Theoretical Study On Transport And Optical Properties For Phosphorene And Its Nanostructures

Black phosphorus,a new layered two-dimensional(2D)material,possesses a direct band gap depending on the thicknesses of black phosphorus samples,a high carrier mobility and strong anisotropy of the excellent physical properties,which bridge the gap between graphene and monolayer transition metal dichalcogenides in the field of optoelectronic devices and become the one of the most potential materials of nano-optoelectronic devices.Phosphorene nanoribbon(PNRs)is the basic building block of future phosphrous photoelectric devices,and the few lay-er and monolayer phosphorene nanoribbons have been successfully synthesized in experiment.Due to the quantum confinement effect and the unique edge effect,the PNRs shows different properties from the 2D black phosphorus.The typical zigzag edged PNRs(ZPNRs)are always metallic due to the quasi-flat edge states,and the armchair edged PNRs(APNRs)are semiconductors with a direct band gap.Most of the previous works on PNRs are based on the first-principles calcu-lation or numerical diagonalization utilizing the Tight Binding(TB)model,and the work of analytical calculation is still lacking.The systematic and complete an-alytical calculation of PNRs is helpful to understand its electronic structure and optical properties,and provides a theoretical basis for phosphoene-based semicon-ductor optoelectronic devices.In this thesis,based on the TB and k·p model,under the framework of linear response theory,and using the scattering matrix and Green function method,we study the quantum transport and optical properties of phosphorene and its nanoribbons,the main work is described as follow:1.We theoretically investigate the Landau level(LLs)and quantum magneto-capacitace(MC)of monolayer BP under a parabolic potential.We find the LLs parabolically depend on the wavevectors and show strong anisotropy when the parabolic potential exerted along different crystal orientations.We obtain ana-lytical expression of LLs from a decoupled single-band Hamiltonian,which agrees well with the numerical data in the low energy regime.The analytical results clearly illustrate that the LLs no longer linearly depend on the magnetic field and LL index in the low energy regime even at the?point due to the confinement of parabolic potential.The anisotropic quantum MC spectrum directly reflect the structure of LLs,and the energy difference between two adjacent peaks in the MC spectrum can be used to determine the band parameters i.e.,the effective masses and the inter-band coupling of phosphorene.2.We analytically study the electronic structure and optical transition of ZPNRs.By directly solving the discrete Schrodinger equation,we obtain the ana-lytical solution of the dispersion relation for the bulk states of ZPNRs.By adding a correction terms,we obtain the dispersion relations of edge states which are in good agreement with the results of numerical diagonalization.According to the symmetry of the supercell and the optical transition matrix element calculated an-alytically,we find the inter-(intra-)band selection rule is?n=odd(even)because the parity of the wavefunction corresponding to the n-th subband in the conduction(valence)band is(-1)ⁿ[(-1)⁽ⁿ⁺¹⁾]owing to the presence of C_2xsymmetry.Exter-nal electric field and impurities will break C_2xsymmetry of even-N ZPNRs,which make the optical transitions between any subbands are possible and enhance op-tical absorption.However,for odd-N ZPNRs the optical transitions between any subbands are possible owing to the absence of C_2xsymmetry.3.We theoretically investigate the electronic structure and optical properties of APNRs under the modulation of uniaxial strain.We analytically obtain the en-ergy spectrum and wavefunction,and reveal the band gap scaling law as 1/(N+1)²for APNRs in the presence and absence of uniaxial strain.We find the band gap of APNRs linearly increases(decreases)with increasing in-plane uniaxial tensile(compressive)strain?_x/y,but shows contrary dependence on the out-of-plane uni-axial strain?_z.The effective mass versus strain exhibits the same behavior to that of band gap but with nonlinear dependence.The inter-band optical transitions obey the rule?=n-n^?=0,but the intra-band transitions are forbidden for both pristine and strained APNRs originating from the orthogonality between the wavefunctions of A and B sublattices belonging to different subbands.The trans-verse electric field or impurities can enhance the optical absorption by breaking the wavefunction orthogonality,which results in that the optical transitions between any subbands are all possible and the optical absorption can be enhanced.4.We investigate the electronic structure and transport properties of ZPNRs modulated by the side gate and discover a phenomenon of quantitative modulation of conductance platform.Applied the side gate with different width along the restricted direction of ZPNRs,only the edge state corresponding to the edge in the range of electric field moves,and the bulk band almost does not change.Under the co-modulation of magnetic and electric field,the oscillatory bending appears on the original horizontal LLs,and the frequency of oscillation increase with the increase of energy level index.Side gate with different width will cause the LLs become bend in different wave vector region,and there are some abnormal conductance peaks appear on the conductance platform,whose values are exactly equal to the number of incoming modes at the same energy.Observing the electron local density of state and the distribution of current in real space,we find the number of transmission modes in the band are corresponding to the channel of current.The number of transmission modes in the band oscillating bending part increases,and the corresponding current channels increase,which make the conductance peaks with a integer height appears on the conductance platform.It can be seen that the height of the conductance platform can be controlled quantitatively by regulating the width and magnitude of side gate,which can promote the design and development of photoelectric devices with logic function.