Interplay between charge, magnetic, and superconducting order in a Kondo lattice with attractive Hubbard interaction

Abstract

We investigate the competition between superconductivity, charge-ordering, magnetic-ordering, and the Kondo effect in a heavy fermion s-wave superconductor described by a Kondo lattice model with an attractive on-site Hubbard interaction. The model is solved using the real-space dynamical mean field theory. For this purpose, we develop a numerical renormalization group (NRG) framework in Nambu space, which is used to solve the superconducting impurity problem. This extended NRG scheme also allows for SU(2) spin symmetry broken solutions, enabling us to examine the competition or cooperation between s-wave superconductivity and incommensurate spin-density waves (SDWs). At half filling, we find an intriguing phase where the magnetic ordering of the f -electrons lifts the degeneracy between the charge density wave (CDW) state and the superconducting state, leading to a strong suppression of superconductivity. In addition, the system may also become a half metal in this parameter regime. Away from half filling, the CDWs vanish and are replaced by superconductivity combined with incommensurate SDWs up to moderate Kondo couplings to the f -electrons. We find that both CDWs as well as superconductivity enhance magnetic ordering due to the suppression of Kondo screening.where µ is the chemical potential, t denotes the hopping parameter between nearest neighbors and J > 0 is a Kondo coupling. c † i,σ creates a conduction electron on site i with spin σ and n i,σ = c † i,σ c i,σ . The last term in Eq. (1) describes the spin-spin interaction between the conduction electron spins s i = σ,σ c † i,σ σ σ,σ c i,σ and the localized f -electron spins S i , with the Pauli matrices σ σ,σ .This model has been investigated in one dimension by means of density matrix renormalization group (DMRG) for a filling of n = 1/3 [28], for different fillings in three dimensions using static mean-field theory [33] and for ferromagnetic couplings J < 0 in two dimensions with the aid of variational minimization and Monte Carlo methods [32]. For U = 0, the model reduces to the ordinary Kondo lattice model, exhibiting a competition between spin-density waves (SDWs) and the Kondo effect, while for J = 0 one obtains the attractive Hubbard model with an on-site pairing term. This on-site pairing may evoke superconductivity and, at half filling, also a charge density wave (CDW) state which is energetically degenerate with the SC state [42,43]. Although CDWs play a crucial role at half filling, previous investigations of the model Eq. (1) have ignored possible CDWs [32,33]. A finite J and attractive U allows us to examine the interplay arXiv:1809.03130v2 [cond-mat.str-el]

Reentrant s-wave superconductivity in the periodic Anderson model with attractive conduction band Hubbard interaction

“…This generically leads to d-wave pairing, though recent studies on CeCu 2 Si 2 surprisingly indicated a fully gapped s-wave state 20 . Hence, theoretical work on the systems with periodic magnetic moments was mostly focused on unconventional d-wave pairing near the antiferromagnetic quantum critical point in the Kondo/Anderson lattice model [21][22][23] , with few exceptions that treated attractive on-site pairing interaction in the Kondo lattice model [24][25][26][27] .…”

“…The repulsive interaction U on f-orbitals is treated within dynamical mean eld theory [28] (DMFT) using continuous time hybridization expansion quantum Monte Carlo (Cthyb QMC) impurity solver [29], while the on-site pairing g is treated on the static mean-eld level. This model is closely related to the Kondo lattice model that has been very recently studied [24,25], but here we focus on nite temperatures and away from half-lling where magnetic and charge density wave instabilities are expected to be weaker. We study the superconductivity phase diagram for different pairing couplings g and hybridization V. For strong coupling g we nd reentrant superconductivity which resembles the one seen in the diluted impurities case.…”

Superconducting Kondo phase in an orbitally separated bilayer

“…The quest for alternative scenarios leading to superconductivity in KLM-like models is therefore a question of current interest. In particular, we note that the Kondo singlet phase (both the insulator at half filling and the doped metallic phase) seems to be quite robust, since the inclusion of local pairing interactions between the conduction electrons only stabilizes superconductivity in the strong attractive coupling limit, or in the weak d-f exchange coupling [24,25]. One possible route towards superconductivity is the introduction of an extra layer, with the purpose of altering the band structure in a fundamental way.…”