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The anisotropic optical absorption edge of $\beta$-Ga$_2$O$_3$ follows a modified Beer-Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in $\beta$-Ga$_2$O$_3$, which arises from the anisotropy and spectral splitting of the physical absorbers i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of $\beta$-Ga$_2$O$_3$. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer-Lambert law arises from the interplay of both the dichroic and birefringent properties of $\beta$-Ga$_2$O$_3$., Comment: 11 pages, 5 figures

In this work we derive the state of strain or stress under symmetry conserving conditions in pseudomorphic lattices with monoclinic symmetry. We compare surface vectors across the template epitaxial layer interface and impose conditions of a stress free epitaxial layer. As a result, we demonstrate the existence, in theory, of exactly three possible unit cells which can establish onto a given template. We demonstrate this approach for a class of templates with $(h0l)$ planes and $\beta$-(Al$_x$Ga$_{1-x}$)$_2$O$_3$ on $(h0l)$ $\beta$-Ga$_2$O$_3$. We discuss the effects of composition $x$ and surface orientation onto the formation of three elastically stable unit cells, their strain and stress tensors, unit cell axes, unit cell volumes, lattice spacing, elastic potential energies, and stress free directions. The previous paradigm for epitaxial layer growth where the stress free direction is always perpendicular to the growing surface is not generally valid for low symmetry materials. In the example here, we find two possible competing domains with stress free direction oblique to the surface of the template for almost all planes $(h0l)$. We calculate the band-to-band transitions for $\beta$-(Al$_{0.1}$Ga$_{0.9}$)$_2$O$_3$ on $(h0l)$ $\beta$-Ga$_2$O$_3$ using the composition dependent deformation parameters and elastic coefficients reported prevoiously [Korlacki~\textit{et al.} Phys. Rev. Appl.~\textbf{18}, 064019 (2022)]., Comment: 10 pages, 8 figures

In this letter, we derive an expression for magnetic dipole transitions that is analogous to the Lyddane-Sachs-Teller relation for dielectric polar lattice vibrations. We thereby define transverse and longitudinal optical frequencies at which paramagnetic resonance and antiresonance occurs, respectively. The relation found here thus permits non-invasive optical analysis of static magnetization properties in paramagnetic materials. Validated through terahertz electron paramagnetic resonance ellipsometry and superconducting quantum interference device measurements on Iron-doped Gallium Nitride, our findings show very good agreement between theory and experiment. We term the excitations associated with the paramagnetic transitions as paramagnetic polaritons which may find use in future photonic applications

Efficient and compact single photon emission platforms operating at room temperature with ultrafast speed and high brightness will be fundamental components of the emerging quantum communications and computing fields. However, so far, it has been very challenging to design practical deterministic single photon emitters based on nanoscale solid state materials that meet the fast emission rate and strong brightness demands. Here we provide a solution to this longstanding problem by using metallic nanocavities integrated with hexagonal boron nitride (hBN) flakes with defects acting as nanoscale single photon emitters (SPEs) at room temperature. The presented hybrid nanophotonic structure creates a rapid speedup and large enhancement in single photon emission at room temperature. Hence, the nonclassical light emission performance is substantially improved compared to plain hBN flakes and hBN on gold layered structures without nanocavity. Extensive theoretical calculations are also performed to accurately model the new hybrid nanophotonic system and prove that the incorporation of plasmonic nanocavity is key to the efficient SPE performance. The proposed quantum nanocavity single photon source is expected to be an element of paramount importance to the envisioned room temperature integrated quantum photonic networks.

A generalized approach derived from Blochs equation of motion of nuclear magnetic moments is presented to model the frequency, magnetic field, spin density, and temperature dependencies in the electromagnetic permeability tensor for materials with magnetic resonances. The resulting tensor model predicts characteristic polarization signatures which can be observed, for example, in fully polarization-resolved Mueller matrix element spectra measured across magnetic resonances as a function of frequency, magnetic field, magnetic moment density, and temperature. When augmented with thermodynamic considerations and suitable Hamiltonian description of the magnetic eigenvalue spectrum, important parameters such as zero-frequency magnetization, spectral amplitude distribution, relaxation time constants, and geometrical orientation parameters of the magnetic moment density can be obtained from comparing the generalized model approach to experimental data. We demonstrate our approach by comparing model calculations with full Mueller matrix element spectra measured at oblique angle of incidence in the terahertz spectral range, across electron spin resonance quintuplet transitions observed in wurtzite-structure GaN doped with iron. Measurements were performed by ellipsometry, using a superconducting cryostat magnet at magnetic fields of 7.23 T and at temperatures of 20 K and 30 K. We detail the occurrence of linear and circular birefringence and dichroism associated with each of the zero-field split spin transitions in the S = 5/2 defect system. We derive the spectral dependence of the magnetic susceptibility function and obtain the temperature and magnetic field dependence of the spin Hamiltonian. Our model correctly predicts the complexity of the polarization signatures observed in the 15 independent elements of the normalized Mueller matrix for both positive and negative magnetic fields.

