Abstract:

The transfer matrix method (TMM) has been used to obtain the reflection coefficient spectrum in aperiodic quantum superlattices using a one-dimensional Fibonacci sequence like potential. Results have been explained comparatively to the case when an equivalent finite periodic potential is used. Results indicate that Fibonacci superlattices also yield electronic bandgaps which exhibit a self-similar behavior. The TMM has been found appropriate for computational Physics laboratory in quantum mechanics courses since it allows solving problems related to particle scattering problems at constant piecewise potentials. At the same time the students learn the Physics concepts they are involved with Mathematical concepts and tools, such as: sequences, non conventional geometries, matrices and numerical methods. In this work, students can find a real application of the Fibonacci sequence to the superlattices of research interest nowadays. The golden ratio which is present in the generalized Bragg´s condition is such a "magic number" which has been widely used in Mathematics and in Arts. Additional lectures, including these Fibonacci based structures, are currently given within the course "Condensed Matter Physics" of the Official Master's Degree in Sensors for Industrial Applications at the Universitat Politècnica de València, Spain.

Keywords:

Fractal potential, Fibonacci sequence, Transfer matrix method, Quantum scattering.