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Quantum field theory in Dirac materials

Grant number: 17/50294-1
Support Opportunities:Regular Research Grants
Duration: May 01, 2018 - April 30, 2020
Field of knowledge:Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
Convênio/Acordo: Universidad de Salamanca
Mobility Program: SPRINT - Projetos de pesquisa - Mobilidade
Principal Investigator:Dmitry Vasilevich
Grantee:Dmitry Vasilevich
Principal researcher abroad: Juan Maria Mateos Guilarte
Institution abroad: Universidad de Salamanca (USAL), Spain
Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

A good part of the progress achieved in condensed matter physics over the recent years is related to the so called Dirac materiais. In these materiais, the quasiparticles obey the Dirac equation. Graphene, topological insulators and Weyl semimetals are the most prominent examples of this c1ass. Quantum Field Theory (QFT) is a natural instrument to study the properties of these materiais. In this project we shall address some geometrical aspects of QFT in the Dirac materiais. In particular, we shall study the parity anomaly for Dirac operator in the presence of boundaries and the induced Chern-Simons actions. We shall apply QFT to compute the Casimir interaction of graphene nanoribbons with anisotropic materiais (strained graphene, e.g.). Besides, we propose to attack the subtleties of Quantum Hall Effect in these materiais forming genus one Riemann surfaces through using the Riemannian Theta Function Theory.We shall study the Kosterlitz-Thouless phase transitions which requires the addition of scalar fields in non-linear sigma models. Topological defects of kink type in linear spin chains or vortexesin planar gauged sigma models, with either Maxwell or Chern-Simons fields, playa crucial role. (AU)

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Scientific publications (14)
(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)
MATEOS GUILARTE, J.; VASSILEVICH, D.. Fractional fermion number and Hall conductivity of domain walls. Physics Letters B, v. 797, . (17/50294-1, 16/03319-6)
ALONSO-IZQUIERDO, A.; FRESNEDA, RODRIGO; MATEOS GUILARTE, J.; VASSILEVICH, D.. Soliton fermionic number from the heat kernel expansion. EUROPEAN PHYSICAL JOURNAL C, v. 79, n. 6, . (17/50294-1, 16/03319-6)
KHUSNUTDINOV, N.; EMELIANOVA, N.. Low-temperature expansion of the Casimir-Polder free energy for an atom interacting with a conductive plane. International Journal of Modern Physics A, v. 34, n. 2, . (17/50294-1, 16/03319-6)
FIALKOVSKY, I.; KURKOV, M.; VASSILEVICH, D.. Quantum Dirac fermions in a half-space and their interaction with an electromagnetic field. Physical Review D, v. 100, n. 4, . (17/50294-1, 16/03319-6)
FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; VASSILEVICH, DMITRI. Quest for Casimir repulsion between Chern-Simons surfaces. PHYSICAL REVIEW B, v. 97, n. 16, p. 11-pg., . (17/50294-1, 16/03319-6)
VASSILEVICH, DMITRI. Index theorems and domain walls. Journal of High Energy Physics, v. N/A, n. 7, p. 13-pg., . (17/50294-1, 16/03319-6)
FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; VASSILEVICH, DMITRI. Quest for Casimir repulsion between Chern-Simons surfaces. Physical Review B, v. 97, n. 16, . (17/50294-1, 16/03319-6)
KHUSNUTDINOV, NAIL; KASHAPOV, RASHID; WOODS, LILIA M.. Thermal Casimir and Casimir-Polder interactions in N parallel 2D Dirac materials. 2D MATERIALS, v. 5, n. 3, . (17/50294-1, 16/03319-6)
RODRIGUEZ-LOPEZ, PABLO; POPESCU, ADRIAN; FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; WOODS, LILIA M.. Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals. COMMUNICATIONS MATERIALS, v. 1, n. 1, . (19/10719-9, 17/50294-1, 16/03319-6)
ALMEIDA, CAIO; ALONSO-IZQUIERDO, ALBERTO; FRESNEDA, RODRIGO; MATEOS GUILARTE, JUAN; VASSILEVICH, DMITRI. Nontopological fractional fermion number in the Jackiw-Rossi model. Physical Review D, v. 103, n. 12, . (16/03319-6, 17/50294-1)
VASSILEVICH, DMITRI. Index theorems and domain walls. Journal of High Energy Physics, n. 7, . (17/50294-1, 16/03319-6)
KHUSNUTDINOV, N.; WOODS, L. M.. Casimir Effects in 2D Dirac Materials (Scientific Summary). JETP LETTERS, v. 110, n. 3, p. 183-192, . (19/10719-9, 17/50294-1, 16/03319-6)
KURKOV, MAXIM; VASSILEVICH, DMITRI. How Many Surface Modes Does One See on the Boundary of a Dirac Material?. Physical Review Letters, v. 124, n. 17, . (17/50294-1, 16/03319-6)
FIALKOVSKY, I.; KURKOV, M.; VASSILEVICH, D.. Quantum Dirac fermions in a half-space and their interaction with an electromagnetic field. PHYSICAL REVIEW D, v. 100, n. 4, p. 13-pg., . (17/50294-1, 16/03319-6)

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