal state around T_{p}≃138 K. Our study details the temperature evolution of the energy gap in the bulk electronic structure. We found that the energy gap closes around T_{p}, where the optical response exhibits characteristic signatures of a Dirac semimetal state, i.e., a linear frequency-dependent optical conductivity extrapolating to the origin (after subtracting a weak Drude response). This finding allows us to reconcile previous diverging reports about the topological nature of ZrTe_{5} in terms of a variation of T_{p} that depends on the crystal growth condition.

Magnetic Field Effects on Optical Conductivity of Doped Armchair Graphene Nanoribbon

We address the optical conductivity of armchair graphene nanoribbon within tight-binding model Hamiltonian using Green’s function approach. The possible effects of ribbon width, magnetic field, and chemical potential on optical absorption are investigated. We have also found the dependence of the optical conductivity for various ribbon widths and chemical potentials. Our results show a peak appears in the frequency dependence of optical conductivity of graphene nanoribbon. Upon increasing ribbon width, the height of the optical conductivity at frequency of peak increases. Also, applying the magnetic field causes an increase of the optical conductivity. However, upon more increase of the magnetic field leads to a decrease of the optical conductivity. Moreover, we study the effects of chemical potentials on frequency behavior of optical absorption of graphene nanoribbon for both metallic and insulator cases.

Shifting in optoelectronic properties from pure K2O and Rb2O compounds to their V- and Cr-doped alloys

First principle calculations within the density functional theory (DFT) have been used in this approach to study the electronic and optical properties of vanadium (V) and chromium (Cr) doped K2O and Rb2O compounds. Based on the structure properties reported in our previous work, the study of electronic and optoelectronic properties of V- and Cr-doped K2O and Rb2O alloys have been vastly investigated. K2O and Rb2O are found to be semiconductors while their V- and Cr-alloys are metallic in nature. The optical functions like complex dielectric constant, complex index of refraction, absorption coefficient, and reflectivity of these alloys are computed and compared with those of pure K2O and Rb2O compounds. It has been shown that due to TM-doping (TM = V and Cr transition metals), many distinguished peaks appeared in the lower energy part (infrared) of the spectrum. The negative value of [Formula: see text] ([Formula: see text]) in this energy range confirmed the metallic behavior of these alloys. Furthermore, the frequency-dependent optical conductivity is also predicted in the entire spectrum, where it increases with increasing photon energy for all the studied alloys. The significant results of [Formula: see text] ([Formula: see text]) predict that all these compounds are useful in different optoelectronic applications in a wide part of the spectrum (between 13 eV and 27 eV).

Electronic structure and optical properties of GdNi2Mnx compounds

The electronic structure and optical properties of GdNi2Mnx compounds (x = 0, 0.4, 0.6) were investigated. Spin-polarized electronic structure calculations were performed in the approximation of local electron spin density corrected for strong electron correlations using the LSDA+U method. The changes in the magnetic moments and exchange interactions in GdNi2Mnx (x = 0, 0.4, 0.6) governing the increase in the Curie temperature with manganese concentration were determined. The optical constants of the compounds were measured by the ellipsometric method in the wide spectral range of 0.22–15 μm. The peculiarities of the evolution of the frequency dependences of optical conductivity with a change in the manganese content were revealed. Based on the calculated densities of electron states, the behavior of these dispersion curves in the region of interband absorption of light was discussed. The concentration dependences of several electronic characteristics were determined.

Spectral properties of RuAl2 and RuGa2 compounds: Ellipsometric analysis

The optical properties of RuAl2 and RuGa2 intermetallic compounds have been investigated in the spectral range of 0.22–14 μm. The nature of interband light absorption has been interpreted based on a comparative analysis of calculated and experimental frequency dependences of optical conductivity. The data obtained confirm the existence of pseudogaps with a width of ~0.8 eV localized at the Fermi level in the electron densities of states of these materials, which was predicted in previous energy-band calculations.

Specific features of the electronic structure and spectral characteristics of the Gd5Si3 compound

The electronic structure and optical properties of the hexagonal intermetallic compound Gd5Si3 are investigated. The spin-polarization calculation of the band spectrum is performed in the local spin density approximation, taking account for the strong electron correlations in the 4 f shell of a Gd ion (LSDA + U method). Optical constants of the compound in the wavelength range of 0.22–15 μm are determined by the ellipsometry technique and some spectral characteristics are calculated. The frequency dependence of optical conductivity in the light quantum absorption region is analyzed on the basis of the calculated electron density of states.

Frequency dependent optical conductivity of strained graphene at T=0 from an effective quantum field theory

An effective quantum field theory (EQFT) graphene sheet with arbitrary one dimensional strain field is derived from a microscopic effective low energy Hamiltonian. The geometric meaning of the strain-induced complex gauge field is clarified. The optical conductivity is also investigated, and a frequency dependent optical conductivity is obtained. The actual value of interband optical conductivity along the deformed direction is C0+C1ω2 in spite of the particular strain fields at T=0.

Dispersion of electromagnetic waves in layered graphene-dielectric metamaterials

 In this paper possibility of creating a medium based on graphene-dielectric (quartz) structures with a hyperbolic shape of the dispersion relation is considered. Using the Bloch theorem and the transfer matrix method, dispersion relations are found for hyperbolic media, consisting of periodically located layers of graphene and a dielectric. The transfer matrix method gives the possibility to relate the amplitudes of the incident and reflected electromagnetic waves at the input to the layered structure with the amplitudes at the output by means of propagation and transfer matrixes. The frequency dependent optical conductivity of graphene sheet is calculated by Kubo formula which takes into account both interband and intraband transitions. It is shown that when the chemical potential of graphene is increased, the elliptic form of the dispersion curve turns into to hyperbolic. This result is due to the fact that the perpendicular component of the permittivity changes its sign when the chemical potential is changed.