Collective Modes in One-Dimensional Kitaev Topological Superconductor

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Asemani, Mostafa | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52314 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Kargarian, Mehdi
Abstract:
In this thesis, we analyze the Higgs mode in one-dimensional Kitaev topological superconductor. We first review the macroscopic (Ginzburg-Landau Theory) and microscopic (BCS Theory) derivation of oscillations of the energy gap in conventional superconductor in the presence of an electromagnetic field as a perturbation. We explain both analytical (based on Anderson pseudospins) and numerical (Density Matrix Formalism) approaches for calculations. The goal is to find the temporal evolution of the superconductor energy gap which is the order parameter of the system. In our investigation, we will see that we could reduce our problem to studying the amplitude of the energy gap in the Kitaev superconductor. We will find that these perturbations lead to generate a p1 t - decaying oscillating behaviour of the energy-gap amplitude that we interpret as the Higgs mode. Moreover, we find that in the regime of small perturbations, the oscillation frequency is proportional to the initial energy gap on the Fermi surface and, more accurately, is proportional to the final state energy gap on the Fermi surface
Keywords:
Landau-Ginzburg Equation ; Bardeen-Cooper-Schrieffer Theory ; Higgs Mode ; Superconductor ; Energy Gap ; Anderson Peseudospin ; Density Matrix Formalism ; Topological Superconductor ; Kitaev Superconductor