Overlap of parafermionic zero modes at a finite distance

Autor(es)

Teixeira, Raphael L. R. C. ; Haller, Andreas ; Singh, Roshni ; Mathew, Amal ; Idrisov, Edvin G. ; da Silva, Luis G. G. V. Dias ; Schmidt, Thomas L.

• Tipo de documento: Artigo Científico
• Fonte: PHYSICAL REVIEW RESEARCH; v. 4, n. 4, p. 9-pg., 2022-11-14.

Resumo

Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground-state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying Z2n symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find good quantitative agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems. (AU)

• Processo FAPESP: 19/11550-8 - Modos parafermiônicos em sistemas de elétrons correlacionados
• Beneficiário: Raphael Levy Ruscio Castro Teixeira
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 21/07602-2 - Excitações parafermionicas em estados de bordas de sistemas Hall quântico fracionário com supercondutividade
• Beneficiário: Raphael Levy Ruscio Castro Teixeira
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado