The transition metal dichalcogenides are about 60 in number. Two-thirds of these assume layer structures. Crystals of such materials can be cleaved down to less than 1000 A and are then transparent in the region of direct band-to-band transitions. The transmission spectra of the family have been correlated group by group with the wide range of electrical and structural data available to yield useful working band models that are in accord with a molecular orbital approach. Several special topics have arisen; these include exciton screening, d-band formation, and the metal/insulator transition; also magnetism and superconductivity in such compounds. High pressure work seems to offer the possibility for testing the recent theory of excitonic insulators.

The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties

The demand for compact ultraviolet laser devices is increasing, as they are essential in applications such as optical storage, photocatalysis, sterilization, ophthalmic surgery and nanosurgery. Many researchers are devoting considerable effort to finding materials with larger bandgaps than that of GaN. Here we show that hexagonal boron nitride (hBN) is a promising material for such laser devices because it has a direct bandgap in the ultraviolet region. We obtained a pure hBN single crystal under high-pressure and high-temperature conditions, which shows a dominant luminescence peak and a series of s-like exciton absorption bands around 215 nm, proving it to be a direct-bandgap material. Evidence for room-temperature ultraviolet lasing at 215 nm by accelerated electron excitation is provided by the enhancement and narrowing of the longitudinal mode, threshold behaviour of the excitation current dependence of the emission intensity, and a far-field pattern of the transverse mode.

Direct-bandgap properties and evidence for ultraviolet lasing of hexagonal boron nitride single crystal.

We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

Atomically thin materials such as graphene and monolayer transition metal dichalcogenides (TMDs) exhibit remarkable physical properties resulting from their reduced dimensionality and crystal symmetry. The family of semiconducting transition metal dichalcogenides is an especially promising platform for fundamental studies of two-dimensional (2D) systems, with potential applications in optoelectronics and valleytronics due to their direct band gap in the monolayer limit and highly efficient light-matter coupling. A crystal lattice with broken inversion symmetry combined with strong spin-orbit interactions leads to a unique combination of the spin and valley degrees of freedom. In addition, the 2D character of the monolayers and weak dielectric screening from the environment yield a significant enhancement of the Coulomb interaction. The resulting formation of bound electron-hole pairs, or excitons, dominates the optical and spin properties of the material. Here recent progress in understanding of the excitonic properties in monolayer TMDs is reviewed and future challenges are laid out. Discussed are the consequences of the strong direct and exchange Coulomb interaction, exciton light-matter coupling, and influence of finite carrier and electron-hole pair densities on the exciton properties in TMDs. Finally, the impact on valley polarization is described and the tuning of the energies and polarization observed in applied electric and magnetic fields is summarized.

Colloquium : Excitons in atomically thin transition metal dichalcogenides

This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrysta...

Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems

By using the effective-mass theory for exciton, the allowed and forbidden direct interband transitions in extremely anisotropic semiconductors are discussed. In this case, the problem is reduced to solving the Schrodinger equation for a hypothetical two-dimensional hydrogen atom. The bound and unbound solutions of the equation are obtained, and the absorption intensities in the discrete, quasi-continuous, and continuous spectral regions are calculated. It is shown that, in the allowed transitions, a small peak may appear just above the absorption edge because of the Coulomb interaction between an excited electron and a hole. This result is compared with the experimental curves of the absorption in layer-type semiconductors, CaS, GaSe, and GaTe.

Interband Optical Transitions in Extremely Anisotropic Semiconductors. I. Bound and Unbound Exciton Absorption

By using the effective-mass theory for exciton, the allowed and forbidden direct interband transitions in extremely anisotropic semiconductors are discussed. In this case, the problem is reduced to solving the Schrodinger equation for a hypothetical two-dimensional hydrogen atom. The bound and unbound solutions of the equation are obtained, and the absorption intensities in the discrete, quasi-continuous, and continuous spectral regions are calculated. It is shown that, in the allowed transitions, a small peak may appear just above the absorption edge because of the Coulomb interaction between an excited electron and a hole. This result is compared with the experimental curves of the absorption in layer-type semiconductors, GaS, GaSe, and GaTe.

Interband Optical Transitions in Extremely Anisotropic Semiconductors

Optical Absorption Edge in Layer-Type Semiconductors

Optical rotatory dispersion of dihedral metal complexes with (3d) n ( n =1, … 9, except for n =5) is studied by means of purely ionic model. Rotational strengths of the first absorption bands are given by considering the second-order asymmetric distortion of the octahedral d -orbitals due to chelation. Taking into account the splitting of the band, dispersion curve is obtained and compared with experiments. Qualitative agreement is obtained for [Crox 3 ]. A physical model is introduced in order to discuss the relation between the geometrical structure and the sign of the optical rotation. With this model, it is shown that for [Coen 3 ], twisting of the ethylenediamine molecules seems to be responsible to the rotatory dispersion. Finally, it is emphasized that molecular orbital treatment is necessary for further quantitative discussions.

Optical Rotatory Dispersion of Dihedral Metal Complexes

The absorption spectrum in the excited states of ruby reported by Kushida is analyzed on the basis of the crystalline field or ligand field theory. Remarkably sharp absorption peaks observed in the infrared region are identified to the t 2 g 3 2 E g → t 2 g 3 2 T 2 g transitions, and a temperature-sensitive broad band also in this region is identified to the t 2 g 3 2 T 1 g → t 2 g 3 2 T 2 g transitions. Several broad peaks observed in the visible region are assigned to the t 2 g 3 2 E g → t 2 g 2 ( 3 T 1 g ) e g 2 T 2 g , t 2 g 2 ( 1 T 2 g ) e g 2 T 1 g , t 2 g 2 ( 3 T 1 g ) e g 2 T 1 g , t 2 g 2 ( 1 T 2 g ) e g 2 T 2 g transition. Unidentified broad peaks in the infrared region are discussed in some detail with the assumption that they are due to the phonon-induced electric dipole transitions.

Masaki Shinada

Papers

Interband Optical Transitions in Extremely Anisotropic Semiconductors. I. Bound and Unbound Exciton Absorption

Interband Optical Transitions in Extremely Anisotropic Semiconductors

Optical Absorption Edge in Layer-Type Semiconductors

Optical Rotatory Dispersion of Dihedral Metal Complexes

Absorption Spectrum of Optically Pumped Ruby. II. Theoretical Analyses