Monoclinic $\beta$-Ga$_2$O$_3$ films grown on $c$-plane sapphire have been shown to exhibit six $(\bar{2}01)$-plane oriented domains, which are equally-spaced-by-rotation around the surface normal and equally-sized-by-volume that render the film optical response effectively uniaxial. We derive and discuss an optical model suitable for ellipsometry data analysis of such films. We model mid- and far-infrared ellipsometry data from undoped and electrically insulating films with an effective uniaxial dielectric tensor based on projections of all phonon modes within the rotation domains parallel and perpendicular to the sample normal, i.e., to the reciprocal lattice vector $\mathbf{g}_{\bar{2}01}$. Two effective response functions are described by model, and found sufficient to calculate ellipsometry data that best-match measured ellipsometry data from a representative film. We propose to render either effective dielectric functions, or inverse effective dielectric functions, each separately for electric field directions parallel and perpendicular to $\mathbf{g}_{\bar{2}01}$, by sums of Lorentz oscillators, which permit to determine either sets of transverse optical phonon mode parameters, or sets of longitudinal optical phonon mode parameters, respectively. Transverse optical modes common to both dielectric functions can be traced back to single crystal modes with $B_{\mathrm{u}}$ character, while modes with $A_{\mathrm{u}}$ character only appear within the dielectric function for polarization perpendicular to the sample surface. The thereby obtained parameter sets reveal all phonon modes anticipated from averaging over the six-fold rotation domains of single crystal $\beta$-Ga$_2$O$_3$, but with slightly shifted transverse optical, and completely different longitudinal optical phonon modes., Comment: 14 pgaes, 8 figures

The inherently weak chiroptical responses of natural materials limit their usage for controlling and enhancing chiral light-matter interactions. Recently, several nanostructures with subwavelength scale dimensions were demonstrated, mainly due to the advent of nanofabrication technologies, as a potential alternative to efficiently enhance chirality. However, the intrinsic lossy nature of metals and inherent narrowband response of dielectric planar thin films or metasurface structures pose severe limitations toward the practical realization of broadband and tailorable chiral systems. Here, we tackle these problems by designing all-dielectric silicon-based L-shaped optical metamaterials based on tilted nanopillars that exhibit broadband and enhanced chiroptical response in transmission operation. We use an emerging bottom-up fabrication approach, named glancing angle deposition, to assemble these dielectric metamaterials on a wafer scale. The reported strong chirality and optical anisotropic properties are controllable in terms of both amplitude and operating frequency by simply varying the shape and dimensions of the nanopillars. The presented nanostructures can be used in a plethora of emerging nanophotonic applications, such as chiral sensors, polarization filters, and spin-locked nanowaveguides.

Nanostructures represent a frontier where meticulous attention to the control and assessment of structural dimensions becomes a linchpin for their seamless integration into diverse technological applications. By using integrative and comprehensive methodical series of studies, we investigate the evolution of the depolarization factors in the anisotropic Bruggeman effective medium approximation, that are extremely sensitive to the changes in critical dimensions of the nanostructure platforms. To this end, we fabricate spatially coherent highly-ordered slanted nanocolumns from zirconia, silicon, titanium, and permalloy on silicon substrates with varying column lengths using glancing angle deposition. In tandem, broad-spectral range Mueller matrix spectroscopic ellipsometry data, spanning from the near-infrared to the vacuum ultraviolet (0.72 eV to 6.5 eV), is analyzed with a best-match model approach based on the anisotropic Bruggeman effective medium theory. We thereby extracted the anisotropic optical properties including complex dielectric function, birefringence, and dichroism. Most notably, our research unveils a universal, material-independent inverse relationship between depolarization factors and column length. We envision that the presented universal relationship will permit accurate prediction of optical properties of nanocolumnar thin films improving their integration and optimization for optoelectronic and photonic device applications., Comment: 20 pages, 10 figures

