Quantum field theory approach to the optical conductivity of strained and deformed graphene

The computation of the optical conductivity of strained and deformed graphene is discussed within the framework of quantum field theory in curved spaces. The analytical solutions of the Dirac equation in an arbitrary static background geometry for one dimensional periodic deformations are computed, together with the corresponding Dirac propagator. Analytical expressions are given for the optical conductivity of strained and deformed graphene associated with both intra and interbrand transitions. The special case of small deformations is discussed and the result compared to the prediction of the tight-binding model.

Calculation of the optical conductivity for the Anderson impurity model using the slave boson technique

The optical conductivity of the Anderson impurity mode l has been calculated by emp l oying the slave boson technique and an expansion in powers of l i N, where N is the d egeneracy o f the f electron level . This method has been used to find the effective mass of the conduction electrons for temperatures above and below the Kondo tempera ture. For low temperatures, the mass enhancement is f ound to be large while a t high t emperatures, the mass enhancement is sma ll. The conductivity i s f ound to be Drude like with frequency dependent effective mass and scattering time for low independent effective mass and temperatures and scattering time f requency for high t emperatures. The behavior of both the effective mass and the conductivity is in qualitative agreement with experimental r esul t s .

Electronic structure and optical signatures of semiconducting transition metal dichalcogenide nanosheets

CONSPECTUS: Two-dimensional (2D) crystals derived from transition metal dichalcogenides (TMDs) are intriguing materials that offer a unique platform to study fundamental physical phenomena as well as to explore development of novel devices. Semiconducting group 6 TMDs such as MoS2 and WSe2 are known for their large optical absorption coefficient and their potential for high efficiency photovoltaics and photodetectors. Monolayer sheets of these compounds are flexible, stretchable, and soft semiconductors with a direct band gap in contrast to their well-known bulk crystals that are rigid and hard indirect gap semiconductors. Recent intense research has been motivated by the distinct electrical, optical, and mechanical properties of these TMD crystals in the ultimate thickness regime. As a semiconductor with a band gap in the visible to near-IR frequencies, these 2D MX2 materials (M = Mo, W; X = S, Se) exhibit distinct excitonic absorption and emission features. In this Account, we discuss how optical spectroscopy of these materials allows investigation of their electronic properties and the relaxation dynamics of excitons. We first discuss the basic electronic structure of 2D TMDs highlighting the key features of the dispersion relation. With the help of theoretical calculations, we further discuss how photoluminescence energy of direct and indirect excitons provide a guide to understanding the evolution of the electronic structure as a function of the number of layers. We also highlight the behavior of the two competing conduction valleys and their role in the optical processes. Intercalation of group 6 TMDs by alkali metals results in the structural phase transformation with corresponding semiconductor-to-metal transition. Monolayer TMDs obtained by intercalation-assisted exfoliation retains the metastable metallic phase. Mild annealing, however, destabilizes the metastable phase and gradually restores the original semiconducting phase. Interestingly, the semiconducting 2H phase, metallic 1T phase, and a charge-density-wave-like 1T' phase can coexist within a single crystalline monolayer sheet. We further discuss the electronic properties of the restacked films of chemically exfoliated MoS2. Finally, we focus on the strong optical absorption and related exciton relaxation in monolayer and bilayer MX2. Monolayer MX2 absorbs as much as 30% of incident photons in the blue region of the visible light despite being atomically thin. This giant absorption is attributed to nesting of the conduction and valence bands, which leads to diversion of optical conductivity. We describe how the relaxation pathway of excitons depends strongly on the excitation energy. Excitation at the band nesting region is of unique significance because it leads to relaxation of electrons and holes with opposite momentum and spontaneous formation of indirect excitons.

Optical response of Cu3Ge thin films

We report an investigation on the optical properties of Cu3Ge thin films displaying very high conductivity, with thickness ranging from 200 to 2000 Å, deposited on Ge substrates. Reflectance, transmittance, and ellipsometric spectroscopy measurements were performed at room temperature in the 0.01-6.0, 0.01-0.6, and 1.4-5.0 eV energy range, respectively. The complex dielectric function, the optical conductivity, the energy-loss function, and the effective charge density were obtained over the whole spectral range. The low-energy free-carrier response was well fitted by using the classical Drude-Lorentz dielectric function. A simple two-band model allowed the resulting optical parameters to be interpreted coherently with those previously obtained from transport measurements, hence yielding the densities and the effective masses of electrons and holes.

