Theoretical Investigations On The Linear And Nonlinear Optical Properties Of Selenium And Tellurium With Different Dimensions

The interaction between strong light field and matters may cause significant nonlinear optical response.Non-centrosymmetric materials with large second-order nonlinear susceptibility exert crucial impacts on the development of modern optical and optoelectronic devices,such as lasers,frequency converters,electro-optic modulators and switches.As a special case of sum frequency,the second harmonic is one of the best-known nonlinear optical responses.Since the 1960s,the second-harmonic generation(SHG)has been investigated extensively in bulk semiconductors and more recently also in one-dimensional and two-dimensional systems.In addition,due to high sensitivity to local structural symmetry,the SHG has become a powerful tool for exploring surfaces and interfaces.Linear electro-optic effect(LEO)can also be realized in nonlinear materials,using electrical signals to control the amplitude,phase and direction of a beam of light,and then can be widely used in high-speed optical modulation and sensing devices.As a third nonlinear optical response,the bulk photovoltaic effect(BPVE)effect has become a research hotspot in recent years.The BPVE refers to the generation of photocurrent and photovoltage in materials without inversion symmetry.In the early days,it was first studied in ferroelectric oxides and other bulk materials.In recent years,several research groups have theoretically studied the bulk photovoltaic effect in two-dimensional systems and found that large shift photocurrent is generated.Therefore,we have empolyed the first-principles method based on the density functional theory to study the linear and nonlinear optical properties of bulk,twodimensional and one-dimensional tellurium and selenium systems.The main research contents include:In the first part of this dissertation,using first-principles method together with the generalized gradient approximation plus scissors correction,we have studied the linear and nonlinear optical(NLO)properties of trigonal selenium and tellurium.The helical chainlike structures of selenium and tellurium possess interesting properties such as nontrivial band topology,gyrotropic effects,and nonlinear optical responses.The results suggest that both systems exhibit large second-harmonic generation and linear electro-optic effect,especially for tellurium.Trigonal tellurium possesses large SHG coefficient in the photon energy range of 0～3 eV,and the maximum magnitude of such SHG coefficient is around 3600 pm/V,exceeding the widely used NLO material GaN by 16 times.Furthermore,trigonal tellurium exhibits gigantic static SHG coefficient χxyy(2)(0)(～1080 pm/V).This maximum SHG coefficient is higher than the maximal second-order nonlinear susceptibility of GaN by 100 times.On the other hand,selenium possesses large LEO coefficient rxxx(0)(～3.6 pm/V),which is 6 times larger than that of GaN.Therefore,bulk tellurium and selenium will have valuable applications in nonlinear optical devices,such as frequency converters,electro-optic switches and optical signal modulators.Further calculations reveal that the χxxx(2)and χxyz(2)values of the two chiral structures of Se and Te are the same,but the sign in χxyz(2)is inverse,indicating that the SHG sectroscopy is a useful probe for studying their chirality.It is important that the calculated static dielectric constants as well as SHG coefficients at CO2 laser frequency agree well with the experimental results.Finally,selenium and tellurium have stronger NLO responses than semiconductors with similar band gaps,due to their quasi-one-dimensional structure with directional covalent bonds and lone pair electrons.These findings will contribute to searching for new materials with large NLO coefficients.In the second part,we have carried out systematic first-principles studies on the electronic,linear and nonlinear optics properties of two-dimensional(2D)selenium and tellurium.The studies are based on density functional theory and generalized gradient approximation plus scissors correction using band gaps from the relativistic hybrid Heyd-Scuseria-Erzerhof functional.The basic structures of these 2D materials are determined by SCAN exchange-correlation functional.Remarkably,we find that 2D Se and Te have large second harmonic generation,linear electro-optic effect and bulk photovoltaic effect.Trilayer(TL)tellurium,in particular,has large second harmonic coefficient χxxx(2)(～15000 pm/V),being up to 65 times larger than that of GaN.Bilayer(BL)Te possesses large static SHG coefficient χxyy(2)(0)(～1080 pm/V),which exceeds 100 times larger than that of GaN.Moreover,ML Se has prominent SHG coefficient,and the maximum value(～160 pm/V)of SHG coefficient χxyy(2)(0)exceeds that of GaN by 6 times.For the linear electro-optic effects,ML Se and BL Te exhibit remarkable linear electro-optic coefficients rxyy(0)and ryzx(0),respectively.Furthermore,trilayer Te possesses strong bulk photovoltaic effect with shift current conductivity of～440μA/V2,being even larger than that of GeS.Although the 2D selenium has comparable photovoltaic effect as that of bulk system,the photovoltaic effect of TL tellurium is so significant that it is more than five times larger than that of 3D system.Finally,the analysis of band structures shows that the 2D selenium and tellurium have stronger nonlinear optical responses than 3D systems,mainly because the 2D materials have low-dimensional structures with high anisotropy,directional covalent bonds,lone pair electrons and relatively small band gaps.In the third part,by performing first-principles calculations,we have studied the linear and nonlinear optical properties of one-dimensional(1D)selenium and tellurium.The results indicate that both the materails exhibit significant nonlinear optical responses,particularly for 1D selenium,which possesses a large second harmonic coefficient χxyz(2)(～1500 pm/V)being up to 7 times larger than that of GaN and even is larger than that of the corresponding bulks.On the other hand,1D tellurium also has significant second-order polarizability and linear electro-optic coefficient.In particular,1D Te chain shows large shift current response and the maximum value exceeds 2 times larger than that of BaTiO3.Therefore,1D Se and Te materials have potential applications in solar energy conversion,photoelectric switch,electro-optical switches,and so on.Finally,by the analysis of the energy band structures and the deformation charge densities,we found that the reason 1D Se and Te have strong NLO effects is due to their one-dimensional structures with high anisotropy,strong covalent bonds and lone pair electrons.Our findings will be helpful for further experimental and theoretical searches for excellent materials with large NLO effect.