We demonstrate a unique class of advanced materials - quantum composites based on polymers with fillers comprised of a van der Waals quantum material that reveals multiple charge-density-wave quantum condensate phases. Materials that exhibit quantum phenomena are typically crystalline, pure, and have few defects because disorder destroys the coherence of the electrons and phonons, leading to collapses of the quantum states. We succeeded in preserving the macroscopic charge-density-wave phases of filler particles after multiple composite processing steps. The prepared composites manifest strong charge-density-wave phenomena even above room temperature. The dielectric constant experiences more than two orders of magnitude enhancement while the material maintains its electrically insulating properties, opening a venue for advanced applications in energy storage and electronics. The results present a conceptually different approach for engineering the properties of materials, extending the application domain for van der Waals materials., Comment: 23 pages, 5 figures

We report the effect of remote surface optical (RSO) phonon scattering on carrier mobility in monolayer graphene gated by ferroelectric oxide. We fabricate monolayer graphene transistors back-gated by epitaxial (001) Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$ films, with field effect mobility up to 23,000 cm$^{2}$V$^{-1}$s$^{-1}$ achieved. Switching the ferroelectric polarization induces nonvolatile modulation of resistance and quantum Hall effect in graphene at low temperatures. Ellipsometry spectroscopy studies reveal four pairs of optical phonon modes in Ba$_{0.6}$Sr$_{0.4}$TiO$_{3}$, from which we extract the RSO phonon frequencies. The temperature dependence of resistivity in graphene can be well accounted for by considering the scattering from the intrinsic longitudinal acoustic phonon and the RSO phonon, with the latter dominated by the mode at 35.8 meV. Our study reveals the room temperature mobility limit of ferroelectric-gated graphene transistors imposed by RSO phonon scattering., Comment: 15 pages, 6 figures

The bowing of the energy of the three lowest band-to-band transitions in $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ alloys was resolved using a combined density functional theory (DFT) and generalized spectroscopic ellipsometry (GSE) approach. The DFT calculations of the electronic band structure of both, $\beta$-Ga$_2$O$_3$ and $\theta$-Al$_2$O$_3$, allow extracting of the linear portion of the energy shift in the alloys, and provide a method for quantifying the role of coherent strain present in the $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ thin films on (010) $\beta$-Ga$_2$O$_3$ substrates. The energies of band-to-band transitions were obtained using the spectroscopic ellipsometry eigenpolarization model approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017)]. After subtracting the effects of strain which also induces additional bowing and after subtraction of the linear portion of the energy shift due to alloying, the bowing parameters associated with the three lowest band-to-band transitions in monoclinic $\beta$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$ are found., Comment: 12 pages, 5 figures

We report on terahertz (THz) electron paramagnetic resonance generalized spectroscopic ellipsometry (THz-EPR-GSE). Measurements of the field and frequency dependencies of the magnetic response due to the spin transitions associated with the nitrogen defect in 4H-SiC are shown as an example. THz-EPR-GSE dispenses with the need of a cavity, permits independently scanning field and frequency parameters, and does not require field or frequency modulation. We investigate spin transitions of hexagonal ($h$) and cubic ($k$) coordinated nitrogen including coupling with its nuclear spin (I=1), and we propose a model approach for the magnetic susceptibility to account for the spin transitions. From the THz-EPR-GSE measurements we can fully determine the polarization properties of the spin transitions and we obtain $g$ and hyperfine splitting parameters using magnetic field and frequency dependent Lorentzian oscillator lineshape functions. We propose frequency-scanning THz-EPR-GSE as a new and versatile method to study properties of spins in solid state materials., Comment: 6 pages, 5 figures

