Theoretical Study Of Exciton-polaritons In Monolayer Transition Metal Dichalcogenides

Monolayer transition metal dichalcogenides are novel two-dimensional?2D?atomic crystals found after graphene,typically represented by MoS2,which has quickly become a research hotspot due to its excellent optical and electronic properties.MoS₂ belongs to hexagonal system,and the monolayer MoS₂ is composed of two layers of sulphur atoms sandwiching a layer of molybdenum atoms,and the atoms are combined by covalent bonds.The monolayer MoS₂ is a direct-bandgap semiconductor.Its first Brillouin zone has two unequal vertices: K points and-K points,corresponding to two valleys: K valley and –K valley.Spin-orbit coupling leads to the split of its valence band,and the antisymmetric breaking forces the valence band with the same electron spin direction to move in the opposite direction,which has an optical selection rule,that is,the left-handed circularly polarized light excites the K valley,and the right-handed The circularly polarized light excites the-K valley,and the mutual locking of this electron spin and valley is called valley polarization.The nature of monolayer MoS₂ valley polarization provides new opportunities for the development of spin switches and logic gate devices.Therefore,some people regard monolayer MoS₂ as an emerging semiconductor material that can replace silicon.The electrons of singer-layer MoS2 are excited from valence band to the conduction band by light,leaving positively charged holes in the valence band.The conduction band electrons and the valence band holes are bounded together by Coulomb interaction to form tightly bounded excitons.The excitons' binding energy is 0.5¹eV,which is two orders of magnitude higher than the exciton binding energy in traditional semiconductor quantum wells and grants excitons with possibility to exist at room temperature.exciton binding can provide the possibility of finding and applying valley polarization at room temperature,but due to the existence of inter-valley electron-hole exchange interaction,excitons are easily inter-valley scattered,which greatly restricts the valley polarization.It is reported that placing a monolayer of transition metal dichalcogenides into a microcavity is a feasible way to realize the existence of valley polarization at room temperature.By this method,the photons bounded in the cavity will couple with excitons,and form the exciton-polaritons.Such exciton-polaritons could greatly improve the polarization of the valley for their photon components' insensitivity to inter-valley scattering.Their enhancement to polarization enables the polarization of the valley at room temperature,and sheds light on realization of chiral light-substance interactions in valley-polarized electronic devices.The main work of this thesis includes:?1?We use the simple microcavity model to derive the expression of the exciton polarizability ? by Maxwell's equations.Using the two-band k p Hamiltonian,considering Coulomb interaction between all electrons and interaction between electronic systems with photons,we constructed the equation of motion of microscopic polarization by using the Heisenberg equation,and again obtained the expression of the exciton polarizability ?.Combining two expressions,we obtained the dispersion relation of the exciton-polaritons,which is used to calcuate Rabi splitting and prove the existence of strong coupling.During the derivation,we found that because of the anisotropy of the two-dimensional material,the non-resonant term can not be neglected when calculating the coupling of excitons and photons,which is far different from the three-dimensional case.?2?Considering the deviation between the photon component and the exciton component in the coupled mode calculated by the traditional coupled oscillator model method,we explored the reason for the existence of the bias and found that it is due to ignore the polarization of exciton components under electrical vectors.To get the more accurate coupled mode component,we constructed the macroscopic polarization equation of the exciton-polaritons,proved that the polarization process of excitons can be regarded as the polarization of a linear resonator,similar to the long-wave optical branch in an ionic crystal,and the energy density expression can be used to calculate the coupled mode component.Using the macroscopic polarization equation,we not only accurately calculated the coupled mode component,indicating that choosing the appropriate incident wave vector is essential for the valley polarization at room temperature,but also successfully explained the physical meaning of the parameters in the dispersion relation.?3?We use the semi-classical method of Fermi's gold rule to derive the expression of exciton lifetime,which is applicable to most two-dimensional transition metal dichalcogenides and semiconductor with similar band structure.Taking into account the broadening of the exciton energy caused by the exciton lifetime,we recalculate the dispersion relation and the splitting width of the exciton polarization and derive the lifetime of the exciton-polaritons.The results show that the existence of exciton lifetime reduces the width of the splitting and weakens the coupling.And it also proved that the lifetime of the exciton-polaritons is directly related to the content of long-lived photons,indicating that manipulating and utilizing middle polariton MP is an important way to achieve valley polarization.