Exciton spectra of monolayer transition metal dichalcogenides (TMDs) in various dielectric environments are studied using an effective mass model incorporating a screened two-dimensional (2D) electron-hole interaction described by the Keldysh potential. Exciton states are calculated by solving a radial equation (RE) with a shooting method including Runge-Kutta integration. Particular attention is paid to the simple models for 2D exciton calculation. The 2D hydrogen model yields much lower exciton energies than the Rydberg series from the RE solution. The screened hydrogen model (SHM) [Phys. Rev. Lett. 116, 056401 (2016)] is examined by comparing its exciton spectra with the RE solutions. While the SHM is found to describe the nonhydrogenic exciton Rydberg series (i.e., the energy's dependence on main quantum number n) reasonably well, it fails to account for the linear decrease of the exciton energy with the orbital quantum number m. The exciton Bohr orbit shrinks as |m| becomes larger resulting in increased strength of the electron-hole interaction and a decrease of the exciton energy. The exciton effective radius expression of the SHM can characterize the exciton radius's dependence on n, but it cannot properly describe the exciton radius's dependence on m, which is the cause of the SHM's poor description of the exciton energy's m-dependence. For monolayer WS 2 on the SiO 2 substrate, our calculated s exciton Rydberg series agrees closely with that measured by optical reflection spectroscopy [Phys. Rev. Lett. 113, 076802 (2014)], while the calculated p excitons offer an explanation for the two broad features of a two-photon absorption spectrum [Nature 513, 214 (2014)]. Our calculated exciton energies for monolayer TMDs in various dielectric environments compare favourably with experimental data. Variational wave functions are obtained for a number of strongly bound exciton states and further used to study the Stark effects in 2D TMDs, an analytical expression being deduced which yields a redshift of the ground state energy to a good accuracy. The numerical solution of the RE combined with the variational method provides a simple and effective approach for the study of 2D excitons in monolayer TMDs. * Electronic address: phyjzzhang@jlu.edu.cn 2

Using two pairs of macroscopic equations deduced from a dipole lattice model including electronic polarization (EP) of ions and local field effects (LFEs) self-consistently, optical lattice vibrations in monolayer hexagonal boron nitride (BN) are studied theoretically for both in-plane and out-of-plane motions. Longitudinal and transverse optical (LO and TO) modes and out-of-plane (ZO) modes are derived, and explicit expressions are obtained for phonon dispersion, group velocity and density of states. The analytical phonon dispersion relations describe previous numerical results very well; the LO phonon dispersion is identical to the analytical expression of Sohier et al, which shows the degeneracy of the LO and TO modes at Γ and the splitting at finite wavevectors due to the long-range macroscopic field. Whilst relating to microscopic quantities, the linear coefficients of the lattice equations are determined by first-principles calculated quantities (such as macroscopic susceptibilities). Therefore the EP and LFEs on the vibrational properties are studied. With no EP or LFEs, all the phonon frequencies are overestimated significantly. Including EP, the LFEs increase (decrease) the in-plane (out-of-plane) dielectric susceptibility by a factor of 2.5-3.5. Both ionic EP and LFEs should be included to obtain an accurate description of the lattice dynamics.

Using the dielectric continuum (DC) and three-dimensional phonon (3DP) models, energy relaxation of the hot electrons in the quasi-two-dimensional channel of lattice-matched InAlN/AlN/GaN heterostructures is studied theoretically, taking into account non-equilibrium polar optical phonons, electron degeneracy, and screening from the mobile electrons. The electron power dissipation and energy relaxation time due to both half-space and interface phonons are calculated as functions of the electron temperature T e using a variety of phonon lifetime values from experiment, and then compared with those evaluated by the 3DP model. Thereby particular attention is paid to examination of the 3DP model to use for the hot-electron relaxation study. The 3DP model yields very close results to the DC model: with no hot phonons or screening the power loss calculated from the 3DP model is 5% smaller than the DC power dissipation, whereas slightly larger 3DP power loss (by less than 4% with a phonon lifetime from 0.1 to 1 ps) is obtained throughout the electron temperature range from room temperature to 2500 K after including both the hot-phonon effect (HPE) and screening. Very close results are obtained also for energy relaxation time with the two phonon models (within a 5% of deviation). However the 3DP model is found to underestimate the HPE by 9%. The Mori-Ando sum rule is restored by which it is proved that the power dissipation values obtained from the DC and 3DP models are in general different in the pure phonon emission process, except when scattering with interface phonons is sufficiently weak, or when the degenerate modes condition is imposed, which is also consistent with Register's scattering rate sum rule. The discrepancy between the DC and 3DP results is found to be caused by how much the high-energy interface phonons contribute to the energy relaxation: their contribution is enhanced in the pure emission process but is dramatically reduced after including the HPE. Our calculation with both phonon models has obtained a great fall in energy relaxation time at low electron temperatures (T e < 750 K) and slow decrease at the high temperatures with the use of decreasing phonon lifetime with T e . The calculated temperature dependence of the relaxation time and the high-temperature relaxation time ∼0.09 ps are in good agreement with experimental results.

Long wavelength polar vibrations in monolayer (ML) transition metal dichalcogenides (TMDs) are systematically studied for in-plane and out-of-plane motions, using two pairs of macroscopic equations deduced from a microscopic dipole lattice model accounting for local field effects (LFEs) and electronic polarization (EP). Longitudinal and transverse optical modes and out-of-plane modes are derived, and the analytical expressions describe previous first-principles calculations very well. Owing to the LFEs, the in-plane dielectric susceptibilities of ML TMDs are one order of magnitude greater than the out-of-plane susceptibilities. Furthermore, the effects of the dielectric environment on the polar vibrations are studied. Both EP and LFEs should be accounted for obtaining an accurate evaluation of dielectric susceptibility and key lattice-dynamical properties such as Born charge and phonon dispersion. A two-dimensional (2D) Lyddane–Sachs–Teller relation and a frequency–susceptibility relation are derived for in-plane and out-of-plane motions, relating the 2D dielectric functions or susceptibilities to the polar phonon frequencies. The results are also compared in detail with those of ML hexagonal boron nitride.

Phonon polaritons (PHPs) in freestanding and supported multilayers of hexagonal boron nitride are systematically studied using a macroscopic optical-phonon model. The PHP properties such as confinement, group velocity, propagation quality factor (PQF), and wavelength scaling are studied. Owing to high-frequency screening, there is an upper frequency limit making the two-dimensional (2D) PHPs have a frequency band and also a maximum PQF occurs near the center frequency. The substrate’s dielectric response should be included to accurately calculate the PHP properties. While the simple electrostatic approximation (ESA) is valid for PHPs with frequencies [Formula: see text] above [Formula: see text] (e.g., [Formula: see text] for the 30-layers; [Formula: see text] is the [Formula: see text] point optical-phonon frequency), it fails to describe the PHP properties near [Formula: see text] and the effect of retardation should be included for a proper description. The PHP wavelength vs layer thickness near [Formula: see text] deviates significantly from a linear scaling law given by the ESA due to strong coupling of photons and longitudinal optical phonons. The calculated PHP dispersion and scaling are compared with experimental data of a number of spectroscopic studies and found to be in good agreement for most of the results. While the frequency of incident light should be near the center frequency to maximize the PQF, the PHP wavelength, confinement, and propagation length can be engineered by varying the multilayer thickness and its dielectric environment.