We determine the anisotropic dielectric functions of rhombohedral $\alpha$-Ga$_2$O$_3$ by far-infrared and infrared generalized spectroscopic ellipsometry and derive all transverse optical and longitudinal optical phonon mode frequencies and broadening parameters. We also determine the high frequency and static dielectric constants. We perform density functional theory computations and determine the phonon dispersion for all branches in the Brillouin zone, and we derive all phonon mode parameters at the Brillouin zone center including Raman-active, infrared-active, and silent modes. Excellent agreement is obtained between our experimental and computation results as well as among all previously reported partial information from experiment and theory. We also compute the same information for $\alpha$-Al$_2$O$_3$, the binary parent compound for the emerging alloy of $\alpha$-(Al$_{x}$Ga$_{1-x}$)$_2$O$_3$, and use results from previous investigations [Schubert, Tiwald, and Herzinger, Phys. Rev. B 61, 8187 (2000)] to compare all properties among the two isostructural compounds. From both experimental and theoretical investigations we compute the frequency shifts of all modes between the two compounds. Additionally, we calculate overlap parameters between phonon mode eigenvectors and discuss the possible evolution of all phonon modes into the ternary alloy system and whether modes may form single mode or more complex mode behaviors.

A complete set of all optical phonon modes predicted by symmetry for bixbyite structure indium oxide is reported here from a combination of far-infrared and infrared spectroscopic ellipsometry, as well as first principle calculations. Dielectric function spectra measured on high quality, marginally electrically conductive melt grown single bulk crystals are obtained on a wavelength-by-wavelength (a.k.a. point-by-point) basis and by numerical reduction of a subtle free charge carrier Drude model contribution. A four-parameter semi-quantum model is applied to determine all sixteen pairs of infrared-active transverse and longitudinal optical phonon modes, including the high-frequency dielectric constant, $\varepsilon_{\infty}=4.05\pm 0.05$. The Lyddane-Sachs-Teller relation then gives access to the static dielectric constant, $\varepsilon_{\mathrm{DC}}=10.55\pm 0.07$. All experimental results are in excellent agreement with our density functional theory calculations and with previously reported values, where existent. We also perform optical Hall effect measurements and determine for the unintentionally doped $n$-type sample a free electron density of $n=(2.81 \pm 0.01)\times 10^{17}$~cm$^{-3}$, mobility of $\mu=(112 \pm 3)$~cm$^{2}$/(Vs), and an effective mass parameter of $(0.208\pm0.006)m_e$. Density and mobility parameters compare very well with results of electrical Hall effect measurements. Our effective mass parameter, which is measured independently of any other experimental technique, represents the bottom curvature of the $\Gamma$ point in In$_2$O$_3$ in agreement with previous extrapolations. We use terahertz spectroscopic ellipsometry to measure the quasi-static response of In$_2$O$_3$, and our model validates the static dielectric constant obtained from the Lyddane-Sachs-Teller relation.

Designing broadband enhanced chirality is of strong interest to the emerging fields of chiral chemistry and sensing, or to control the spin orbital momentum of photons in recently introduced nanophotonic chiral quantum and classical optical applications. However, chiral light-matter interactions have an extremely weak nature, are difficult to be controlled and enhanced, and cannot be made tunable or broadband. In addition, planar ultrathin nanophotonic structures to achieve strong, broadband, and tunable chirality at the technologically important visible to ultraviolet spectrum still remain elusive. Here, we tackle these important problems by experimentally demonstrating and theoretically verifying spectrally tunable, extremely large, and broadband chiroptical response by nanohelical metamaterials. The reported new designs of all-dielectric and dielectric-metallic (hybrid) plasmonic metamaterials permit the largest and broadest ever measured chiral Kuhn dissymmetry factor achieved by a large-scale nanophotonic structure. In addition, the strong circular dichroism of the presented bottom-up fabricated optical metamaterials can be tuned by varying their dimensions and proportions between their dielectric and plasmonic helical subsections. The currently demonstrated ultrathin optical metamaterials are expected to provide a substantial boost to the developing field of chiroptics leading to significantly enhanced and broadband chiral light-matter interactions at the nanoscale.

We use a combined generalized spectroscopic ellipsometry and density functional theory approach to determine and analyze the anisotropic dielectric functions of an $\alpha$-Ga$_2$O$_3$ thin film. The sample is grown epitaxially by plasma-assisted molecular beam epitaxy on $m$-plane sapphire. Generalized spectroscopic ellipsometry data from multiple sample azimuths in the spectral range from 0.73 eV to 8.75 eV are simultaneously analyzed. Density functional theory is used to calculate the valence and conduction band structure. We identify, for the indirect-bandgap material, two direct band-to-band transitions with $M_0$-type van Hove singularities for polarization perpendicular to the $c$ axis, $E_{0,\perp}=5.46(6)$ eV and $E_{0,\perp}=6.04(1)$ eV, and one direct band-to-band transition with $M_1$-type van Hove singularity for polarization parallel with $E_{0,||}=5.44(2)$ eV. We further identify excitonic contributions with small binding energy of 7 meV associated with the lowest ordinary transition, and a hyperbolic exciton at the $M_1$-type critical point with large binding energy of 178 meV., Comment: 7 pages, 4 figures, in submission to Applied Physics Letters

