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Optical conductivity of superconducting K 0.8 Fe 2 - y Se 2 single crystals: Evidence for a Josephson-coupled phase
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Determination of optical conductivity and different optical energy losses for non-crystalline Vanadyl tetra tert-butyl 2,3 Naphthalocyanine thinfilms
Amorphous Vanadyl Tetra Tert Butyl 2, 3 naphthalocyanine thin films (VTTBNc) have been deposited using Physical Vapor Deposition technique. By analyzing the X-ray diffraction, the structure of as deposited films is found to be non-crystalline. Different optical properties of these thin films have been investigated by means of optical absorption and reflection spectra. Various optical constants like band gap energy, E{sub g} the width of band tails of localized states into the gap, E{sub U} and steepness parameter, {beta} gets calculated and the variation of different optical parameters like refractive index, extinction coefficient, dielectric constants, optical conductivity and surface and volume energy losses with photon energy are estimated.
Contrasting pressure evolution of f -electron hybridized states in CeRhIn 5 and YbNi 3 Ga 9 : An optical conductivity study
Optical conductivity [σ(ω)] of CeRhIn 5 and YbNi 3 Ga 9 have been measured at external pressures to 10 GPa and at low temperatures to 6 K. Regarding CeRhIn 5 , at ambient pressure the main feature in σ(ω) is a Drude peak due to free carriers. With increasing pressure, however, a characteristic midinfrared (mIR) peak rapidly develops in σ(ω), and its peak energy and width increase with pressure. These features are consistent with an increased conduction (c)-f electron hybridization at high pressure and show that pressure has tuned the electronic state of CeRhIn 5 from very weakly to strongly hybridized ones. As for YbNi 3 Ga 9 , in contrast, a marked mIR peak is observed already at ambient pressure, indicating a strong c-f hybridization. At high pressures, however, the mIR peak shifts to lower energy and becomes diminished and seems to merge with the Drude component at 10 GPa. Namely, CeRhIn 5 and YbNi 3 Ga 9 exhibit some opposite tendencies in the pressure evolution of σ(ω) and electronic structure. Further, these results are discussed in terms of the pressure evolution of c-f hybridized electronic states in Ce and Yb compounds, in particular in terms of the electron-hole symmetry often considered between Ce and Yb.
Nonequilibrium optical conductivity: General theory and application to transient phases
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Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite
We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to expose the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field. We consider an experimental manifestation (optical conductivity) of a new state of matter (so-called fermion condensate) realized in quantum spin liquids, for, in many ways, they exhibit typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite produce important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of a strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to reveal the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field.
Power-law dependence of the optical conductivity observed in the quantum spin-liquid compound κ -(BEDT-TTF) 2 Cu 2 (CN) 3
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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.
An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance
This work presents an improved thin film approximation to extract the optical conductivity from infrared transmittance in a simple yet accurate way. This approximation takes into account the incoherent reflections from the backside of the substrate. These reflections are shown to have a significant effect on the extracted optical conductivity and hence on derived parameters as carrier mobility and density. By excluding the backside reflections, the error for these parameters for typical chemical vapor deposited (CVD) graphene on a silicon substrate can be as high as 17% and 45% for the carrier mobility and density, respectively. For the mid- and near-infrared, the approximation can be simplified such that the real part of the optical conductivity is extracted without the need for a parameterization of the optical conductivity. This direct extraction is shown for Fourier transform infrared (FTIR) transmittance measurements of CVD graphene on silicon in the photon energy range of 370–7000 cm{sup −1}. From the real part of the optical conductivity, the carrier density, mobility, and number of graphene layers are determined but also residue, originating from the graphene transfer, is detected. FTIR transmittance analyzed with the improved thin film approximation is shown to be a non-invasive, easy, and accurate measurement and analysis method for assessing the quality of graphene and can be used for other 2-D materials.
Strain effects on the optical conductivity of gapped graphene in the presence of Holstein phonons beyond the Dirac cone approximation
In this paper we study the optical conductivity and density of states (DOS) of doped gapped graphene beyond the Dirac cone approximation in the presence of electron-phonon (e-ph) interaction under strain, i.e., within the framework of a full π-band Holstein model, by using the Kubo linear response formalism that is established upon the retarded self-energy. A new peak in the optical conductivity for a large enough e-ph interaction strength is found which is associated to transitions between the midgap states and the Van Hove singularities of the main π-band. Optical conductivity decreases with strain and at large strains, the system has a zero optical conductivity at low energies due to optically inter-band excitations through the limit of zero doping. As a result, the Drude weight changes with e-ph interaction, temperature and strain. Consequently, DOS and optical conductivity remains stable with temperature at low e-ph coupling strengths.
Higgs oscillations in time-resolved optical conductivity
Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Nonequilibrium superconductors are often studied using time-resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven nonequilibrium state requires careful attention in the time domain. We calculate the time-resolved optical conductivity of a pumped superconducting state using a nonequilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full vertex corrections and used to characterize the transient superconducting state. The transient optical conductivity shows the suppression of the superconducting order parameter in the time domain. The subsequent recovery of the order parameter exhibits oscillatory behavior that corresponds to the Higgs amplitude mode, and may be seen in several parts of the spectrum.
