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Quantum field theory in Dirac materials


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 (11)
(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)
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 JUN 21 2021. Web of Science Citations: 0.
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 APR 29 2020. Web of Science Citations: 0.
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 MAR 26 2020. Web of Science Citations: 3.
MATEOS GUILARTE, J.; VASSILEVICH, D. Fractional fermion number and Hall conductivity of domain walls. Physics Letters B, v. 797, OCT 10 2019. Web of Science Citations: 0.
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 AUG 28 2019. Web of Science Citations: 0.
KHUSNUTDINOV, N.; WOODS, L. M. Casimir Effects in 2D Dirac Materials (Scientific Summary). JETP LETTERS, v. 110, n. 3, p. 183-192, AUG 2019. Web of Science Citations: 0.
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 JUN 20 2019. Web of Science Citations: 1.
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 JAN 20 2019. Web of Science Citations: 1.
VASSILEVICH, DMITRI. Index theorems and domain walls. Journal of High Energy Physics, n. 7 JUL 16 2018. Web of Science Citations: 2.
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 JUL 2018. Web of Science Citations: 4.
FIALKOVSKY, IGNAT; KHUSNUTDINOV, NAIL; VASSILEVICH, DMITRI. Quest for Casimir repulsion between Chern-Simons surfaces. Physical Review B, v. 97, n. 16 APR 24 2018. Web of Science Citations: 6.

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