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.

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.

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.

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.

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.

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.

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.

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.

Size and morphology dependent evolution of resonant modes in ZnO microspheres grown by hydrothermal synthesis.

We report the correlation between inner morphology, size and whispering gallery mode (WGM) behavior in ZnO microspheres (MSs) grown by hydrothermal method. WGMs in different ZnO microspheres with diameters in the range of 2 - 6 µm were analyzed by a modified refractive index (MRI) scheme. We found that the size dependence of WGMs in our system is more complicated than others because of the appearance of porosity inside each sphere. Such features might account for the refractive index change and peak shift. Despite that, our MRI scheme can detect such complex features and reproduce universal relations between all important quantities of a microsphere WGM resonator.

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%.

Quantum interference and structure-dependent orbital-filling effects on the thermoelectric properties of quantum dot molecules.

The quantum interference and orbital filling effects on the thermoelectric (TE) properties of quantum dot (QD) molecules with high figure of merit are illustrated via the full solution to the Hubbard-Anderson model in the Coulomb blockade regime. It is found that under certain conditions in the triangular QD molecule (TQDM), destructive quantum interference (QI) can occur, which leads to vanishingly small electrical conductance, while the Seebeck coefficient is modified dramatically. When the TQDM is in the charge localization state due to QI, the Seebeck coefficient is seriously suppressed at low temperature, but is highly enhanced at high temperature. Meanwhile, the behavior of the Lorenz number reveals that it is easier to block charge transport via destructive QI than the electron heat transport at high temperatures. The maximum power factor (PF) in the TQDM occurs under full-filling conditions. Nevertheless, low-filling conditions are preferred for getting the maximum PF in serially coupled triple QDs in general. In double QDs, the maximum PF can be achieved either with orbital-depletion or orbital-filling as a result of electron-hole symmetry. Our theoretical work provides a useful guideline for the advancement of the nanoscale TE technology.

Quantum interference and electron correlation in charge transport through triangular quantum dot molecules.

We study the charge transport properties of triangular quantum dot molecules (TQDMs) connected to metallic electrodes, taking into account all correlation functions and relevant charging states. The quantum interference (QI) effect of TQDMs resulting from electron coherent tunneling between quantum dots is revealed and well interpreted by the long distance coherent tunneling mechanism. The spectra of electrical conductance of TQDMs with charge filling from one to six electrons clearly depict the many-body and topological effects. The calculated charge stability diagram for conductance and total occupation numbers matches well with the recent experimental measurements. We also demonstrate that the destructive QI effect on the tunneling current of TQDMs is robust with respect to temperature variation, making the single electron QI transistor feasible at higher temperatures.

Finite-difference time-domain analysis for the dynamics and diffraction of exciton-polaritons.

We adopted a finite-difference time-domain (FDTD) scheme to simulate the dynamics and diffraction of exciton-polaritons, governed by the coupling of polarization waves with electromagnetic waves. The polarization wave, an approximate solution to the Schrödinger's equation at low frequencies, essentially captures the exciton behavior. Numerical stability of the scheme is analyzed and simple examples are provided to prove its validity. The system considered is both temporally and spatially dispersive, for which the FDTD analysis has attracted less attention in the literature. Here, we demonstrate that the FDTD scheme could be useful for studying the optical response of the exciton-polariton and its dynamics. The diffraction of a polariton wave from a polaritonic grating is also considered, and many sharp resonances are found, which manifest the interference effect of polariton waves. This illustrates that the measurement of transmittance or reflectance near polariton resonance can reveal subwavelength features in semiconductors, which are sensitive to polariton scattering.

Crystallinity effects on scaling properties of photoinduced modes in silver nanoprisms.

The crystallinity effects on scaling properties of photoinduced modes in crystalline silver nanoprisms with C3v symmetry are studied using a realistic atomistic model and group theory. Among all vibrational modes, photoinduced modes can be identified as those vibrational modes which possess larger in-phase radial atomic displacement and can be projected out by the projected density of states method. We found that the properties of vibrations in silver nanoprisms strongly depend on the particle's aspect ratio (bisector length over thickness). By considering crystallinity of silver nanoprisms, the dominant modes with the in-plane oscillation become several closely spaced modes, and become obvious for nanoprisms with a smaller aspect ratio. The oscillation spectra show that the dominant planar modes are insensitive to thickness change. On the contrary, the atomic displacements show significantly different patterns for nanoprisms of different thicknesses. We also found that, for nanoprisms with same aspect ratio that is larger than 4, the vibrational properties of dominant modes exhibit scaling similarity. By using a simple linear transformation, the vibration frequencies for large-sized nanoprisms of aspect ratio 6 can be obtained by a corresponding scaling factor. The calculated results are in good agreement with experimental data.