Chemical pressure effect on the optical conductivity of the nodal-line semimetals ZrSi Y ( Y = S,Se,Te) and ZrGe Y ( Y = S,Te)
ZrSiS is a nodal-line semimetal, whose electronic band structure contains a diamond-shaped line of Dirac nodes. We carried out a comparative study on the optical conductivity of ZrSiS and the related compounds ZrSiSe, ZrSiTe, ZrGeS, and ZrGeTe by reflectivity measurements over a broad frequency range combined with density functional theory calculations. The optical conductivity exhibits a distinct U shape, ending at a sharp peak at around 10 000 cm –1 for all studied compounds except for ZrSiTe. The U shape of the optical conductivity is due to transitions between the linearly dispersing bands crossing each other along the nodal line. The sharp high-energy peak is related to transitions between almost parallel bands, and its energy position depends on the interlayer bonding correlated with the c/a ratio, which can be tuned by either chemical or external pressure. For ZrSiTe, another pair of crossing bands appears in the vicinity of the Fermi level, corrugating the nodal-line electronic structure and leading to the observed difference in optical conductivity. Here, the findings suggest that the Dirac physics in ZrXY compounds with X = Si,Ge and Y = S,Se,Te is closely connected to the interlayer bonding.
Current-enabled optical conductivity of superconductors
In most superconductors, optical excitations require impurity scattering or the presence of multiple bands. This is because in clean single-band superconductors, the combination of particle-hole and inversion symmetries prevents momentum-conserving transitions. In this Letter we show how the flow of supercurrent can lead to new contributions to optical conductivity. As the supercurrent breaks inversion symmetry, transitions across the superconducting gap become allowed even in clean superconductors and dominate over impurity-induced contributions for energies comparable to the gap width. Further, the response is dependent on the nature of the underlying normal state as well as on the type of superconducting order. Use of an external magnetic field to produce a screening supercurrent with controllable magnitude and direction, enables a detailed investigation of the superconducting state, allowing determination of the gap symmetry in unconventional superconductors for which other techniques have not been practicable.
Drude weight and optical conductivity of a two-dimensional heavy-hole gas with k-cubic spin-orbit interactions
We present a detailed theoretical study on zero-frequency Drude weight and optical conductivity of a two-dimensional heavy-hole gas (2DHG) with k-cubic Rashba and Dresselhaus spin-orbit interactions. The presence of k-cubic spin-orbit couplings strongly modifies the Drude weight in comparison to the electron gas with k-linear spin-orbit couplings. For large hole density and strong k-cubic spin-orbit couplings, the density dependence of Drude weight deviates from the linear behavior. We establish a relation between optical conductivity and the Berry connection. Unlike two-dimensional electron gas with k-linear spin-orbit couplings, we explicitly show that the optical conductivity does not vanish even for equal strength of the two spin-orbit couplings. We attribute this fact to the non-zero Berry phase for equal strength of k-cubic spin-orbit couplings. The least photon energy needed to set in the optical transition in hole gas is one order of magnitude smaller than that of electron gas. Types of two van Hove singularities appear in the optical spectrum are also discussed.
Interpretation of optical conductivity of zinc oxide nanowires
The frequency dependent optical response of Zinc Oxide (ZnO) nanowires is theoretically analyzed within the two component schemes: one is the motion of coherent Drude electrons within the ZnO nanowire and the other is incoherent motion of electrons from one nanowire to other. The model has only one free parameter, the relaxation rate. The frequency dependent relaxation rates are expressed in terms of memory functions. The coherent Drude carriers form a sharp peak at zero frequency and a long tail at higher frequencies, i.e. in the infrared region. However, the hopping of carriers from one nanowire to other (incoherent motion of electrons) yields a peak value in the optical conductivity around mid infrared region. It is found that both the Drude and hopping carriers will contribute to the optical process of conduction in ZnO nanowire.
Optical conductivity of multi-Weyl node semimetals due to electromagnetic and axial pseudogauge fields
Here, we compute the optical conductivity of a multi-Weyl semimetal in the presence of electromagnetic and axial fields. In the first part of the paper we use a U(1) gauge field to compute the current of a multi-Weyl semimetal. The current is used in the computation of the optical conductivity within the Kubo-Matsubara formalism. We consider a multi-Weyl semimetal with two nodal points in the z-direction. The multi-Weyl semimetal has a width D in the transverse direction which is smaller than the length L in the longitudinal direction. Due to the width D we replace the model by a sum of transverse modes in 1+1 dimensions. We then regularize the model in 1+1 dimensions. The nodal points are responsible for a constant axial field and a static anomalous Hall effect. In the second part we study the effect of dynamic axial fields. An elastic deformation couples to the two electronic chiralities, and represents the axial pseudogauge field $\vec{a}$ 5 . As a consequence, the system is excited by two kinds of field, the electromagnetic one and the axial srain field. For a Weyl system this is represented by the triangle diagram, which is responsible for the anomalous Hall effect. We can obtain the anomalous Hall effect also by a chiral transformation in 1+1 dimensions using regularization. The chiral transformation modifies the path integration measure and is the source of the induced anomalous Hall effect. The latter is controlled by a combination of strain waves and electromagnetic fields.
Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials
In the presence of an external magnetic field, the optical response of two-dimensional materials, whose charge carriers behave as massless Dirac fermions with arbitrary anisotropic Fermi velocity, is investigated. Using Kubo formalism, we obtain the magneto-optical conductivity tensor for these materials, which allows to address the magneto-optical response of anisotropic Dirac fermions from the well known magneto-optical conductivity of isotropic Dirac fermions. As an application, we analyse the combined effects of strain-induced anisotropy and magnetic field on the transmittance, as well as on the Faraday rotation, of linearly polarized light after passing strained graphene. The reported analytical expressions can be a useful tool to predict the absorption and the Faraday angle of strained graphene under magnetic field. Finally, our study is extended to anisotropic two-dimensional materials with Dirac fermions of arbitrary pseudospin. - Highlights: • The magneto-optical response of anisotropic massless Dirac fermions is investigated. • The conductivity tensor is obtained from the Kubo formula. • We study effects of strain and magnetic field on the light absorption of graphene. • The Faraday rotation in strained graphene is analytically determined.