Universal Optical Conductivity Research Articles

Optical absorption window in Na3Bi based three-dimensional Dirac electronic system

We present a detailed theoretical study of the optoelectronic properties of a Na3Bi based three-dimensional Dirac electronic system (3DDES). The optical conductivity is evaluated using the energy-balance equation derived from a Boltzmann equation, where the electron Hamiltonian is taken from a simplified k⋅p approach. We find that for short-wavelength irradiation, the optical absorption in Na3Bi is mainly due to inter-band electronic transitions. In contrast to the universal optical conductance observed for graphene, the optical conductivity for Na3Bi based 3DDES depends on the radiation frequency but not on temperature, carrier density, and electronic relaxation time. In the radiation wavelength regime of about 5μm<λ<200 μm, an optical absorption window is found. This is similar to what is observed in graphene. The position and width of the absorption window depend on the direction of the light polarization and sensitively on temperature, carrier density, and electronic relaxation time. Particularly, we demonstrate that the inter-band optical absorption channel can be switched on and off by applying the gate voltage. This implies that similar to graphene, Na3Bi based 3DDES can also be applied in infrared electro-optical modulators. Our theoretical findings are helpful in gaining an in-depth understanding of the basic optoelectronic properties of recently discovered 3DDESs.

The optical conductivity of few-layer black phosphorus by infrared spectroscopy

The strength of light-matter interaction is of central importance in photonics and optoelectronics. For many widely studied two-dimensional semiconductors, such as MoS2, the optical absorption due to exciton resonances increases with thickness. However, here we will show, few-layer black phosphorus exhibits an opposite trend. We determine the optical conductivity of few-layer black phosphorus with thickness down to bilayer by infrared spectroscopy. On the contrary to our expectations, the frequency-integrated exciton absorption is found to be enhanced in thinner samples. Moreover, the continuum absorption near the band edge is almost a constant, independent of the thickness. We will show such scenario is related to the quanta of the universal optical conductivity of graphene (σ0 = e2/4ħ), with a prefactor originating from the band anisotropy.

Optical properties of surface states in two-dimensional topological insulators.

We present a simple and tractable approach to investigate the optical properties of surface states in two-dimensional (2D) topological insulators (TIs). The analytic expression of optical conductivity of surface states in 2D TIs are obtained based on the kinetic equations. It is found that universal optical conductance can be observed in the high frequency region, which does not depend on the temperature, the chemical potential, or the bandgap of the systems. This universal optical conductance is similar to that in graphene. However, the optical absorption edge of such surface states strongly depend on the chemical potential and the bandgap of the systems. There are obvious optical absorption peaks at low temperature in the low frequency region, which are very different from that in graphene. The bandgaps in surface states can be accurately experimentally measured by the optical absorption edges or the peaks. We expect that our theoretical results offer transparent understandings for the experimental results and applications of 2D TIs.

Effects of long-range disorder and electronic interactions on the optical properties of graphene quantum dots

We theoretically investigate the effects of long-range disorder and electron-electron interactions on the optical properties of hexagonal armchair graphene quantum dots consisting of up to 10806 atoms. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. Imperfections in the graphene quantum dots are modelled as a long-range random potential landscape, giving rise to electron-hole puddles. We show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet.

Universal optical conductivity of a disordered Weyl semimetal.

Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in the semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid. We demonstrate that the correction to the dielectric constant and optical conductivity in a dirty Weyl semimetal due to weak disorder is independent of the actual nature of point-like impurity scatterers. Therefore, optical conductivity can be used as an experimentally measurable quantity to study the critical properties and to pin the universality class of the disorder-driven quantum phase transition in Weyl semimetals.

Universal absorption of two-dimensional systems

We discuss the optical conductivity of several non-interacting two-dimensional (2D) semiconducting systems focusing on gapped Dirac and Schr\"odinger fermions as well as on a system mixing these two types. Close to the band-gap, we can define a universal optical conductivity quantum of $\sigma_0=\frac{1}{16}\frac{e^2}{\hbar}$ for the pure systems. The effective optical conductivity then depends on the degeneracy factors $g_s$ (spin) and $g_v$ (valley) and on the curvature around the band-gap $\nu$, i.e., it generally reads $\sigma=g_sg_v\nu\sigma_0$. For a system composed of both types of carriers, the optical conductivity becomes non-universal.

