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Studies on fermions and bosons in low dimensions and their applications in graphene and topological insulators

Grant number: 18/20577-4
Support type:Research Grants - Visiting Researcher Grant - Brazil
Duration: January 02, 2019 - January 01, 2020
Field of knowledge:Physical Sciences and Mathematics - Physics
Principal Investigator:Antonio Soares de Castro
Grantee:Antonio Soares de Castro
Visiting researcher: Luis Rafael Benito Castro
Visiting researcher institution: Universidade Federal do Maranhão (UFMA). Centro de Ciências Exatas e Tecnologia (CCET), Brazil
Home Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil


The main purpose of this work plan is the detailed study of fermion and boson systems in low dimensions that present bound states and/or scattering states. The analytical solutions will be obtained by studying the Dirac (fermions) and Duffin-Kemmer-Petiau (bosons) equations. These solutions will be used for applications in the quantum Hall effect, spin quantum Hall effect and topological insulation for fermionic and bosonic systems. On the other hand, due to the analogy between disclinations in solids and cosmic strings, several results obtained from the analysis of cosmic strings can be useful in the study of condensed matter systems. In this context, as another objective of this work plan, we intend to deepen in the study of the effects of considering space-time of a cosmic string in the quantum Hall effect and topological insulators for fermionic and bosonic systems. (AU)

Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
NETO, FRANCISCO A. CRUZ; DA SILVA, FRANCIELE M.; SANTOS, LUIS C. N.; CASTRO, LUIS B. Scalar bosons with Coulomb potentials in a cosmic string background: scattering and bound states. EUROPEAN PHYSICAL JOURNAL PLUS, v. 135, n. 1 JAN 2020. Web of Science Citations: 0.
LIMA, DANIEL F.; ANDRADE, FABIANO M.; CASTRO, LUIS B.; FILGUEIRAS, CLEVERSON; SILVA, EDILBERTO O. On the 2D Dirac oscillator in the presence of vector and scalar potentials in the cosmic string spacetime in the context of spin and pseudospin symmetries. EUROPEAN PHYSICAL JOURNAL C, v. 79, n. 7 JUL 15 2019. Web of Science Citations: 1.
AQUINO CURI, ELVIS J.; CASTRO, LUIS B.; DE CASTRO, ANTONIO S. Proper treatment of scalar and vector exponential potentials in the Klein-Gordon equation: Scattering and bound states. EUROPEAN PHYSICAL JOURNAL PLUS, v. 134, n. 6 JUN 2019. Web of Science Citations: 1.

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