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The electronic band structure of MoS2, MoSe2, WS2, and WSe2, crystals has been studied at various hydrostatic pressures experimentally by photoreflectance (PR) spectroscopy and theoretically within the density functional theory (DFT). In the PR spectra direct optical transitions (A and B) have been clearly observed and pressure coefficients have been determined for these transitions to be: αA = 2.0 ± 0.1 and αB = 3.6 ± 0.1 meV/kbar for MoS2, αA = 2.3 ± 0.1 and αB = 4.0 ± 0.1 meV/kbar for MoSe2, αA = 2.6 ± 0.1 and αB = 4.1 ± 0.1 meV/kbar for WS2, αA = 3.4 ± 0.1 and αB = 5.0 ± 0.5 meV/kbar for WSe2. It has been found that these coefficients are in an excellent agreement with theoretical predictions. In addition, a comparative study of different computational DFT approaches has been performed and analyzed. For indirect gap the pressure coefficient have been determined theoretically to be −7.9, −5.51, −6.11, and −3.79, meV/kbar for MoS2, MoSe2, WS2, and WSe2, respectively. The negative values of this coefficients imply a narrowing of the fundamental band gap with the increase in hydrostatic pressure and a semiconductor to metal transition for MoS2, MoSe2, WS2, and WSe2, crystals at around 140, 180, 190, and 240 kbar, respectively.

Bi-induced changes in the band structure of Ga-V-Bi and In-V-Bi alloys are calculated within the density functional theory (DFT) for alloys with Bi ⩽3.7% and the observed chemical trends are discussed in the context of the virtual crystal approximation (VCA) and the valence band anticrossing (VBAC) model. It is clearly shown that the incorporation of Bi atoms into III-V host modifies both the conduction band (CB) and the valence band (VB). The obtained shifts of bands in GaP 1−x

Band gap alignment in GaAs1−xBix/GaAs quantum wells (QWs) was studied experimentally by photoreflectance (PR) and theoretically, ab initio, within the density functional theory in which the supercell based calculations are combined with the alchemical mixing approximation applied to a single atom in a supercell. In PR spectra, the optical transitions related to the excited states in the QW (i.e., the transition between the second heavy-hole and the second electron subband) were clearly observed in addition to the ground state QW transition and the GaAs barrier transition. This observation is clear experimental evidence that this is a type I QW with a deep quantum confinement in the conduction and valence bands. From the comparison of PR data with calculations of optical transitions in GaAs1−xBix/GaAs QW performed for various band gap alignments, the best agreement between experimental data and theoretical calculations has been found for the valence band offset of 52 ± 5%. A very similar valence band offset was obtained from ab initio calculations. These calculations show that the incorporation of Bi atoms into GaAs host modifies both the conduction and the valence band. For GaAs1−xBix with 0 < x < 0.074, the conduction band shifts lineary at a rate of ∼33 meV per % Bi, which only slightly decreases with Bi concentration. Whereas the valance band shift is clearly non-linear. Reducing initially at a rate of ∼51 meV per % Bi for low concentrations of Bi and then at a significantly reduced rate of ∼20 meV per % Bi near the end of the studied composition range. The overall reduction rate of the band gap is parabolic and the reduction rates change from ∼84 to ∼53 meV per % Bi for lower and higher Bi concentrations, respectively. The calculated shifts of valence and conduction bands give the variation of valence (conduction) band offset between GaAs1−xBix and GaAs in the range of ∼60%–40% (∼40%–60%), which is in good agreement with our conclusion derived from PR measurements.

Modulated reflectance (contactless electroreflectance (CER), photoreflectance (PR), and piezoreflectance (PzR)) has been applied to study direct optical transitions in bulk MoS2, MoSe2, WS2, and WSe2. In order to interpret optical transitions observed in CER, PR, and PzR spectra, the electronic band structure for the four crystals has been calculated from the first principles within the density functional theory for various points of Brillouin zone including K and H points. It is clearly shown that the electronic band structure at H point of Brillouin zone is very symmetric and similar to the electronic band structure at K point, and therefore, direct optical transitions at H point should be expected in modulated reflectance spectra besides the direct optical transitions at the K point of Brillouin zone. This prediction is confirmed by experimental studies of the electronic band structure of MoS2, MoSe2, WS2, and WSe2 crystals by CER, PR, and PzR spectroscopy, i.e., techniques which are very sensitive to critical points of Brillouin zone. For the four crystals besides the A transition at K point, an AH transition at H point has been observed in CER, PR, and PzR spectra a few tens of meV above the A transition. The spectral difference between A and AH transition has been found to be in a very good agreement with theoretical predictions. The second transition at the H point of Brillouin zone (BH transition) overlaps spectrally with the B transition at K point because of small energy differences in the valence (conduction) band positions at H and K points. Therefore, an extra resonance which could be related to the BH transition is not resolved in modulated reflectance spectra at room temperature for the four crystals.

Contactless electroreflectance is applied to study the band gap (E 0) and spin-orbit splitting (D SO) in InP 1Àx Bi x alloys with 0 < x 0.034. The E 0 transition shifts to longer wavelengths very significantly (À83 meV/% Bi), while the E 0 þ D SO transition shifts very weakly (À13 meV/% Bi) with the rise of Bi concentration. These changes in energies of optical transitions are discussed in the context of the valence band anticrossing model and ab initio calculations. Shifts of E 0 and E 0 þ D SO transitions, obtained within ab-initio calculations, are À106 and À20 meV per % Bi, respectively, which is in a good agreement with experimental results. V

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Optical transitions in atomically thin MoS2 samples made by sulfidation of a metallic molybdenum layer have been studied by photoreflectance (PR) and photoacoustic (PA) spectroscopy. The obtained spectra are compared with PR and PA spectra of bulk MoS2. It is shown that the absorption edge observed in the PA spectrum shifts to blue when moving from the bulk MoS2 to the atomically thin MoS2 layers, whereas the direct optical transitions at the K point of the Brillouin zone (A and B transitions), which are observed in the PR spectrum, do not shift spectrally in a significant manner. On the other hand, the AH transition, which is related to the direct optical transition at the H point of the Brillouin zone and is typical of bulk MoS2, is not observed for atomically thin MoS2 layers. Moreover, a strong and broad PR resonance related to the band nesting (C transition) is identified in the PR spectra of studied samples. In this case, C and CH transitions are observed for bulk MoS2, while only a C transition is observed for atomically thin MoS2.