Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons.

We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.

Density Functional Theory for Buckyballs within Symmetrized Icosahedral Basis.

We have developed a highly efficient computation method based on density functional theory (DFT) within a set of fully symmetrized basis functions for the C60 buckyball, which possesses the icosahedral (Ih) point-group symmetry with 120 symmetry operations. We demonstrate that our approach is much more efficient than the conventional approach based on three-dimensional plane waves. When applied to the calculation of optical transitions, our method is more than one order of magnitude faster than the existing DFT package with a conventional plane-wave basis. This makes it very convenient for modeling optical and transport properties of quantum devices related to buckyball crystals. The method introduced here can be easily extended to other fullerene-like materials.

Contact Effects on Thermoelectric Properties of Textured Graphene Nanoribbons.

The transport and thermoelectric properties of finite textured graphene nanoribbons (t-GNRs) connected to electrodes with various coupling strengths are theoretically studied in the framework of the tight-binding model and Green's function approach. Due to quantum constriction induced by the indented edges, such t-GNRs behave as serially coupled graphene quantum dots (SGQDs). These types of SGQDs can be formed by tailoring zigzag GNRs (ZGNRs) or armchair GNRs (AGNRs). Their bandwidths and gaps can be engineered by varying the size of the quantum dot and the neck width at indented edges. Effects of defects and junction contact on the electrical conductance, Seebeck coefficient, and electron thermal conductance of t-GNRs are calculated. When a defect occurs in the interior site of textured ZGNRs (t-ZGNRs), the maximum power factor within the central gap or near the band edges is found to be insensitive to the defect scattering. Furthermore, we found that SGQDs formed by t-ZGNRs have significantly better electrical power outputs than those of textured ANGRs due to the improved functional shape of the transmission coefficient in t-ZGNRs. With a proper design of contact, the maximum power factor (figure of merit) of t-ZGNRs could reach 90% (95%) of the theoretical limit.

Theory of magnetic-field effect on trions in two-dimensional materials.

In this work, we present a theoretical method to study the effect of magnetic field on trions in two-dimensional materials. The trion is modeled by a three-particle Schrödinger equation and the magnetic-field interaction is included by means of a vector potential in symmetric gauge. By using a coordinate transformation and a unitary transformation, the trion Hamiltonian can be converted into the sum of a translational term describing the Landau quantization for the trion center-of-mass motion, an internal term describing the trion binding, and a translational-internal coupling term depending linearly on the magnetic-field strength. The trion eigenenergy and wavefunction can then be calculated efficiently by using a variational method, and the quantum numbers of trions in magnetic fields can be assigned. The eigenenergies, binding energies, and correlation energies of three trion branches, which correspond to the ground-state trion and two excited-state trions solved from the trion Hamiltonian in zero magnetic field, are studied numerically in finite magnetic fields. The present method is applied to study the magnetic-field dependence of trion energy levels in hole-doped WSe2 monolayers. The binding energies and correlation energies of positive trions in WSe2 are investigated over a range of magnetic fields up to 25 T.

Autofocus of imaging ellipsometry.

Through polarized light interacting with samples, imaging ellipsometry is capable of aiding in the study of semitransparent biological cells microscopically; it is also possible to find applications in marker-free nondestructive disease diagnosis. Often a living biological cell is sensitive to environmental conditions, and fast measurement is preferred. Fast and accurate locating of the focal plane is important for biosensing. By analyzing our previous published through-focus ellipsometry images for S. mutans cells on Au film, we have found an efficient method of locating the focal plane position, i.e., through edge detection of cells in ellipsometry images. The method is not sample-dependent. As the edges are decided only by a sample's own features, the method is robust against noise or small shifts of images. It is also easy to use without the need to choose a threshold value as in the Laplace filtering method. The method can be further useful for biosensing applications.

Near-field spectroscopic imaging of exciton quenching at atomically sharp MoS2/WS2 lateral heterojunctions.

