Optical properties of supercrystals

We present a systematic study of the dependence of the optical properties on the geometry of the quantum dots, which form a quantum dots chain. We obtain electronic structure of 1D supercrystals by using a tight-binding method based on the s and p orbitals and wave functions of the quantum dots for the on-site parameters. For the hopping parameter we choose the extended Hückel method. We find a drastic dependence on this parameter especially on the electronic band structure. We also relate the tight-binding matrix elements with the momentum matrix elements taking the k-space gradient of the Hamiltonian for calculating the dielectric spectra of supercrystals made of cylindrical, spherical, and conical quantum dots. We compare the optical behavior of the chains in the three geometries and report anomalies for the conical quantum dots chain.