Antiferromagnetic fluctuations, symmetry and shape of the gap function in the electron-doped superconductors: the functional renormalization-group analysis

The problem of the symmetry of the superconducting pairing and the form of the gap function in the electron-doped superconductors is reconsidered within the temperature-cutoff functional renormalization group approach combined with the Bethe-Salpeter equations. The momentum dependence of the order parameter for antiferromagnetic and superconducting instabilities in these compounds is analyzed. The gap function in the antiferromagnetic (particle-hole) channel has its maxima at the hot-spots, or at the diagonal of the Brilloin zone in their absence. The wavefunction in the singlet superconducting channel is non-monotonic in the vicinity of the (pi,0) and (0,pi) points, in striking similarity with recent experimental data. An instability in the triplet superconducting channel is much weaker than the singlet one and has an f-wave like form of the gap function.Comment: 4 pages, RevTe

The effect of six-point one-particle reducible local interactions in the dual fermion approach

We formulate the dual fermion approach to strongly correlated electronic systems in terms of the lattice and dual effective interactions, obtained by using the covariation splitting formula. This allows us to consider the effect of six-point one-particle reducible interactions, which are usually neglected by the dual fermion approach. We show that the consideration of one-particle reducible six-point (as well as higher order) vertices is crucially important for the diagrammatic consistency of this approach. In particular, the relation between the dual and lattice self-energy, derived in the dual fermion approach, implicitly accounts for the effect of the diagrams, containing 6-point and higher order local one-particle reducible vertices, and should be applied with caution, if these vertices are neglected. Apart from that, the treatment of the self-energy feedback is also modified by 6-point and higher order vertices; these vertices are also important to account for some non-local corrections to the lattice self-energy, which have the same order in the local 4-point vertices, as the diagrams usually considered in the approach. These observations enlighten an importance of 6-point and higher order vertices in the dual fermion approach, and call for development of new schemes of treatment of non-local fluctuations, which are based on one-particle irreducible quantities.Comment: 12 pages, 3 figure

Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider Polchinski or Wick-ordered schemes with amputation of full (instead of bare) Green functions, as well as more general schemes, and eastablish their relation to the `dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16, 171 (2007)]. While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is not also evident, how the mean-field (MF) solution of these problems is recovered in this scheme. For Wick ordered scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize usefullness of the schemes, which are local in cutoff parameter, and compare them to the one-particle irreducible approach.Comment: 13 pages; updated and extended versio

On the fulfillment of Ward identities in the functional renormalization group approach

I consider the fulfillment of conservation laws and Ward identities in the one- and two-loop functional renormalization group approach. It is shown that in a one-particle irreducible scheme of this approach Ward identities are fulfilled only with the accuracy of the neglected two-loop terms O(V^3) at one-loop order, and with the accuracy O(V^4) at two-loop order (V is the effective interaction vertex at scale \Lambda). The one-particle self-consistent version of the two-loop RG equations which leads to smaller errors in Ward identities due to the absence of the terms with non-overlapping loops, is proposed. In particular, these modified equations exactly satisfy Ward identities in the ladder approximation.Comment: 4 pages, 1 figure, RevTe

Effect of weak impurities on electronic properties of graphene: functional renormalization-group analysis

We consider an effect of weak impurities on electronic properties of graphene within the functional renormalization-group approach. The energy dependences of the electronic self-energy and density of states near the neutrality point are discussed. Depending on the symmetry of the impurities, the electronic damping $\Gamma$ and density of states $\rho$ can deviate substantially from those given by the self-consistent Born approximation. We investigate the crossover from the results of the self-consistent Born approximation, which are valid far from the neutrality point to the strong-coupling (diffusive) regime near the neutrality point. For impurities, which are diagonal in both, valley and sublattice indices, we obtain finite density of states at the Fermi level with the values, which are much bigger than the results of the self-consistent Born approximation.Comment: 4+1 pages, 5 figure

Competing phases in the extended U-V-J Hubbard model near the van Hove fillings

The phase diagram of the two-dimensional extended one-band U-V-J Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization group (RG) approaches near the van Hove band fillings. At small t' and J>0 mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach, which predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. At the same time, there is a complex competition between SDW, CF phases, and d-wave superconductivity in two- and many-patch RG approaches. While the spin-flux (SF) phase is not stable at the mean-field level, it is identified as a possible ground state at J<0 in both RG approaches. With increasing t' the results of all three approaches merge: d-wave superconductivity at J>0 and ferromagnetism at J<0 become the leading instabilities. For large enough V the charge-density-wave (CDW) state occurs.Comment: This is the extended version of the paper, which includes both two- and many-patch RG analyse

Renormalization group analysis of magnetic and superconducting instabilities near van Hove band fillings

Phase diagrams of the two-dimensional one-band t-t' Hubbard model are obtained within the two-patch and the temperature-cutoff many-patch renormalization group approach. At small t' and at van Hove band fillings antiferromagnetism dominates, while with increasing t' or changing filling antiferromagnetism is replaced by d-wave superconductivity. Near t'=t/2 and close to van Hove band fillings the system is unstable towards ferromagnetism. Away from van Hove band fillings this ferromagnetic instability is replaced by a region with dominating triplet p-wave superconducting correlations. The results of the renormalization-group approach are compared with the mean-field results and the results of the T-matrix approximation.Comment: 29 pages, 17 figure