Heterojunctions made by laterally stitching two different transition metal dichalcogenide monolayers create a unique one-dimensional boundary with intriguing local optical properties that can only be characterized by nanoscale-spatial-resolution spectral tools. Here, we use near-field photoluminescence (NF-PL) to reveal the narrowest region (105 nm) ever reported of photoluminescence quenching at the junction of a laterally stitched WS2/MoS2 monolayer. We attribute this quenching to the atomically sharp band offset that generates a strong electric force at the junction to easily dissociate excitons. Besides the sharp heterojunction, a model considering various widths of the alloying interfacial region under low or high optical pumping is presented. With a spatial resolution six times better than that of confocal microscopy, NF-PL provides an unprecedented spectral tool for non-scalable 1D lateral heterojunctions.

Electrically Switchable Intervalley Excitons with Strong Two-Phonon Scattering in Bilayer WSe2.

We report the observation of QΓ intervalley exciton in bilayer WSe2 devices encapsulated by boron nitride. The QΓ exciton resides at ∼18 meV below the QK exciton. The QΓ and QK excitons exhibit different Stark shifts under an out-of-plane electric field due to their different interlayer dipole moments. By controlling the electric field, we can switch their energy ordering and control which exciton dominates the luminescence of bilayer WSe2. Remarkably, both QΓ and QK excitons exhibit unusually strong two-phonon replicas, which are comparable to or even stronger than the one-phonon replicas. By detailed theoretical simulation, we reveal the existence of numerous (≥14) two-phonon scattering paths involving (nearly) resonant exciton-phonon scattering in bilayer WSe2. To our knowledge, such electric-field-switchable intervalley excitons with strong two-phonon replicas have not been found in any other two-dimensional semiconductors. These make bilayer WSe2 a distinctive valleytronic material with potential novel applications.

Characteristics of multi-mode lasing in cesium lead bromide perovskite microwires with an isosceles right triangle cross-section.

The CsPbBr3 microwires with unique isosceles right triangle cross-sections are commonly observed via chemical vapor deposition method. In this work, we study the correlations between measured multi-mode lasing behaviors and the simulation of the mode patterns inside the triangular-rod microcavity. We confirm that lasing action with higher-order transverse modes can well sustain, even when these modes experience large optical loss due to the isosceles triangle cross-section. By comparing the experimental and simulation results, the higher-order transverse modes tend to show up prior to the fundamental transverse modes for wider microwires. We attribute this behavior to the nonuniform field distribution caused by the high absorption efficiency of CsPbBr3. We also elaborate on the difficulties to sustain the whispering gallery mode in the CsPbBr3 triangular-rod microcavity, which implies that the lateral dimension and geometry of the cavity should be considered carefully for the future design of low threshold wire-based laser devices.

Exciton-polaron Rydberg states in monolayer MoSe2 and WSe2.

Exciton polaron is a hypothetical many-body quasiparticle that involves an exciton dressed with a polarized electron-hole cloud in the Fermi sea. It has been evoked to explain the excitonic spectra of charged monolayer transition metal dichalcogenides, but the studies were limited to the ground state. Here we measure the reflection and photoluminescence of monolayer MoSe2 and WSe2 gating devices encapsulated by boron nitride. We observe gate-tunable exciton polarons associated with the 1 s-3 s exciton Rydberg states. The ground and excited exciton polarons exhibit comparable energy redshift (15~30 meV) from their respective bare excitons. The robust excited states contradict the trion picture because the trions are expected to dissociate in the excited states. When the Fermi sea expands, we observe increasingly severe suppression and steep energy shift from low to high exciton-polaron Rydberg states. Their gate-dependent energy shifts go beyond the trion description but match our exciton-polaron theory. Our experiment and theory demonstrate the exciton-polaron nature of both the ground and excited excitonic states in charged monolayer MoSe2 and WSe2.

Variationally optimized orbital approach to trions in two-dimensional materials.