Optimization of high-Q coupled nanobeam cavity for label-free sensing.

We numerically and experimentally investigated the lateral coupling between photonic crystal (PhC) nanobeam (NB) cavities, pursuing high sensitivity and figure of merit (FOM) label-free biosensor. We numerically carried out 3D finite-difference time-domain (3D-FDTD) and the finite element method (FEM) simulations. We showed that when two PhC NB cavities separated by a small gap are evanescently coupled, the variation in the gap width significantly changes the coupling efficiency between the two coupled NB cavities and the resulting resonant frequencies split. Experimentally, we fabricated laterally-coupled PhC NB cavities using (InGaAsP) layer on the InP substrate. For sensing, we showed that the laterally coupled PhC NB cavities sensor exhibits higher sensitivity than the single PhC NB cavity. The higher sensitivity of laterally coupled PhC NB cavities is due to the strong evanescent coupling between nearby PhC NB cavities, which depends on the gap width and it is attributed to the large confinement of the electromagnetic field in the gap (air or liquid). As a result of the lateral coupling, both even (symmetric) and odd (asymmetric) modes exist. We show that even modes are more sensitive than odd modes. In addition, higher-order modes exhibit higher sensitivity. Hence, we characterized and examined the fabricated PhC NB cavity as a label-free biosensor, and it exhibits high figure of merit due to its high Q-factor. This illustrates a potentially useful method for optical sensing at nanoscale.

Effect of clustering on ellipsometric spectra of randomly distributed gold nanoparticles on a substrate.

We present a theoretical model for describing light scattering from randomly distributed Au nanoparticles on a substrate, including the clustering effect. By using the finite-element Green's function method and spherical harmonic basis functions, we are able to calculate the polarization-dependent reflectivity spectra of the system (modeled by randomly distributed nanoparticles coupled with clusters) efficiently and accurately. The calculated ellipsometric spectra of the system with clusters can adequately describe the experimental data for the whole frequency range. We find that the clustering effect leads to some prominent features in the low frequency range of the ellipsometric spectra, which are attributed to plasmonic resonances associated with the coupling of Au nanoparticles and clusters.

Optical cavity modes of a single crystalline zinc oxide microsphere.

A detailed study on the optical cavity modes of zinc oxide microspheres under the optical excitation is presented. The zinc oxide microspheres with diameters ranging from 1.5 to 3.0 µm are prepared using hydrothermal growth technique. The photoluminescence measurement of a single microsphere shows prominent resonances of whispering gallery modes at room temperature. The experimentally observed whispering gallery modes in the photoluminescence spectrum are compared with theoretical calculations using analytical and finite element methods in order to clarify resonance properties of these modes. The comparison between theoretical analysis and experiment suggests that the dielectric constant of the ZnO microsphere is somewhat different from that for bulk ZnO. The sharp resonances of whispering gallery modes in zinc oxide microspheres cover the entire visible window. They may be utilized in realizations of optical resonators, light emitting devices, and lasers for future chip integrations with micro/nano optoelectronic circuits, and developments of optical biosensors.

Thermoelectric properties of a quantum dot array connected to metallic electrodes.

The thermoelectric properties of a quantum dot array (QDA) embedded in a nanowire connected to metallic electrodes are investigated theoretically via the extended Hubbard model in the Coulomb blockade regime. Coupled quantum dots (QDs) with dot number N = 2-5 are considered. It is found that the thermoelectric properties converge to almost the same results when N approaches 5, indicating that our results are applicable for a QDA with a large number of QDs. Our studies indicate that in order to achieve the optimal figure of merit (ZT), it is preferable to have the QD energy levels above the Fermi energy (EF) of the electrodes of the QDA junction. The effects of QD energy level and interdot coupling variations (due to the QD size and position fluctuation) on the thermoelectric properties are also examined. We find that the QD size fluctuation significantly suppresses the maximum ZT in the weak interdot hopping strength (tℓ,j). We also find that the Seebeck coefficient is insensitive to tℓ,j and the tunneling rates when the QD energy levels are far above EF. For a given tℓ,j and large on-site Coulomb interactions, increasing the QD number N in the QDA would suppress the maximum ZT value. It is possible to achieve an optimal ZT larger than 3 by tailoring the physical parameters of the QDA junction system.