## SCL Seminar by Milica Milovanovic

Scientific Computing Laboratory seminar will be held on Friday, 7 October 2016 at 14:00 in the library reading room “Dr. Dragan Popović" of the Institute of Physics Belgrade. The talk entitled

will be given by Dr. Milica Milovanović (Scientific Computing Laboratory, Institute of Physics Belgrade).

The composite fermions (CFs) describe a Fermi liquid state that is supported by the system of strongly correlated electrons in the presence of a magnetic field at half-filling. In the first part of the seminar we will review, recently introduced in Ref. [1], Dirac CF theory which generalizes the usual CF approach to the case of particle-hole symmetric half-filled Landau level. The Dirac nature of the underlying fermionic quasiparticle in the particle-hole symmetric case was also confirmed by a numerical experiment in Ref. [2].The system of electrons at half-filling is a stage for BCS pairing of CFs and, in that context, famous Pfaffian (Moore-Read) state - the first proposal and platform for Majorana fermions and topological quantum computing. Thus it is important to understand the BCS pairing properties in the particle-hole symmetric case with Dirac CFs.

In the second part of the seminar we will discuss BCS paired Dirac CFs in the context of monolayer [3] and bilayer [4]. In the monolayer case we will point out to the possibility of the coexistence of the singlet and triplet pairing among spinor components of Dirac CFs. We will emphasize the importance of the triplet pairing, which leads to anisotropic effects. This is consistent with numerical and real world experiments which show that systems at half-filling may sustain and even harbor anisotropy. Under an inclusion of a particle-hole symmetry breaking mass, which may represent a Landau level mixing, the superpositions of singlet and triplet pairings may evolve into the Pfaffian state of ordinary (non-relativistic) CFs. In the bilayer case, with a pseudospin degree of freedom, we will describe the interplay of magnetic ordering and metallic states of Dirac CFs, as a stage for their pairing.

[1] D.T. Son, Phys. Rev. X 5, 031027 (2015).

[2] S. D. Geraedts, Michael P. Zaletel, R. S. K. Mong, M. A. Metlitski, A. Vishwanath, O. I. Motrunich, Science 352, 197 (2016).

[3] M.V. Milovanović, M. Dimitrijević Ćirić, and V. Juričić, Phys. Rev. B 94, 115304 (2016).

[4] M.V. Milovanović, E. Dobardžić, and Z. Papić, Phys. Rev. B 92, 195311 (2015).

**"BCS Instabilities of Dirac Composite Fermions"**will be given by Dr. Milica Milovanović (Scientific Computing Laboratory, Institute of Physics Belgrade).

**Abstract of the talk:**The composite fermions (CFs) describe a Fermi liquid state that is supported by the system of strongly correlated electrons in the presence of a magnetic field at half-filling. In the first part of the seminar we will review, recently introduced in Ref. [1], Dirac CF theory which generalizes the usual CF approach to the case of particle-hole symmetric half-filled Landau level. The Dirac nature of the underlying fermionic quasiparticle in the particle-hole symmetric case was also confirmed by a numerical experiment in Ref. [2].The system of electrons at half-filling is a stage for BCS pairing of CFs and, in that context, famous Pfaffian (Moore-Read) state - the first proposal and platform for Majorana fermions and topological quantum computing. Thus it is important to understand the BCS pairing properties in the particle-hole symmetric case with Dirac CFs.

In the second part of the seminar we will discuss BCS paired Dirac CFs in the context of monolayer [3] and bilayer [4]. In the monolayer case we will point out to the possibility of the coexistence of the singlet and triplet pairing among spinor components of Dirac CFs. We will emphasize the importance of the triplet pairing, which leads to anisotropic effects. This is consistent with numerical and real world experiments which show that systems at half-filling may sustain and even harbor anisotropy. Under an inclusion of a particle-hole symmetry breaking mass, which may represent a Landau level mixing, the superpositions of singlet and triplet pairings may evolve into the Pfaffian state of ordinary (non-relativistic) CFs. In the bilayer case, with a pseudospin degree of freedom, we will describe the interplay of magnetic ordering and metallic states of Dirac CFs, as a stage for their pairing.

[1] D.T. Son, Phys. Rev. X 5, 031027 (2015).

[2] S. D. Geraedts, Michael P. Zaletel, R. S. K. Mong, M. A. Metlitski, A. Vishwanath, O. I. Motrunich, Science 352, 197 (2016).

[3] M.V. Milovanović, M. Dimitrijević Ćirić, and V. Juričić, Phys. Rev. B 94, 115304 (2016).

[4] M.V. Milovanović, E. Dobardžić, and Z. Papić, Phys. Rev. B 92, 195311 (2015).