The two-dimensional density of states in normal and superconducting compounds

In this work, we present a review for the numerical calculation of the density of states (DOS) for two-dimensional tight-binding models with first neighbors in its normal state and for two superconducting order parameters. One is a singlet scalar state and the other is a triplet vector state. At the beginning an emphasis is given to the general expressions commonly used to the calculation of the density of states as the number of partial and total number of states, the degrees of freedom and the ab-initio methods most commonly used to its calculation. Then, the transition that happens to the normal states density of states by varying the Fermi energy and the hopping parameter is investigated. After that, the numerical calculation of the superconducting density of states using the zero temperature scattering cross-section is performed for the two order parameters. Finally, the residual density of states depending on disorder and the scattering potential strength using the Larkin equation are calculated for the two different in nature order parameter symmetries.