Optical Conductivity Of The Two-dimensional Lattice

The optical properties of strongly interacting electron systems closely relate to theproperties of the high Tc materials, and optical absorption is one of the basic tools instudies of the spectral properties of strongly correlated electron systems[1,2]. The opticalconductivityσ(ω) represents the rate at which electrons absorb the incident photons atenergyω, and is a useful probe in determining electronic characteristics of the materialunder study.We study D and optical conductivity of the two-dimensional(2D) lattices at halffilling with hopping integrals modulated by staggered magnetic fluxes(SMF). Althoughthe energy spectral and transport properties of lattice electrons under spatially modulatedmagnetic fields have been investigated in detail[3–10], the corresponding optical propertiesof such systems have rarely been explored. Obviously, an external staggered magneticflux (SMF) will create a special type of inhomogeneity in lattice electron systems, andhence should lead to SMF-induced optical absorption.The systems we have studied are similar to the perfect networks of Aharonov-Bohm(AB) rings in some aspects. So we also study the AB effect[11] in this system. Under theeffect of an external magnetic field the waves describing the currents propagating from leftto right, along two branches of the ring (the AB ring), suffer a phase shift. Because of thephase shift, the quantum interference effect occurs and will be reflected in the behaviorof physical quantities which become periodic functions of the magnetic flux with periodφ0 = hc/e. We will first take tight-binding model to study D and optical conductivityin 2D square lattice and triangular lattice respectively, and then take Hubbard model toinvestigate D and optical conductivity in 2D square lattice. We will give the dependenceof the mean kinetic energy, D and the optical conductivity on SMF and U of 2D squarelattice at half filling. And then we determine the D as a function of the system size. Lastly we calculate the finite frequency part of the optical conductivity,σ_reg(ω), and getσ_reg(ω) versusωfor different U/t andδ(the SMF)at half filling. We will combine well-controlled analytical and numerical methods to determine the D and optical conductivityof the 2D lattices, and also the f-sum rule and Hellmann-Feynman relation will be used.