Infrared to terahertz absorption window in mono- and multi-layer graphene systems

We present a theoretical study on optical properties such as optical conductance and light transmission coefficient for mono- and multi-layer graphene systems with AB- and ABC-stacking. Considering an air/graphene/dielectric-wafer structure, the optical coefficients for those graphene systems are examined and compared. The universal optical conductance σ0N=Nπe2/(2h) for N layer graphene systems in the visible region is verified. For N≥3 layer graphene, the mini-gap induced absorption edges can be observed in odd layers AB-stacked multilayer graphene, where the number and position of the absorption edges are decided by the layers number N. Meanwhile, we can observe the optical absorption windows for those graphene systems in the infrared to terahertz bandwidth (0.2–150THz). The absorption window is induced by different transition energies required for inter- and intra-band optical absorption channels. We find that the depth and width of the absorption window can be tuned not only via varying temperature and electron density but also by changing the number of graphene layers and the stacking order. These theoretical findings demonstrate that mono- and multi-layer graphene systems can be applied as frequency tunable optoelectronic devices working in infrared to terahertz bandwidth.

Effect of Oxygen Plasma on the Optical Properties of Monolayer Graphene

The significant alteration of absorption (A) of monolayer graphene under mild oxygen plasma exposure has been observed. The first important effect is the reduction of the excitonic resonance peak at 4.64 eV. Secondly, in the near infrared range, A is gradually suppressed below an exposure-dependent threshold in sense that A << A0. Quantity A0 (given by πα and α is the fine structure constant) denotes constant absorption and relates to universal optical conductivity σ0. The suppression of A0 can be thought as the weakening of electron-hole interaction as displayed by the reduction of the excitonic resonance peak at 4.64 eV. The weakening of this interaction is due to the disorder introduced by the oxygen plasma exposure.

Terahertz transmission and sheet conductivity of randomly stacked multi-layer graphene

We investigate transmission characteristics and sheet conductivity of mono- to multi-layer graphene deposited on quartz in the terahertz (THz) frequency region. The free carrier absorption and Fabry-Perot interference between graphene layers give rise to nonlinear decrease of THz transmission from 76.7% to 27% for mono- to 12-layer graphene. These phenomena are well explained with a modified theoretical model based on Drude conductivity. The optical sheet conductivity of multi-layer graphene, made by layer-by-layer random stacking of high-quality mono-layer graphene, at 1 THz exhibits two orders of magnitude higher values than the universal optical conductivity due to intraband transition of intrinsic graphene.

Optoelectronic properties of ABC‐stacked trilayer graphene

AbstractWe present a theoretical study on the optoelectronic properties of ABC‐stacked trilayer graphene (TLG). The optical conductance and light transmittance are evaluated through using the energy‐balance equation derived from the Boltzmann equation for an air/graphene/dielectric‐wafer system in the presence of linearly polarized radiation field. The results obtained from two band structure models are examined and compared. For short wavelength radiation, the universal optical conductance $\sigma _{0} = 3e^{2} /(4\hbar )$ can be obtained. Importantly, there exists an optical absorption window in the radiation wavelength range 10–200 µm, which is induced by different transition energies required for inter‐ and intra‐band optical absorption channels. As a result, we find that the position and width of this window depend sensitively on temperature and carrier density of the system, especially the lower frequency edge. There is a small characteristic absorption peak at about 82 µm where the largest interband transition states exist in the ABC‐stacked TLG model, in contrast to the relatively smooth curves in a simplified model. These theoretical results indicate that TLG has some interesting and important physical properties which can be utilized to realize infrared or THz optoelectronic devices.

Infrared Spectroscopy of Wafer-Scale Graphene

We report spectroscopy results from the mid- to far-infrared on wafer-scale graphene, grown either epitaxially on silicon carbide or by chemical vapor deposition. The free carrier absorption (Drude peak) is simultaneously obtained with the universal optical conductivity (due to interband transitions) and the wavelength at which Pauli blocking occurs due to band filling. From these, the graphene layer number, doping level, sheet resistivity, carrier mobility, and scattering rate can be inferred. The mid-IR absorption of epitaxial two-layer graphene shows a less pronounced peak at 0.37 ± 0.02 eV compared to that in exfoliated bilayer graphene. In heavily chemically doped single-layer graphene, a record high transmission reduction due to free carriers approaching 40% at 250 μm (40 cm(-1)) is measured in this atomically thin material, supporting the great potential of graphene in far-infrared and terahertz optoelectronics.