The quasi-static anisotropic permittivity parameters of electrically insulating gallium oxide (beta-Ga2O3) were determined by terahertz spectroscopy. Polarization-resolved frequency domain spectroscopy in the spectral range from 200 GHz to 1 THz was carried out on bulk crystals along different orientations. Principal directions for permittivity were determined along crystallographic axes c, and b, and reciprocal lattice direction a*. No significant frequency dispersion in the real part of dielectric permittivity was observed in the measured spectral range. Our results are in excellent agreement with recent radio-frequency capacitance measurements as well as with extrapolations from recent infrared measurements of phonon mode and high frequency contributions, and close the knowledge gap for these parameters in the terahertz spectral range. Our results are important for applications of beta-Ga2O3 in high-frequency electronic devices, Comment: Main Manuscript is 6 pages long with 3 figures and 1 table. The submission also contains a Supplementary Info section

Presented here is the development and demonstration of a tunable cavity-enhanced terahertz frequency-domain optical Hall effect technique. The cavity consists of at least one fixed and one tunable Fabry-P\'erot resonator. The approach is suitable for enhancement of the optical signatures produced by the optical Hall effect in semi-transparent conductive layer structures with plane parallel interfaces. The physical principle is the constructive interference of electric field components that undergo multiple optical Hall effect induced polarization rotations upon multiple light passages through the conductive layer stack. Tuning one of the cavity parameters, such as the external cavity thickness, permits shifting of the frequencies of the constructive interference, and enhancement of the optical signatures produced by the optical Hall effect can be obtained over large spectral regions. A cavity-tuning optical stage and gas flow cell are used as examples of instruments that exploit tuning an external cavity to enhance polarization changes in a reflected terahertz beam. Permanent magnets are used to provide the necessary external magnetic field. Conveniently, the highly reflective surface of a permanent magnet can be used to create the tunable external cavity. The signal enhancement allows the extraction of the free charge carrier properties of thin films, and can eliminate the need for expensive super-conducting magnets. Furthermore, the thickness of the external cavity establishes an additional independent measurement condition, similar to, for example, the magnetic field strength, terahertz frequency, and angle of incidence. A high electron mobility transistor structure and epitaxial graphene are studied as examples. We discuss the theoretical background, instrument design, data acquisition, and data analysis procedures., Comment: 12 pages, 8 figures

Here we present the use of Fabry-P\'erot enhanced terahertz (THz) Mueller matrix ellipsometry to measure an electromagnon excitation in monoclinic cupric oxide (CuO). As a magnetically induced ferroelectric multiferroic, CuO exhibits coupling between electric and magnetic order. This gives rise to special quasiparticle excitations at THz frequencies called electromagnons. In order to measure the electromagnons in CuO, we exploit single-crystal CuO as a THz Fabry-P\'erot cavity to resonantly enhance the excitation's signature. This enhancement technique enables the complex index of refraction to be extracted. We observe a peak in the absorption coefficient near 0.705 THz and 215 K, which corresponds to the electromagnon excitation. This absorption peak is observed along only one major polarizability axis in the monoclinic a-c plane. We show the excitation can be represented using the Lorentz oscillator model, and discuss how these Lorentz parameters evolve with temperature. Our findings are in excellent agreement with previous characterizations by THz time-domain spectroscopy (THz-TDS), which demonstrates the validity of this enhancement technique.

