Ponto quântico com interação de Rashba no limite de largura de banda zero

Abstract

Quantum dots have been studied using two electrodes, represented by two conduction bands, coupled to an Anderson impurity. This impurity can be empty, occupied by an electron with energy f or two electrons with energy 2 f + U, where U is the Coulomb interaction between the electrons. The calculation of thermodynamic and transport properties in this model is rather complex, since the interaction U between the orbital electrons of the impurity induce many body interaction via the hybridization of the orbital levels with the conduction bands. Interactions of this type require sophisticated methods of many body calculation, usually numeric, with great computational demand In this Dissertation we use the above model in a simplified form, in the zero limit of the conduction bands width, and introduced the Rashba spin-orbit interaction to the conduction electrons. Thus, the conduction bands are replaced by their respective Fermi levels that are coupled to a third level, which represents the quantum dot. The advantage of the above model is that we can treat it exactly, without making any approach concerning their parameters. As the model is represented by three energy levels and each level can be unoccupied, occupied by an electron with spin up or spin down, or two electrons, one with spin up and the other with spin down, the Hamiltonian can be represented by a 64x64 matrix, which makes it difficult to perform an exact diagonalization. To work around this issue, we find that the studied Hamiltonian conserves charge and parity. This allows us to rewrite the Hamiltonian in the form of matrices whose basis belong to subspaces of the same charge and parity. With this procedure, the 64x64 matrix is replaced by a 1x1 matrix in the zero charge subspace, two 3x3 matrices in the one charge subspace, two 3x3 matrices and one 9x9 matrix in the two charge subspace, two 1x1 matrices and two 9x9 matrices in the three charge subspace, two 3x3 matrices and one 9x9 matrix in the four charge subspace, two 3x3 matrices in the five charge subspace, and one 1x1 matrix in the six charge subspace. Knowing the eigenstates (eigenvalues and eigenvectors) of the Hamiltonian of the studied model, we determined their corresponding thermodynamic and transport properties. Thus, we present the behavior of the energy spectrum, the occupation number, the magnetic susceptibility, the specific heat and the electrical conductance as a function of the parameters of the model.