Optical evidence for the proximity to a spin-density-wave metallic state in Na0.7CoO2

We present the optical properties of Na0.7CoO2 single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate (Gamma) and effective mass (m*) of the itinerant charge carriers. We find that Gamma(omega) at low temperatures and for similar to omega. This suggests that Na0.7CoO2 is at the verge of a spin-density-wave metallic phase.

Far infrared reflectance and optical properties of organic superconductor (TMTSF)2ClO4 /

Polarized reflectance measurements of the quasi I-D charge-transfer salt (TMTSFh CI04 were carried out using a Martin-Puplett-type polarizing interferometer and a 3He refrigerator cryostat, at several temperatures between 0.45 K and 26 K, in the far infrared, in the 10 to 70 cm- 1 frequency range. Bis-tetramethyl-tetraselena-fulvalene perchlorate crystals, grown electrochemically and supplied by K. Behnia, of dimensions 2 to 4 by 0.4 by 0.2 mm, were assembled on a flat surface to form a mosaic of 1.5 by 3 mm. The needle shaped crystals were positioned parallel to each other along their long axis, which is the stacking direction of the planar TMTSF cations, exposing the ab plane face (parallel to which the sheets of CI04 anions are positioned). Reflectance measurements were performed with radiation polarized along the stacking direction in the sample. Measurements were carried out following either a fast (15-20 K per minute) or slow (0.1 K per minute) cooling of the sample. Slow cooling permits the anions to order near 24 K, and the sample is expected to be superconducting below 1.2 K, while fast cooling yields an insulating state at low temperatures. Upon the slow cooling the reflectance shows dependence with temperature and exhibits the 28 cm- 1 feature reported previously [1]. Thermoreflectance for both the 'slow' and 'fast' cooling of the sample calculated relative to the 26 K reflectance data indicates that the reflectance is temperature dependent, for the slow cooling case only. A low frequency edge in the absolute reflectance is assigned an electronic origin given its strong temperature dependence in the relaxed state. We attribute the peak in the absolute reflectance near 30 cm-1 to a phonon coupled to the electronic background. Both the low frequency edge and the 30 cm-1 feature are noted te shift towards higher frequcncy, upon cntering the superconducting state, by an amount of the order of the expected superconducting energy gap. Kramers-Kronig analysis was carried out to determine the optical conductivity for the slowly cooled sample from the measured reflectance. In order to do so the low frequency data was extrapolated to zero frequency using a Hagen-Ru bens behaviour, and the high frequency data was extended with the data of Cao et al. [2], and Kikuchi et al. [3]. The real part of the optical conductivity exhibits an asymmetric peak at 35 cm-1, and its background at lower frequencies seems to be losing spectral weight with lowering of the temperature, leading us to presume that a narrow peak is forming at even lower frequencies.

The infared optical properties of Sr2RuO4 and SmTiO3 including an object-oriented resistivity interface /

The perovskite crystal structure is host to many different materials from insulating to superconducting providing a diverse range of intrinsic character and complexity. A better fundamental description of these materials in terms of their electronic, optical and magnetic properties undoubtedly precedes an effective realization of their application potential. SmTiOa, a distorted perovskite has a strongly localized electronic structure and undergoes an antiferromagnetic transition at 50 K in its nominally stoichiometric form. Sr2Ru04 is a layered perovskite superconductor (ie. Tc % 1 K) bearing the same structure as the high-tem|>erature superconductor La2_xSrrCu04. Polarized reflectance measurements were carried out on both of these materials revealing several interesting features in the far-infrared range of the spectrum. In the case of SmTiOa, although insulating, evidence indicates the presence of a finite background optical conductivity. As the temperature is lowered through the ordering temperature a resonance feature appears to narrow and strengthen near 120 cm~^ A nearby phonon mode appears to also couple to this magnetic transition as revealed by a growing asymmetry in the optica] conductivity. Experiments on a doped sample with a greater itinerant character and lower Neel temperature = 40 K also indicate the presence of this strongly temperature dependent mode even at twice the ordering temperature. Although the mode appears to be sensitive to the magnetic transition it is unclear whether a magnon assignment is appropriate. At very least, evidence suggests an interesting interaction between magnetic and electronic excitations. Although Sr2Ru04 is highly anisotropic it is metallic in three-dimensions at low temperatures and reveals its coherent transport in an inter-plane Drude-like component to the highest temperatures measured (ie. 90 K). An extended Drude analysis is used to probe the frequency dependent scattering character revealing a peak in both the mass enhancement and scattering rate near 80 cm~* and 100 cm~* respectively. All of these experimental observations appear relatively consistent with a Fermi-liquid picture of charge transport. To supplement the optical measurements a resistivity station was set up with an event driven object oriented user interface. The program controls a Keithley Current Source, HP Nano-Voltmeter and Switching Unit as well as a LakeShore Temperature Controller in order to obtain a plot of the Resistivity as a function of temperature. The system allows for resistivity measurements ranging from 4 K to 290 K using an external probe or between 0.4 K to 295 K using a Helium - 3 Cryostat. Several materials of known resistivity have confirmed the system to be robust and capable of measuring metallic samples distinguishing features of several fiQ-cm.

