2022/11/12 by M. B. Alves, Alves, M. B., O. M. Del Cima +5
Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Graphene research and applications #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Spectral Theory in Mathematical Physics #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2211.06765
openalex publication_date 2022/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of the spectral properties of the Weyl-Dirac or massless Dirac operators, describing the behavior of quantum quasi-particles in dimension 2 in a homogeneous magnetic field, B\rm ext, perturbed by a chiral-magnetic field, b\rm ind, with decay at infinity and a short-range scalar electric potential, V, of the Bessel-Macdonald type. These operators emerge from the action of a pristine graphene-like QED3 model recently proposed in Eur. Phys. J. B93 (2020) 187. First, we establish the existence of states in the discrete spectrum of the Weyl-Dirac operators between the zeroth and the first (degenerate) Landau level assuming that V=0. In sequence, with Vs \not= 0, where Vs is an attractive potential associated with the s-wave, which emerges when analyzing the s- and p-wave Møller scattering potentials among the charge carriers in the pristine graphene-like QED3 model, we provide lower bounds for the sum of the negative eigenvalues of the operators |\boldsymbolσ ⋅ \boldsymbolp_\boldsymbolA_±|+ Vs. Here, \boldsymbolσ is the vector of Pauli matrices, \boldsymbolp_\boldsymbolA_±=\boldsymbolp-\boldsymbolA_±, with \boldsymbolp=-i\boldsymbol∇ the two-dimensional momentum operator and \boldsymbolA_± certain magnetic vector potentials. As a by-product of this, we have the stability of bipolarons in graphene in the presence of magnetic fields.