Theoretical approach for the description of a single quantum dot using geometry

An alternative theoretical approach based on the geometry of the states space is proposed in order to describe the physical properties of a single quantum dot. Analytical expressions for the Fermi energy and density of states were obtained, from which we studied the electron states and some thermodynamic properties of the system. After careful analysis of the results, we observed that the application of the technique is more suitable for devices containing a large number of electrons and it also provides limitations for the system by controlling the magnetic and temperature. Comparisons of our results with the literature are also performed.