Competing effective interactions of Dirac electrons in the Spin–Fermion system

Abstract

Recently discovered advanced materials 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 the (AF) Heisenberg-Kondo lattice model, describing a set of localized spins on a square lattice with anti-ferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like. These interact with the localized spins through a Kondo magnetic interaction. By integrating out the localized degrees of freedom we obtain a set of different effective interactions among the itinerant electrons. This 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.

Antiferromagnetic phase diagram of the cuprate superconductors

“…Recently, also starting from the spin-fermion model, we have obtained an effective interaction among the charge carriers of the system, which produces a domeshaped SC high critical temperature versus doping [2] plot that qualitatively reproduces the SC phase diagram experimentally observed. Hence, combining our results, the following picture emerges: for the effective model of the localized spins presented here, where the itinerant fermions have been integrated out, we get the suppression of the magnetic order as charge carriers are added to the system; for the effective model of the itinerant fermionic fields, where the localized magnetic moments have been integrated out, we have the appearance of a dome-shape SC critical temperature with the addition of charge carriers [2]. Therefore, we have a theory where the AF order is suppressed and the SC phase arises as charge carriers added to the system, which is the phenomenology observed for several strongly correlated electronic systems [26].…”

“…where β = 1/k B T , with k B denoting the Boltzmann's constant and T the system temperature, and H = H H + H K + H 0 , is given by (1), (2) and 3respectively.…”

“…Recently, starting from a spin-fermion model, which has been employed previously to describe the cuprate superconductors [1] we have derived an effective model Email addresses: lizardonunes@ufsj.edu.br (L. H. C. M. Nunes), marino@if.ufrj.br (E. C. Marino) for the charge carriers [2] and the superconductivity in our model arises from a novel mechanism, that yields a high critical temperature which is comparable to the experimental values. Moreover, by including doping effects a dome-shaped dependence of the critical temperature is found as charge carriers are added to the system, in agreement with the experimental phase diagram [3].…”

Superconducting and pseudogap transition temperatures in high-Tc cuprates and the Tc dependence on pressure

“…We first trace out the localized degrees of freedom, represented by the copper spins S I . For this, we follow the usual procedure (see Appendix A; also [17,24] for instance) which employs spin coherent states, in order to express the partition function as a functional integral over a classic unit vector field N, which replaces the localized spin operator S I /2 in H AF and H K . The second operation consists in performing a second order t p /U p perturbative expansion in H U + H ′ 0 , where H ′ 0 is the spin-flip part of H 0 .…”

Temperature × doping phase diagram of cuprate superconductors

“…Employing the polar representations of the bosonic fields, z α = ρ α e i θα / √ 2, we can perform the functional integration over the Schwinger boson fields assuming constant ρ α and we obtain the resulting effective Lagrangian density for the fermion fields associated to the charge carriers [33],…”