Optoelectronic properties of graphene in the presence of optical phonon scattering

We study in detail the optoelectronic properties of graphene. Considering the electron interactions with photons and phonons, we employ the mass- and energy-balance equations to self-consistently evaluate the photoinduced carrier densities, the optical conductance, and the transmission coefficient in the presence of a linearly polarized radiation field. We demonstrate that the photoinduced carrier densities increase around the electron-photon-phonon resonant transition. They depend strongly on the radiation intensity and frequency, temperature, and dark carrier density. For short-wavelength radiation $(\mathcal{L}l3\text{ }\ensuremath{\mu}\text{m})$, we obtain the universal optical conductance ${\ensuremath{\sigma}}_{0}={e}^{2}/(4\ensuremath{\hbar})$. Importantly, there exists an optical-absorption window in the radiation wavelength range $4--100\text{ }\ensuremath{\mu}\text{m}$, which is induced by different transition energies required for interband and intraband optical absorption. The position and width of this window depend sensitively on the temperature and the carrier density of the system. These theoretical results are in line with recent experimental findings and indicate that graphene exhibits important features not only in the visible regime but also in the midinfrared bandwidth.

Photo-excited carriers and optical conductance and transmission in graphene in the presence of phonon scattering

We present a theoretical study of the optoelectronic properties of monolayer graphene. Including the effect of the electron–photon–phonon scattering, we employ the mass- and energy-balance equations derived from the Boltzmann equation to evaluate self-consistently the carrier densities, optical conductance and transmission coefficient in graphene in the presence of linearly polarized radiation field. We find that the photo-excited carrier density can be increased under infrared radiation and depend strongly on radiation intensity and frequency. For short wavelengths ( λ < 3 μ m ), the universal optical conductance σ 0 = e 2 / 4 ℏ is obtained and the light transmittance is about 0.97–0.98. Interestingly, there is an optical absorption window in the range 4 – 100 μ m which is induced by different transition energies required for inter- and intra-band optical absorption. The position and width of this absorption window depend sensitively on temperature and carrier density of the system. These results are relevant for applications of recently developed graphene devices in advanced optoelectronics such as the infrared photodetectors.

Optical conductance and transmission in bilayer graphene

We present a theoretical study of the optoelectronic properties of bilayer graphene. The optical conductance and transmission coefficient are calculated using the energy-balance equation derived from a Boltzmann equation for an air/graphene/dielectric-wafer system. For short wavelengths (λ&amp;lt;0.2 μm), we obtain the universal optical conductance σ=e2/(2ℏ). Interestingly, there exists an optical absorption window in the wavelength range 10–100 μm, which is induced by different transition energies required for inter- and intra-band optical absorptions in the presence of the Moss–Burstein effect. As a result, the position and width of this absorption window depend sensitively on temperature, carrier density, and sample mobility of the system. These results are relevant for applications of recently developed graphene devices in advanced optoelectronics such as the infrared photodetectors.

Origin of Universal Optical Conductivity and Optical Stacking Sequence Identification in Multilayer Graphene

We show that the origin of the universal optical conductivity in a normal N-layer graphene multilayer is an emergent chiral symmetry which guarantees that sigma(omega) = Nsigma_{uni} in both low and high-frequency limits. [sigma_{uni} = (pi/2)e;{2}/h]. We use this physics to relate intermediate frequency conductivity trends to qualitative characteristics of the multilayer stacking sequence.

Counting graphene layers on glass via optical reflection microscopy

We show that optical reflection microscopy is a reliable method to simultaneously locate and count graphene layers deposited on bulk, transparent substrates such as soda-lime glass. The visible contrast in optical reflection versus graphene layer number is resolvable on bulk substrates. A simple Fresnel theory based on the universal optical conductance of graphene layers accurately models optical reflection images taken at a wavelength of 550±5 nm. We directly count one to nine layers of graphene using reflection microscopy.

Optical constants of graphene layers in the visible range

We show that the optical constants of graphene in the visible range can be estimated by means of a very simple procedure involving their consistence with universal optical conductivity and experimentally measured optical spectra, within the framework of Fresnel coefficients calculation. The obtained complex refractive index allows for accurate prediction of the optical behavior of graphene in the visible range, from the two-dimensional limit (single atomically thick graphene layer) to the bulk limit (graphite). Therefore, it may result very useful for quantitative optical analysis of graphene layers and graphitic structures in general.