Introduction to edge states in insulators

• Grant number: 12/06034-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2012
• End date: December 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Rodrigo Gonçalves Pereira
• Grantee: Rafael Sobrinho Laporte
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Localized surface states account for nontrivial transport properties in some insulating phases of electron systems. Examples include the quantum Hall effect and topological insulators. In this project, we propose a theoretical study of edge states that show up in noninteracting lattice models in one and two dimensions, such as the Su-Schrieffer-Heeger model for polyacetylene and the model for graphene with mass terms. The approach will rely on the numerical diagonalization of the Hamiltonian for a single particle on a inhomogeneous lattice characterized by interfaces between domains. The numerical study will be accompanied by the study of analytical solutions based on effective field theories valid in the continuum limit. By analyzing the resulting spectrum, we intend to investigate the conditions for the existence of edge states and to discuss how the number of such states can change at topological phase transitions.