In this work, trions in two-dimensional (2D) space are studied by the variational method with trial wavefunctions being constructed by 2D slater-type orbitals. Via this method, trion energy levels and wavefunctions can be calculated efficiently with fairly good accuracy. We first apply this method to study trion energy levels in a 2D hydrogen-like system with respect to a wide range of mass ratios and screening lengths. We find that the ground-state trion is bound for the whole parameter range, and an excited-state trion with antisymmetric permutation of electrons with finite angular momentum is bound for large electron-hole mass ratios or long screening lengths. The binding energies of ground-state trions calculated by the present method agree well with those calculated by more sophisticated but computationally demanding methods. We then calculate trion binding energies in various monolayer transition metal dichalcogenides (TMDCs) by using this method with the inclusion of electron-hole exchange (EHX) interaction. For TMDCs, we found that the effect of EHX can be significant in determining the trion binding energy and the possible existence of stable excited-state trions.

Signatures of moiré trions in WSe2/MoSe2 heterobilayers.

Moiré superlattices formed by van der Waals materials can support a wide range of electronic phases, including Mott insulators1-4, superconductors5-10 and generalized Wigner crystals2. When excitons are confined by a moiré superlattice, a new class of exciton emerges, which holds promise for realizing artificial excitonic crystals and quantum optical effects11-16. When such moiré excitons are coupled to charge carriers, correlated states may arise. However, no experimental evidence exists for charge-coupled moiré exciton states, nor have their properties been predicted by theory. Here we report the optical signatures of trions coupled to the moiré potential in tungsten diselenide/molybdenum diselenide heterobilayers. The moiré trions show multiple sharp emission lines with a complex charge-density dependence, in stark contrast to the behaviour of conventional trions. We infer distinct contributions to the trion emission from radiative decay in which the remaining carrier resides in different moiré minibands. Variation of the trion features is observed in different devices and sample areas, indicating high sensitivity to sample inhomogeneity and variability. The observation of these trion features motivates further theoretical and experimental studies of higher-order electron correlation effects in moiré superlattices.

Multipath Optical Recombination of Intervalley Dark Excitons and Trions in Monolayer WSe_{2}.

Excitons and trions (or exciton polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe_{2}. We observe the intervalley dark excitons, which can recombine by the assistance of defect scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths-through intravalley or intervalley electron-hole recombination-into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.

Landau-Quantized Excitonic Absorption and Luminescence in a Monolayer Valley Semiconductor.

We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe_{2} under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors n=+0, +1 in the bottom conduction band and n=-0 to -6 in the top valence band, including the Berry-curvature-induced n=±0 LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accompanied by sharp oscillations in the exciton absorption width and magnitude. This peculiar exciton behavior can be simulated by semiempirical calculations. The experimentally deduced g factors of the conduction band (g∼2.5) and valence band (g∼15) exceed those predicted in a single-particle model (g=1.5, 5.5, respectively). Such g-factor enhancement implies strong many-body interactions in gated monolayer WSe_{2}. The complex interplay between Landau quantization, excitonic effects, and many-body interactions makes monolayer WSe_{2} a promising platform to explore novel correlated quantum phenomena.

Photonic Crystal Circular Nanobeam Cavity Laser with Type-II GaSb/GaAs Quantum Rings as Gain Material.

The optical emission from type-II semiconductor nanostructures is influenced by the long carrier lifetime and can exhibit remarkable thermal stability. In this study, utilizing a high quality photonic crystal circular nanobeam cavity with a high quality factor and a sub-micrometer mode volume, we demonstrated an ultra-compact semiconductor laser with type-II gallium antimonide/gallium arsenide quantum rings (GaSb/GaAs QRs) as the gain medium. The lasing mode localized around the defect region of the nanobeam had a small modal volume and significant coupling with the photons emitted by QRs. It leads the remarkable shortening of carrier lifetime observed from the time-resolved photoluminescence (TRPL) and a high Purcell factor. Furthermore, a high characteristic temperature of 114 K was observed from the device. The lasing performances indicated the type-II QRs laser is suitable for applications of photonic integrated circuit and bio-detection applications.

