Temperature-dependent optical constants of monolayer $${\text {MoS}}_2$$, $${\text {MoSe}}_2$$, $${\text {WS}}_2$$, and $${\text {WSe}}_2$$: spectroscopic ellipsometry and first-principles calculations

Abstract The temperature-dependent ( $$T = 4.5 \, \hbox {-} \, 500 \, \hbox {K}$$ T = 4.5 - 500 K ) optical constants of monolayer $${\text {MoS}}_2$$ MoS 2 , $${\text {MoSe}}_2$$ MoSe 2 , $${\text {WS}}_2$$ WS 2 , and $${\text {WSe}}_2$$ WSe 2 were investigated through spectroscopic ellipsometry over the spectral range of 0.73–6.42 eV. At room temperature, the spectra of refractive index exhibited several anomalous dispersion features below 800 nm and approached a constant value of 3.5–4.0 in the near-infrared frequency range. With a decrease in temperature, the refractive indices decreased monotonically in the near-infrared region due to the temperature-dependent optical band gap. The thermo-optic coefficients at room temperature had values from $$6.1 \times 10^{-5}$$ 6.1 × 10 - 5 to $$2.6 \times 10^{-4} \, \hbox {K}^{-1}$$ 2.6 × 10 - 4 K - 1 for monolayer transition metal dichalcogenides at a wavelength of 1200 nm below the optical band gap. The optical band gap increased with a decrease in temperature due to the suppression of electron–phonon interactions. On the basis of first-principles calculations, the observed optical excitations at 4.5 K were appropriately assigned. These results provide basic information for the technological development of monolayer transition metal dichalcogenides-based photonic devices at various temperatures.