We report on fabrication of spatially-coherent columnar plasmonic nanostructure superlattice-type thin films with high porosity and strong optical anisotropy using glancing angle deposition. Subsequent and repeated depositions of silicon and gold lead to nanometer-dimension subcolumns with controlled lengths. The superlattice-type columns resemble bamboo structures where smaller column sections of gold form junctions sandwiched between larger silicon column sections ("nano-bamboo"). We perform generalized spectroscopic ellipsometry measurements and finite element method computations to elucidate the strongly anisotropic optical properties of the highly-porous nano-bamboo structures. The occurrence of a strongly localized plasmonic mode with displacement pattern reminiscent of a dark quadrupole mode is observed in the vicinity of the gold subcolumns. We demonstrate tuning of this quadrupole-like mode frequency within the near-infrared spectral range by varying the geometry of the nano-bamboo structure. In addition, coupled-plasmon-like and inter-band transition-like modes occur in the visible and ultra-violet spectral regions, respectively. We elucidate an example for the potential use of the nano-bamboo structures as a highly porous plasmonic sensor with optical read out sensitivity to few parts-per-million solvent levels in water.

WO3 thin films were grown by atomic layer deposition and spectroscopic ellipsometry data gathered in the photon energy range of 0.72-8.5 eV and from multiple samples was utilized to determine the frequency dependent complex-valued isotropic dielectric function for WO3. We employ a critical-point model dielectric function analysis and determine a parameterized set of oscillators and compare the observed critical-point contributions with the vertical transition energy distribution found within the band structure of WO3 calculated by density functional theory. We investigate surface roughness with atomic force microscopy and compare to ellipsometric determined effective roughness layer thickness.

We present a terahertz (THz) frequency-domain spectroscopic (FDS) ellipsometer design which suppresses formation of standing waves by use of stealth technology approaches. The strategy to suppress standing waves consists of three elements \textit{geometry}, \textit{coating} and \textit{modulation}. The instrument is based on the rotating analyzer ellipsometer principle and can incorporate various sample compartments, such as a superconducting magnet, \textit{in-situ} gas cells or resonant sample cavities, for example. A backward wave oscillator and three detectors are employed, which permit operation in the spectral range of 0.1--1~THz (3.3--33~cm$^{-1}$ or 0.4--4~meV). The THz frequency-domain ellipsometer allows for standard and generalized ellipsometry at variable angles of incidence in both reflection and transmission configurations. The methods used to suppress standing waves and strategies for an accurate frequency calibration are presented. Experimental results from dielectric constant determination in anisotropic materials, and free charge carrier determination in optical Hall effect, resonant-cavity enhanced optical Hall effect and \textit{in-situ} optical Hall effect experiments are discussed. Examples include silicon and sapphire optical constants, free charge carrier properties of two dimensional electron gas in group-III nitride high electron mobility transistor structure, and ambient effects on free electron mobility and density in epitaxial graphene.

Mid-infrared optical Hall effect measurements are used to determine the free charge carrier parameters of an unintentionally doped wurtzite-structure $c$-plane oriented In$_{0.33}$Ga$_{0.67}$N epitaxial layer. Room temperature electron effective mass parameters of $m^{*}_{\bot}=(0.205 \pm 0.013)~m_0$ and $m^{*}_{\parallel}=(0.204 \pm 0.016)~m_0$ for polarization perpendicular and parallel to the $c$-axis, respectively, were determined. The free electron concentration was obtained as $(1.7 \pm 0.2)\times 10^{19}~$cm$^{-3}$. Within our uncertainty limits we detect no anisotropy for the electron effective mass parameter and we estimate the upper limit of the possible effective mass anisotropy is 7$\%$. We discuss the influence of band nonparabolicity on the electron effective mass parameter as a function of In content. The effective mass parameter is consistent with a linear interpolation scheme between the conduction band mass parameters in GaN and InN when the strong nonparabolicity in InN is included. The In$_{0.33}$Ga$_{0.67}$N electron mobility parameters were found to be anisotropic supporting previous experimental findings for wurtzite-structure GaN, InN, and Al$_{x}$Ga$_{1-x}$N epitaxial layers with $c$-plane growth orientation., Comment: 5 pages, 3 figures, 1 table

The isotropic average conduction band minimum electron effective mass in Sn-doped monoclinic single crystal $\beta$-Ga$_2$O$_3$ is experimentally determined by mid-infrared optical Hall effect to be $(0.284\pm0.013)m_{0}$ combining investigations on ($010$) and ($\bar{2}01$) surface cuts. This result falls within the broad range of values predicted by theoretical calculations for undoped $\beta$-Ga$_2$O$_3$. The result is also comparable to recent density functional calculations using the Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, which predict an average effective mass of $0.267m_{0}$ (arXiv:1704.06711 [cond-mat.mtrl-sci]). Within our uncertainty limits we detect no anisotropy for the electron effective mass, which is consistent with most previous theoretical calculations. We discuss upper limits for possible anisotropy of the electron effective mass parameter from our experimental uncertainty limits, and we compare our findings with recent theoretical results.

