Article

# Quantum Criticality and Superconductivity in Quasi-Two-Dimensional Dirac Electronic Systems

Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil

Nuclear Physics B (Impact Factor: 3.95). 03/2006; DOI: 10.1016/j.nuclphysb.2006.02.025 Source: arXiv

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**ABSTRACT:**It is known that a constant magnetic field is a strong catalyst of dynamical chiral symmetry breaking in 2+1 dimensions, leading to generating dynamical fermion mass even at weakest attraction. In this work we investigate the collective modes associated with the dynamical chiral symmetry breaking in a constant magnetic field in the (2+1)-dimensional Nambu--Jona-Lasinio model with continuous U(1) chiral symmetry. We introduce a self-consistent scheme to evaluate the propagators of the collective modes at the leading order in $1/N$. The contributions from the vacuum and from the magnetic field are separated such that we can employ the well-established regularization scheme for the case of vanishing magnetic field. The same scheme can be applied to the study of the next-to-leading order correction in $1/N$. We show that the sigma mode is always a lightly bound state with its mass being twice the dynamical fermion mass for arbitrary strength of the magnetic field. Since the dynamics of the collective modes is always 2+1 dimensional, the finite temperature transition should be of the Kosterlitz-Thouless (KT) type. We determine the KT transition temperature $T_{\rm KT}$ as well as the mass melting temperature $T^*$ as a function of the magnetic field. It is found that the pseudogap domain $T_{\rm KT}<T<T^*$ is enlarged with increasing strength of the magnetic field. The influence of a chiral imbalance or axial chemical potential $\mu_5$ is also studied. We find that even a constant axial chemical potential $\mu_5$ can lead to inverse magnetic catalysis of the KT transition temperature in 2+1 dimensions. The inverse magnetic catalysis behavior is actually the de Haas--van Alphen oscillation induced by the interplay between the magnetic field and the Fermi surface.Physical Review D 09/2014; 90(05):056005. · 4.86 Impact Factor -
##### Article: The Kohn-Luttinger effect and anomalous pairing in new superconducting systems and graphene

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**ABSTRACT:**We present a review of theoretical investigations into the Kohn-Luttinger nonphonon superconductivity mechanism in various 3D and 2D repulsive electron systems described by the Fermi-gas, Hubbard, and Shubin-Vonsovsky models. Phase diagrams of the superconducting state are considered, including regions of anomalous $s$-, $p$-, and $d$-wave pairing. The possibility of a strong increase in the superconducting transition temperature $T_c$ even for a low electron density is demonstrated by analyzing the spin-polarized case or the two-band situation. The Kohn-Luttinger theory explains or predicts superconductivity in various materials such as heterostructures and semimetals, superlattices and dichalcogenides, high-$T_c$ superconductors and heavy-fermion systems, layered organic superconductors, and ultracold Fermi gases in magnetic traps. This theory also describes the anomalous electron transport and peculiar polaron effects in the normal state of these systems. The theory can be useful for explaining the origin of superconductivity and orbital currents (chiral anomaly) in systems with the Dirac spectrum of electrons, including superfluid $^3$He-A, doped graphene, and topological superconductors.Journal of Experimental and Theoretical Physics 11/2014; 118(6). · 0.93 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin–Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu–Jona-Lasinio-like, excitonic term and a spin–spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.Annals of Physics 01/2014; 340(1):13–24. · 3.07 Impact Factor

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