Optical Conductivity Of Honeycomb Lattice

The optical properties of electron systems closely relate to the prop-erties of the materials, and optical absorption is one of the basic tools inreseatch of the spectral properties of electron systems [1,2]. The opticalconductivityσ(ω) represents the rate at which electrons absorb the inci-dent photons at energyω, and is a useful probe in determining electroniccharacteristics of the material under study.We study D and optical conductivity of the two-dimensional(2D) hon-eycomb lattices at half filling with hopping integrals modulated by zigzagand armchair staggered magnetic fluxes(SMF). Although the energy spec-tral and transport properties of lattice electrons under spatially modulatedmagnetic fields have been investigated in detail[3–5,7,8,18],even more the cor-responding optical properties of triangular and square lattices systems havebeen explored[19–21], the honeycomb lattice has been rarely researched. Ob-viously, an external staggered magnetic flux (SMF) will create a specialtype of inhomogeneity in lattice electron systems, and hence should leadto SMF-induced optical absorption.The systems we have studied are similar to the perfect networks ofAharonov-Bohm (AB) rings . So we also study the AB effect [22] in thissystem. Under the effect of an external magnetic field the waves describ-ing the currents propagating from left to right, along two branches of the ring (the AB ring), suffer a phase shift. Because of the phase shift, thequantum interference effect occurs and will be reflected in the behavior ofphysical quantities which become periodic functions of the magnetic fluxwith periodφ0 = hc/e. We will take tight-binding model to study D andoptical conductivity in 2D honeycomb lattice under di?erent SMF respec-tively. We will give the dependence of the mean kinetic energy, D and theoptical conductivity on SMF of 2D honeycomb lattice at half filling. Andthen we determine the D as a function of two di?erent system size. Lastlywe calculate the finite frequency part of the optical conductivity,σreg(ω),and getσreg(ω) versusσfor differentδ(the SMF)at half filling. We willcombine well-controlled analytical and numerical methods to determine theD and optical conductivity of the 2D lattices, and also the f-sum rule andHellmann-Feynman relation will be used.