Optical properties of organic superconductor K-(BETS)2FeBr4 /

/c-(BETS)2FeBr4 is the first antiferromagnetic organic superconductor with successive antiferromagnetic and superconducting transitions at Ta^=2.5K and Tc=l.lK respectively at ambient pressure. Polarized reflectance measurements were performed on three single crystalsamples of this material using a Briiker IFS66V/S Interferometer, and a Bolometer detector or an MCT detector, at seven temperatures between 4K and 300K, in both the far-infrared and mid-infrared frequency range. After the reflectance results were obtained, the Kramers-Kronig dispersion relation was apphed to determine the optical conductivity of /c-(BETS)2FeBr4 at these seven temperatures. Additionally, the optical conductivity spectra were fitted with a Drude/Lorentz Oscillator model in order to study the evolution of the optical conductivity with temperature along the a-axis and c-axis. The resistivities calculated from the Drude model parameters along the a-axis and c-axis agreed reasonably with previous transport measurements.

Far infrared optical properties of V and Cr doped Sb2Te3 /

The far infrared reflectance of Sb2Te3 , Sbi.97Vo.o3Te3 and Sbi.94Cr .o6Te3 was measured near normal incidence at different temperatures (between 45K and 300K). The direct current resistivities of the above samples were also measured between the temperatures of 4K and 300K. Also Kramers Kronig (KK) analyses were performed on the reflectance spectra to obtain the optical conductivities. In the doped samples, it was observed that a phonon at 62cm-1 softens to about 55cm-1 on decreasing the temperature from 295K to 45K. Also, it was observed that the plasma frequency of the doped samples is independent of doping. The scattering rate for the vanadium doped sample was seen to be greater than that for the chromium doped sample despite the fact that vanadium impurity density is less than that of chromium. The Drude-Lorentz model fits to the KK optical conductivity show that the samples used in this work are conventional metals. Definitive measurements of the temperature dependence of the scattering rate across the ferromagnetic transition await equipment changes allowing measurements at low temperature using the mercury cadmium telluride (MCT) detector.

Crystal growth, Raman scattering and optical properties of the superconductor Cd2Re2O7(16O, 18O)/

Using the Physical Vapor Transport method, single crystals of Cd2Re207 have been grown, and crystals of dimensions up to 8x6x2 mm have been achieved. X-ray diffraction from a single crystal of Cd2Re207 has showed the crystal growth in the (111) plane. Powder X-ray diffraction measurements were performed on ^^O and ^^O samples, however no difference was observed. Assigning the space group Fd3m to Cd2Re207 at room temperature and using structure factor analysis, the powder X-ray diffraction pattern of the sample was explained through systematic reflection absences. The temperatiure dependence of the resistivity measurement of ^^O has revealed two structural phase transitions at 120 and 200 K, and the superconducting transition at 1.0 K. Using Factor Group Analysis on three different structiures of Cd2Re207, the number of IR and Raman active phonon modes close to the Brillouin zone centre have been determined and the results have been compared to the temperature-dependence of the Raman shifts of ^^O and ^*0 samples. After scaling (via removing Bose-Einstein and Rayleigh scattering factors from the scattered light) all spectra, each spectrum was fitted with a number of Lorentzian peaks. The temperature-dependence of the FWHM and Raman shift of mode Eg, shows the effects of the two structurjil phase transitions above Tc. The absolute reflectance of Cd2Re207 - '^O single crystals in the far-infrared spectral region (7-700 cm~^) has been measured in the superconducting state (0.5 K), right above the superconducting state (1.5 K), and in the normal state (4.2 K). Thermal reflectance of the sample at 0.5 K and 1.5 K indicates a strong absorption feature close to 10 cm~^ in the superconducting state with a reference temperature of 4.2 K. By means of Kramers-Kronig analysis, the absolute reflectance was used to calculate the optical conductivity and dielectric function. The real part of optical conductivity shows five distinct active phonon modes at 44, 200, 300, 375, and 575 cm~' at all temperatures including a Drude-like behavior at low frequencies. The imaginary part of the calculated dielectric function indicates a mode softening of the mode 44 cm~' below Tc.