Full consideration of acoustic phonon scatterings in two-dimensional Dirac materials.

The in-plane acoustic phonon scattering in graphene is solved by considering fully inelastic acoustic phonon scatterings in two-dimensional (2D) Dirac materials for a large range of temperatures (T) and chemical potentials (µ). Rigorous analytical solutions and symmetry properties of Fermionic and Bosonic functions are obtained. We illustrate how doping alters the temperature dependence of acoustic phonon scattering rates. It is shown that the quasi-elastic and ansatz equations previously derived for acoustic phonon scatterings in graphene are limiting cases of the inelastic-scattering equations derived here. For heavily-doped graphene, we found that the high-T behavior of resistivity is better described by ρ(T,µ) ∝T(1 -ζaµ2/3(kBT)2) rather than a linear T behavior, and in the low T regime we found τ-1∝ (kBT)4 but with a different prefactor (i.e.∼3 times smaller) in comparison with the existing quasi-elastic expressions. Furthermore, we found a simple analytic "semi-inelastic" expression of the form τ-1∝ (kBT)4/(1 + cT3) which matches nearly perfectly with the full inelastic results for any temperature up to 500 K and µ up to 1 eV. Our simple analytical results agree well with previous first-principles studies and available experimental data. Moreover, we obtain an analytical form for the acoustic gauge field . Our analyses pave a way for investigating scatterings between electrons and other fundamental excitations with linear dispersion relation in 2D Dirac material-based heterostructures such as bogolon-mediated electron scattering in graphene-based hybrid Bose-Fermi systems.

Efficient Modeling of Optical Excitations of Colloidal Core-Shell Semiconductor Quantum Dots by Using Symmetrized Orbitals.

An efficient method for the theoretical investigation of optical properties of semiconductor core-shell quantum dots (CSQDs) is introduced within the multiband k·p approach, which takes the advantage of the symmetry of the system. The heteroepitaxial strain and excitonic effect are included in the calculation of energy levels, envelope wave functions, exciton binding energy, and linear absorption coefficient. The adoption of symmetrized orbitals allows improvement of the computation time significantly. To avoid appearance of spurious solutions caused by imbalance of basis functions adopted, we consider an 8-band k·p model which is block-diagonalized into two conduction bands and six valence bands, that we call the 2 + 6-band model. The band nonparabolicity effect is modeled by an energy-dependent k·p term, such that the density of states obtained can mimic the actual density of states of a full-band model. The simulated absorption spectra of ZnTe/ZnSe CSQD are in good agreement with those observed experimentally, including the high rise of absorption at energies far above the absorption edge.

Well-aligned Vertically Oriented ZnO Nanorod Arrays and their Application in Inverted Small Molecule Solar Cells.

This manuscript describes how to design and fabricate efficient inverted solar cells, which are based on a two-dimensional conjugated small molecule (SMPV1) and [6,6]-phenyl-C71-butyric acid methyl ester (PC71BM), by utilizing ZnO nanorods (NRs) grown on a high quality Al-doped ZnO (AZO) seed layer. The inverted SMPV1:PC71BM solar cells with ZnO NRs that grew on both a sputtered and sol-gel processed AZO seed layer are fabricated. Compared with the AZO thin film prepared by the sol-gel method, the sputtered AZO thin film exhibits better crystallization and lower surface roughness, according to X-ray diffraction (XRD) and atomic force microscope (AFM) measurements. The orientation of the ZnO NRs grown on a sputtered AZO seed layer shows better vertical alignment, which is beneficial for the deposition of the subsequent active layer, forming better surface morphologies. Generally, the surface morphology of the active layer mainly dominates the fill factor (FF) of the devices. Consequently, the well-aligned ZnO NRs can be used to improve the carrier collection of the active layer and to increase the FF of the solar cells. Moreover, as an anti-reflection structure, it can also be utilized to enhance the light harvesting of the absorption layer, with the power conversion efficiency (PCE) of solar cells reaching 6.01%, higher than the sol-gel based solar cells with an efficiency of 4.74%.

