Parafermionic modes in correlated electron systems

• Grant number: 19/11550-8
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2020
• End date: March 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Luis Gregório Godoy de Vasconcellos Dias da Silva
• Grantee: Raphael Levy Ruscio Castro Teixeira
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated scholarship(s): 21/07602-2 - Parafermionic excitations in superconducting fractional quantum Hall edge states, BE.EP.DR

Abstract

The study of topological phases with exotic quasiparticles is one of the most active topics in condensed matter physics today. A well-studied recent example are Z_2-symmetric Majorana bound states in topological superconductors, with possible applications in topological quantum computation protocols. Another promising, albeit much less studied, example are Z_n-symmetric parafermionic modes, a natural generalization of Majorana quasiparticles, which could be used as the building blocks of an universal topological quantum computer''. This is not an easy task as out of the many proposals for the realization of parafermions in condensed matter systems , only a few works show the existence of topologically protected parafermionic states. This project intends to study the emergence of Z_n parfermionic states with n=3,4 in interacting 1D lattice models. As a first step, we will identify strongly interacting electronic (i.e., fermionic) models from exact mappings of parafermionic lattice models. We will then employ Density-Matrix Renormalization-Group (DMRG) calculations to investigate the topological phases of these models. To this end, we will calculate quantitities such as density correlations and other local and non-local properties which can be probed in experiments. We will also characterize the topological phases using the entanglement entropy of the system. As a result, we expect to identify both the type of interactions and the the range of parameters in which the topological phases appear in order to guide the experimental investigations in these systems. (AU)

Scientific publications

(6)

(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)

TEIXEIRA, RAPHAEL L. R. C.; HALLER, ANDREAS; SINGH, ROSHNI; MATHEW, AMAL; IDRISOV, EDVIN G.; DA SILVA, LUIS G. G. V. DIAS; SCHMIDT, THOMAS L.. Overlap of parafermionic zero modes at a finite distance. PHYSICAL REVIEW RESEARCH, v. 4, n. 4, p. 9-pg., 2022-11-14. (19/11550-8, 21/07602-2)

DE MEDEIROS, MARCOS H. L.; TEIXEIRA, RAPHAEL L. R. C.; SIPAHI, GUILHERME M.; DIAS DA SILVA, V, LUIS G. G.. Electric field induced edge-state oscillations in InAs/GaSb quantum wells. Physical Review B, v. 104, n. 19, NOV 19 2021. (16/18495-4, 19/11550-8)

TEIXEIRA, RAPHAEL L. R. C.; KUZMANOVSKI, DUSHKO; BLACK-SCHAFFER, ANNICA M.; DIAS DA SILVA, LUIS G. G., V. Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges. PHYSICAL REVIEW B, v. 102, n. 16, p. 11-pg., 2020-10-22. (19/11550-8, 16/18495-4)

TEIXEIRA, RAPHAEL L. R. C.; KUZMANOVSKI, DUSHKO; BLACK-SCHAFFER, ANNICA M.; DIAS DA SILVA, V, LUIS G. G.. Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges. Physical Review B, v. 102, n. 16, OCT 22 2020. (16/18495-4, 19/11550-8)

TEIXEIRA, RAPHAEL L. R. C.; DIAS DA SILVA, V, LUIS G. G.. Quantum dots as parafermion detectors. PHYSICAL REVIEW RESEARCH, v. 3, n. 3, JUL 2 2021. (19/11550-8)

TEIXEIRA, RAPHAEL L. R. C.; DIAS DA SILVA, LUIS G. G., V. Edge Z(3) parafermions in fermionic lattices. PHYSICAL REVIEW B, v. 105, n. 19, p. 12-pg., 2022-05-13. (19/11550-8, 21/07602-2)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

TEIXEIRA, Raphael Levy Ruscio Castro. Parafermionic modes in correlated electron systems. 2023. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Física (IF/SBI) São Paulo.