Study On Collective Excitation Spectrum In Low Dimensional Systems

Research on collective excitations in semiconductor low dimensional structures such as superlattices,quantum wells and quantum wires is an important hotspot in condensed matter physics.Theoretical analysis and experimental results show that plasmons in three-dimensional systems are hard to excite because there is a considerable energy gap in the excitation spectra of plasmon when wave vector tends to zero.On the contrary,the dispersion relation of plasmons in two dimensional systems behaves as ?q=?p(?)+3/8vF2q3/2.It shows that the plasmon of the two-dimensional system has no energy gap and is easy to excite.In this thesis,according the self-consistent field(SCF)theory,we derive the general expression of the dielectric function tensor of plasmons in low dimensional systems.Applying our general expression to quantum well structures,we deduce the equation to determine the dispersion relations of the plasmons in quantum wells.According to the many-body theory and based on the eigen equation of density operator,we derive the general expression of the dielectric function matrix of plasmons in low dimensional systems.As an example,we apply our results to quantum well structures and obtain the equation that the dispersion relation of the plasmons satisfies.Based on the finite-subband model,we derive the dispersion relations of plasmons in semiconductor quantum well superlattices for three different representations(tensor representation,matrix representation and Fourier representation),respectively,and establish the transform relations among the matrix expression,the tensor expression,and Fourier expression.We perform numerical computation and confirm the equivalence of the three expressions of dielectric function on plasmons in these three representations.We investigate the interwell coupling effect on the dispersion of the plasmons.We find that in the case of qz?0,as the width of the barrier layer decreases,the dispersion relations of the plasmons change little.On the contrary,in the case of qz = 0,the dispersion relation of the plasmons change remarkably.The frequency of the intra-subband mode increases with the decrease of the barrier layer.When the coupling is strong enough,this mode enters the single particle excitation region and disappears.The frequency of the inter-subband modes decreases as the width of the barrier layer decreases.