We present a comprehensive study of the band structure of two- and three-dimensional hexagonal layered materials using Landau Level optical Hall effect spectroscopy investigations, employing graphene and graphite as model systems. We study inter-Landau-level transitions in highly oriented pyrolytic graphite and a stack of multilayer graphene on C-face 6\textit{H}-SiC, using data from reflection-type optical Hall effect measurements in the mid-infrared spectral range at sample temperatures of $T=1.5$~K and magnetic fields up to $B=8$~T. We describe a comprehensive dielectric polarizability model for inter-Landau-level transitions, which permits analysis of the optical Hall effect data. From their magnetic field dependence we identify sets of H- and K-point inter-Landau-level transitions in graphite and sets of inter-Landau-level transition from decoupled graphene single, and coupled graphene bi-, tri-, and quad-layer for the multilayer graphene stack. For inter-Landau-level transitions in decoupled graphene single-layers and H-point transitions in graphite we observe polarization mode preserving behavior, requiring symmetric magneto-optical contributions to the corresponding dielectric tensors. Inter-Landau-level transitions in coupled graphene layers as well as K-point transitions in graphite exhibit polarization mode mixing behavior, requiring antisymmetric magneto-optical contributions to the corresponding dielectric tensors. From the circular-polarization-averaged inter-Landau-level transition energies and the energy splitting between right- and left-handed circular polarized inter-Landau-level transitions we determine the model parameters in the Slonczewski-Weiss-McClure band structure approximation for two- and three-dimensional hexagonal layered materials, with graphene and graphite as examples.

We employ an eigen polarization model including the description of direction dependent excitonic effects for rendering critical point structures within the dielectric function tensor of monoclinic \beta-Ga2O3 yielding a comprehensive analysis of generalized ellipsometry data obtained from 0.75 eV--9 eV. The eigen polarization model permits complete description of the dielectric response, and we obtain single-electron and excitonic band-to-band transition anisotropic critical point structure model parameters including their polarization eigenvectors within the monoclinic lattice. We compare our experimental analysis with results from density functional theory calculations performed using a recently proposed Gaussian-attenuation-Perdue-Burke-Ernzerhof hybrid density functional, and we present and discuss the order of the fundamental direct band-to-band transitions and their polarization selection rules, the electron and hole effective mass parameters for the three lowest band-to-band transitions, and their exciton binding energy parameters, in excellent agreement with our experimental results. We find that the effective masses for holes are highly anisotropic and correlate with the selection rules for the fundamental band-to-band transitions, where the observed transitions are polarized closely in the direction of the lowest hole effective mass for the valence band participating in the transition.

A generalization of the Lyddane-Sachs-Teller relation is presented for polar vibrations in materials with monoclinic and triclinic crystal systems. The generalization is derived from an eigen displacement vector summation approach, which is equivalent to the microscopic Born-Huang description of polar lattice vibrations. An expression for a general oscillator strength is also described for materials with monoclinic and triclinic crystal systems. A generalized factorized dielectric response function characteristic for monoclinic and triclinic materials is proposed. The generalized Lyddane-Sachs-Teller relation is found valid for monoclinic $\beta$-Ga$_2$O$_3$, where accurate experimental data became available recently from a comprehensive generalized ellipsometry investigation. Data for triclinic crystal systems can be measured by generalized ellipsometry as well, and are anticipated to become available soon and results can be compared with the generalized relations presented here, Comment: 5 pages, 1 figure

Highly-ordered and spatially-coherent cobalt slanted columnar thin films were deposited by glancing angle deposition onto silicon substrates, and subsequently oxidized by annealing at 475 $^{\circ}$C. Scanning electron microscopy, Raman scattering, generalized ellipsometry, and density functional theory investigations reveal shape-invariant transformation of the slanted nanocolumns from metallic to transparent metal-oxide core-shell structures with properties characteristic of spinel cobalt oxide. We find passivation of Co-SCTFs yielding CoAl$_2$O$_3$ core-shell structures produced by conformal deposition of a few nanometers of alumina using atomic layer deposition fully prevents cobalt oxidation in ambient and from annealing up to 475 $^{\circ}$C., Comment: 5 pages, 5 figures, 2 tables