Far-infrared optical properties of the heavy fermion superconductor UB[E13]

Temperature dependent resistivity, p, magnetic susceptibility, X, and far-infrared reflectance measurements were made on the low Tc superconductor UBe13. Two variants of UBe13 have been proposed, named 'L'- (for low Tc ) and 'H'-type (for high Tc ). Low temperature resistivity measurements confirmed that our sample was of H-type and that the transition temperature was at 0.9 K. This was further confirmed with the observation of this transition in the AC-susceptibility. Low temperature reflectance measurements showed a decrease in the reflectivity as the temperature is lowered from 300 to 10 K, which is in qualitative agreement with the increasing resistivity in this temperature range as temperature is lowered. No dramatic change in the reflectivity was observed between 10 and 0.75 K. A further decrease of the reflectance was observed for the temperature of 0.5 K. The calculated optical conductivity shows a broad minimum near 80 cm-1 below 45 K. Above 45 K the conductivity is relatively featureless. As the temperature is lowered, the optical conductivity decreases. The frequency dependent scattering rate was found to be flat for temperatures between 300 and 45 K. The development of a peak, at around 70 cm-1 was found for temperatures of 45 K and below. This peak has been associated with the energy at which the transition to a coherent state occurs from single impurity scattering in other heavy fermion systems. The frequency dependent mass enhancement coefficient was found to increase at low frequencies as the frequency decreases. Its' magnitude as frequency approaches zero also increased as the temperature decreased.

Set-up and evaluation of a mid-infrared reflectometer and investigation of the optical properties of doped tin telluride

A system comprised of a Bomem interferometer and a LT3-110 Heli-Tran cryostat was set up to measure the reflectance of materials in the mid-infrared spectral region. Several tests were conducted to ensure the consistency and reliability of the system. Silicon and Chromium, two materials with well known optical properties were measured to test the accuracy of the system, and the results were found to be in good agreement with the literature. Reflectance measurements on pure SnTe and several Pb and Mn-doped alloys were carried out. These materials were chosen because they exhibit a strong plasma edge in the mid infrared region. The optical conductivity and several related optical parameters were calculated from the measured reflectance. Very low temperature measurements were carried out in the far-infrared on Sn9SMn2Te, and the results are indicative of a spin glass phase at 0.8 K. Resistivity measurements were made at room temperature. The resistivity values were found, as expected, to decrease with increasing carrier concentration and to increase with increasing manganese concentration.

Optical Properties of Sb2Te3, and Dilute Magnetic Semiconductors Sb1.97 VO.03 Te3 and Sb1.94 CrO.06 Te3

This thesis reports on the optical properties of the dilute magnetic semiconductors, Sb1.97 V 0.03 Te3 and Sb1.94Cr0.06Te3, along with the parent compound Sb2Te3' These materials develop a ferromagnetic state at low temperature with Curie temperatures of 22 K and 16 K respectively. All three samples were oriented such that the electric field vector of the light was perpendicular to the c-axis. The reflectance profile of these samples in the mid-infrared (500 to 3000 cm-1) shows a pronounced plasma edge which retracts with decreasing temperature. The far-infrared region of these samples exhibits a phonon at ~ 60 cm-1 which softens as temperature decreases. Kramers-Kronig analysis and a Drude-Lorentz model were employed to determine the optical constants of the bulk samples. The real part of the optical conductivity is shown to consist of intraband contributions at frequencies below the energy gap (~0.26 eV) and interband contributions at frequencies above the energy gap. The temperature dependence of the scattering rate show that a mix of phonon and impurity scattering are present, while the signature of traditional spin disorder (magnetic) scattering was difficult to confirm.

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling

We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the theta and beta crystal structures.