Banca de DEFESA: JOSÉ ROBERTO MOREIRA DA SILVA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE : JOSÉ ROBERTO MOREIRA DA SILVA
DATA : 30/07/2018
HORA: 14:00
LOCAL: ANFITEATRO A - CCET
TÍTULO:

Topological Phonon States in One-Dimensional Quasicrystals

PALAVRAS-CHAVES:

phonon's spectra, Hofstadter's butterfly, edge-states

PÁGINAS: 67
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

Theoretical models for predicting the properties of quasicrystalline materials have been of considerable interest to the scientific community recently. However, they are mainly related to the optical and electronic characteristics of the system, and a study of the elementary oscillations, such as phonons, of one-dimensional quasicrystalline lattices is still necessary. Recently published works have shown that the localization properties of the Harper model can be modeled in a quasicrystal through the Hamiltonian of Aubry-André, considering the immeasurable potential with the lattice parameter. This model proved to present itself as a topological insulator, exhibiting border states and nontrivial phases for the electronic case. Motivated by these results, in this work, we present a study on the vibrational properties of one-dimensional quasi-crystals, highlighting the topological states of edge. For this, we model a one-dimensional quasicristal through the Aubry-André model with the potential parameter defined by the golden ratio (b = (1+) / 2). We performed the numerical calculations from the exact numerical diagonalization of the Hamiltonian. In our results, we find the multifractal frequency spectrum known as the "Hofstadter's butterfly", which emerges as a critical state of a transition from metal-insulating type states to the value of modulation of the dimensionless spring constant of 1.0. We also show by calculating the wavelength, that there exist certain states that cross the largest gaps of the spectrum (as a function of the phi phase) are edge states in the system, where there are state locations in them.

MEMBROS DA BANCA:
Presidente - 1354851 - MANOEL SILVA DE VASCONCELOS
Interno - 1519258 - DORY HELIO AIRES DE LIMA ANSELMO
Externo à Instituição - JOSE DE MIRANDA HENRIQUES NETO - UFCG