Resumen El modelo de Ginzburg - Landau (TDGLM) es una fuerte herramienta ampliamente utilizada para analizar la magnetización de un estado de vórtice simple en una muestra superconductor mesoscópica en presencia de un campo magnético. El algoritmo implementado es aplicado a una geometria cuadrada rodeada de diferentes tipos de materiales (simulados por la longitude de extrapolación de deGennes b). El interior de la muestra se mantiene a una temperatura constante Ti, mientras su frontera permanece a una temperatura Ts Esta variación de temperatura en la muestra puede ser generada por una onda laser continua inyectada en todos los puntos internos, excepto en una delgada capa en la superficie del material. Encontramos que, el valor de b en Ts = Ti = 0.0, cual imita la curva de magnetización para un respectivo Ts, presenta una dependencia lineal con la temperature. Por lo tanto, aunque dentro del dominio de validez de la TDGLM el parametro b es considerado independiente de la temperature en la vecindad de la temperatura crítica volumétrica y que b depende de la densidad de estados cercal a la superficie, proponemos una dependencia simple de b usando TDGLM.

Abstract The Time-dependent Ginzburg-Landau model (TDGLM) is a robust tool widely used to analyze the magnetization of the single-vortex state of a mesoscopic superconducting sample in presence of a magnetic field. The algorithm implemented in this work is applied to a square geometry surrounded by different kinds of materials simulated by deGennes extrapolation length b. The inside of the sample remains at constant temperature Ti, while its boundary remains at temperature Ts. This temperature variation in the sample can be generated by a continuous laser wave injected into all the internal points, except for a thin surface layer in the boundary of the material. We found that the b value at Ts = Ti = 0.0, which mimics the magnetization curve for a corresponding Ts, presents a linear dependence with the temperature. Therefore, although within the domain of validity TDGLM the parameter b is to be considered temperature-independent in the vicinity of the bulk critical temperature and that b depends on the density of states near the surface, we propose a simple dependence of b using a TDGLM.

We analyze the effect of the potential shape on the ground state energy of the off-axis neutral donor in GaAs/Ga1-xAl xAs cylindrical nanotube in the presence of the uniform magnetic field applied along the symmetry axis. To take into account the mixing of the low lying subbands we express the wave function as a product of combination of 1s and 2p x,y wave functions with an unknown envelope function that depends only on electron-ion separation. By using variational principle and the functional derivative procedure we derive a one-dimensional differential equation for the envelope function, which we solve numerically by using of the trigonometric sweep method. Results of calculation of the ground state binding energy dependencies on the distance from the donor position to the axis and on the strength of the external magnetic field for square-well, soft-edge-barrier and parabolic bottom potentials are presented. It is shown that the additional peaks in the curves of the density of impurity states appear due to the presence of the repulsive core is nanotube.