2025-10-222025-10-222021-12-01MELO, Kéllen Garcia de. Conexões entre a integração no plano complexo e a física dos isolantes topológicos. Orientador: Leandro Oliveira do Nascimento. 2021. 35 f. Trabalho de Curso (Licenciatura em Ciências Naturais) – Faculdade de Ciências Naturais, Campus Universitário de Breves, Universidade Federal do Pará, Breves, 2021. Disponível em: https://bdm.ufpa.br/handle/prefix/8730. Acesso em: .https://bdm.ufpa.br/handle/prefix/8730In the present work, a literary review was carried out on integration in the complex plane and general aspects of the theory of topological states of matter. We present a brief review, on the history and definition of the set of complex numbers z, necessary to study the integration in the complex plane. We discuss in detail the winding number, a topological invariant characteristic of systems in (1+1) D. This mathematical object, when applied to the energy band of topological insulators, is able to describe the topological phases (filling number non-zero) and non-topological phase (fill number equal to zero). Then, the concept of topological insulators (IT's) is presented, emphasizing systems that present topological phases, such as the quantum Hall effect (EHQ), which occurs when electrons are subjected to a strong magnetic field; and polyacetylene, an organic polymer formed by carbon chains containing conjugated bonds (C=C). Also, we solve calculations in the complex plane integration, obtaining a result that satisfies the residual theorem. Furthermore, we highlight the importance of research in the area of systems with topological phases, considering that these will be of great use in the field of science and technology.Acesso AbertoNúmeros complexos zIntegração no plano complexoIsolantes topológicosComplex z numbersComplex plane integrationTopological insulatorsWinding numberCNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA GERAL::FISICA CLASSICA E FISICA QUANTICA MECANICA E CAMPOSTrabalho de Curso - Graduação - MonografiaAttribution-NonCommercial-NoDerivs 3.0 Brazil