Top Illuminated Hysteresis-Free Perovskite Solar Cells Incorporating Microcavity Structures on Metal Electrodes: A Combined Experimental and Theoretical Approach.

Further technological development of perovskite solar cells (PSCs) will require improvements in power conversion efficiency and stability, while maintaining low material costs and simple fabrication. In this Research Article, we describe top-illuminated ITO-free, stable PSCs featuring microcavity structures, wherein metal layers on both sides on the active layers exerted light interference effects in the active layer, potentially increasing the light path length inside the active layer. The optical constants (refractive index and extinction coefficient) of each layer in the PSC devices were measured, while the optical field intensity distribution was simulated using the transfer matrix method. The photocurrent densities of perovskite layers of various thicknesses were also simulated; these results mimic our experimental values exceptionally well. To modify the cavity electrode surface, we deposited a few nanometers of ultrathin MoO3 (2, 4, and 6 nm) in between the Ag and poly(3,4-ethylenedioxythiophene):polystyrenesulfonate (PEDOT:PSS) layers provide hydrophobicity to the Ag surface and elevate the work function of Ag to match that of the hole transport layer. We achieved a power conversion efficiency (PCE) of 13.54% without hysteresis in the device containing a 4 nm-thick layer of MoO3. In addition, we fabricated these devices on various cavity electrodes (Al, Ag, Au, Cu); those prepared using Cu and Au anodes displayed improved device stability of up to 72 days. Furthermore, we prepared flexible PSCs having a PCE of 12.81% after incorporating the microcavity structures onto poly(ethylene terephthalate) as the substrate. These flexible solar cells displayed excellent stability against bending deformation, maintaining greater than 94% stability after 1000 bending cycles and greater than 85% after 2500 bending cycles performed with a bending radius of 5 mm.

Sensing of Streptococcus mutans by microscopic imaging ellipsometry.

Microscopic imaging ellipsometry is an optical technique that uses an objective and sensing procedure to measure the ellipsometric parameters ? and ? in the form of microscopic maps. This technique is well known for being noninvasive and label-free. Therefore, it can be used to detect and characterize biological species without any impact. Microscopic imaging ellipsometry was used to measure the optical response of dried Streptococcus mutans cells on a glass substrate. The ellipsometric ? and ? maps were obtained with the Optrel Multiskop system for specular reflection in the visible range ( ? = 450 to 750 nm). The ? and ? images at 500, 600, and 700 nm were analyzed using three different theoretical models with single-bounce, two-bounce, and multibounce light paths to obtain the optical constants and height distribution. The obtained images of the optical constants show different aspects when comparing the single-bounce analysis with the two-bounce or multibounce analysis in detecting S. mutans samples. Furthermore, the height distributions estimated by two-bounce and multibounce analyses of S. mutans samples were in agreement with the thickness values measured by AFM, which implies that the two-bounce and multibounce analyses can provide information complementary to that obtained by a single-bounce light path.

Enhance the light-harvesting capability of the ITO-free inverted small molecule solar cell by ZnO nanorods.

The ITO-free inverted SMPV1:PC71BM solar cells with an Al doped ZnO (AZO) transparent electrodes are fabricated. The AZO thin film prepared by pulsed laser deposition (PLD) technique exhibits high transmission (>85%) and low sheet resistance (~30 Ω/sq) and the power conversion efficiency (PCE) of devices based on AZO electrode can reach around 4%. To further enhance the light harvesting of the absorption layer of solar cells, ZnO nanorods interlayer is grown on the AZO layer before the deposition the active layer. The absorption spectrums of devices under various conditions are also simulated by RCWA method to identify the optical saturation length of the ZnO nanorods. The PCE of ITO-free inverted small molecule solar cell improved with ZnO nanorods can reach 6.6%.