The effect of magnetic pressure on the optical response of vanadium dioxide

Abstract

Several physical parameters, such as temperature, pressure, exciton confinement effect, quantum size effect and magnetic field effect, influence the gap of a semiconductor. In this study, we focuss on the impact of a directed magnetic field applied along one direction (oz) on bulk vanadium dioxide ($\hbox {VO}_2$), a material with a gap energy of 0.7 eV. This magnetic pressure resulted in the widening of the spectral absorption range of the material. To understand the effects of the magnetic field, we solved the Schrödinger equation of an electron in the conduction band. By neglecting the Coulombic interaction term and considering the spin of the electron, we obtained the energy of the Landau levels. Our results showed that the $\hbox {VO}_2$ gap growth was relatively low, indicating that the technique used in this study may have a limited impact on the material. This paper investigates how the reduced mass affects the optical properties of $\hbox {VO}_2$ quasielectron holes. The results show that when the reduced mass is increased from 3$m_0$ to 21$m_0$, the absorption gap increases, favouring an increase in absorption. This suggests that reduced mass can be used to adapt the optical properties of the materials. However, it is important to note that this study focusses on a specific case. Other factors may also affect the optical properties of the materials. For example, when a magnetic field of intensity (30 T at 500 T, where T is the unit of magnetic B-field) is applied and the material is subjected to a magnetic pressure P, there is a noticeable change in the gap energy. The objective of this study is to provide insight into the impact of a uniform magnetic field on the semiconducting state of $\hbox {VO}_2$ and how it widens the gap in the material. The findings of this study can contribute to a better understanding of the optical properties of $\hbox {VO}_2$ and help develop new applications.

Appendix

$$\begin{aligned}{} & {} {[}\sigma _{{x}}, \sigma _{{y}}]=2 {i} \sigma _{{z}} \end{aligned}$$

(21)

$$\begin{aligned}{} & {} {[}\sigma _{{y}}, \sigma _{{z}}]=2 {i} \sigma _{{x}} \end{aligned}$$

(22)

$$\begin{aligned}{} & {} {[}\sigma _{{z}}, \sigma _{{x}}]=2 {i} \sigma _{{y}} \end{aligned}$$

(23)

$$\begin{aligned}{} & {} \gamma =\frac{2}{\hbar } \mu _{{B}} \end{aligned}$$

(24)

$$\begin{aligned}{} & {} \mu _{{B}}=\frac{{e\hbar }}{2 {~m}^*} \end{aligned}$$

(25)

$$\begin{aligned}{} & {} \vec {{M}}=-\gamma \vec {{S}} \end{aligned}$$

(26)

$$\begin{aligned}{} & {} \frac{1}{m_c}+\frac{1}{m_v}=\frac{1}{\mu } \end{aligned}$$

(27)

$$\begin{aligned}{} & {} \omega _{{c}}=\frac{{eB}}{\mu } \end{aligned}$$

(28)

$$\begin{aligned}{} & {} \gamma =\frac{\hbar \omega _{{c}}}{2 {R}^*}=\mu _{{B}} \cdot \frac{{m}_0}{{~m}^*} \cdot \frac{{B}}{{R}^*} \end{aligned}$$

(29)

$$\begin{aligned}{} & {} {R}^*=\frac{{m}^* {e}^4}{2 \varepsilon _{\infty }^2 \hbar ^2}. \end{aligned}$$

(30)