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Summary Mutant alleles of several genes in the DNA repair pathway have been found to predispose women to breast cancer. From a public health perspective, the importance of a given allele in a population is determined by the frequency of the allele and by the relative risk of breast cancer that it confers. In Poland founder alleles of the BRCA1, CHEK2 and NBS1 genes have been associated with an increased risk of breast cancer, but the relative contribution of each of these alleles to the overall breast cancer burden has not yet been determined. We screened 2012 unselected cases of breast cancer and 4000 population controls for 7 different mutations in these genes. Overall, a mutation was found in 12% of the cases and in 6% of the controls. Mutations in BRCA1 and CHEK2 contributed in approximately equal measure to the burden of breast cancer in Poland. A BRCA1 mutation was present in 3% of the cases. The missense BRCA1 mutation C61G was associated with a higher odds ratio for breast cancer (OR=15) than were either of the truncating BRCA1 mutations 4153delA (OR=2.0) and 5382insC (OR=6.2). In contrast, a higher odds ratio was seen for truncating CHEK2 mutations (OR=2.1) than for the missense mutation I157T (OR=1.4). This study suggests that cancer risks may be specific for particular alleles of a susceptibility gene and that these different risks should be taken into account by genetic counselors.

We have investigated anisotropic density-wave phase with arbitrary ordering wave vector (Q) and estimated the value of Qthat corresponds to the minimum of the free energy. We have found that for a wide range of model parameters the commensurate d-density-wave (DDW) is actually the most stable density-wave state. However, for moderate doping the commensurate DDW state is stable only at finite temperatures and disappears when the temperature is sufficiently low. These features may assist in clarification of the mechanism of the pseudogap.

We discuss the phonon self-energy in the presence of isotropic and anisotropic gaps, which originate from the charge (CDW) and spin-density waves (SDW). In order to connect our results to the problem of high-temperature superconductivity a two-dimensional lattice has been considered. The shift of the phonon frequency and the modification of the linewidth is investigated for different phonon momenta. We show that the onset of a gap leads predominantly to the hardening of low frequency modes and softening of modes, which correspond to higher frequencies. In the latter case the modification of phonon properties depends on the symmetry of the gap. For the isotropic gap the softening of frequencies is important only for phonons with small momentum, whereas for the d-wave gap also properties of phonons with large momentum can seriously be modified.

We discuss the influence of charge-density wave (CDW) order on the electron–phonon vertex and the Cooper-pair susceptibility. These quantities are investigated for different values of occupation numbers, phonon momenta and frequencies, as well as for different directions and commensurabilities of the CDW scattering vector. For the half-filled band, the onset of a CDW state results in a considerable enhancement of the electron–phonon interaction, especially when the phonon momentum is close to the scattering vector. Our results suggest that for imperfect nesting different parts of the Fermi surface contribute to a CDW and d-wave superconducting state. This feature is of particular importance for the coexistence of both phases.

The two-dimensional Hubbard model coupled to phonons has been considered in the U→ ∞ limit. We have introduced fluctuations of the auxiliary boson fields over their mean-field value to allow for the phonon-free pairing mechanism. Vertex corrections to the Eliashberg equations in electron–boson and electron–phonon channels have been taken into account. The superconducting transition temperature Tchas been evaluated as a function of the occupation number. It has been found that phonon-mediated and correlation-mediated pairing mechanisms cooperate in the formation of a d-wave superconducting state for physically interesting concentrations of holes. It is vertex corrections in the electron–phonon channel that causes vanishing of Tcwhen approaching half-filling. Vertex corrections in the electron–boson channel are of minor importance in the underdoped region. However, they suppress the superconducting transition temperature at optimal doping and in the overdoped region causing the occupation number dependence of Tcto become similar to the experimentally observer behavior.

The interlayer tunneling in high-temperature superconductors has been reconsidered beyond the mean-field approximation. The modification of the quasiparticle spectrum originating from the momentum-conserving interlayer transportation of Cooper pairs has been taken into account exactly. The pronounced reduction of the superconducting transition temperature when compared to the mean-field solution can be observed. Our self-consistent Green's functions approach allows for incorporation of Coulomb correlation and gives support for the mixed s- and d-wave scenario of high-temperature superconductivity.

We consider the two-dimensional Hubbard model including electron-phonon interaction. Strong local correlations (U?8 limit) are taken into account within the mean-field approximation for auxiliary boson fields. Phonon-assisted transitions between intraand interlayer states are introduced as the source of coupling between two-dimensional CuO2 layers. This type of processes effectively leads to the nonlinear (quadratic) interaction of intralayer electrons withc-axis phonons. We construct the Eliashberg equations for the resulting Hamiltonian and evaluate the superconducting transition temperatureTc. Our model calculation demonstrates that a pronounced enhancement ofTc in thed-wave channel is possible. The largest enhancement ofTc tends to take place for small hole concentrations. This means that the coupling toc-axis phonons could compete with two-dimensional correlations responsible for the onset of antiferromagnetic order. It is remarkable that the two-dimensional features in the normal state are hardly affected by this specific interlayer interaction. Therefore,c-axis two-phonon-mediated interlayer coupling can cooperate with interlayer pair tunneling and substantially contribute to an increased pairing.

We have investigated anisotropic superconductivity originating from intersite pairing between holes in nearest and next nearest neighboring sites in the Emery model. Strong local Coulomb correlations among holes in copper orbitals have been taken into account within the Hubbard I approximation scheme. The superconducting transition temperature has been evaluated as a function of the hole concentration. It has been shown that with the onset of superconductivity, pairing among oxygen-like quasiparticles in the mixeds-wave+d-wave channel plays the dominating role, being replaced by pairing in the extendeds-wave channel for higher concentration of holes. Superconducting correlations are mostly effective for a rather narrow range of the model parameter values, close to values derived from band structure calculations. Therefore, the coupling betweens-wave andd-wave channels seems to be a general feature of superconductivity in CuO2 planes.

We discuss the impact of the strong electron-phonon interactions on the physical properties of correlated electrons in the two-dimensional Hubbard model. An easy access to the physical properties of the superconducting state is obtained by solving the Eliashberg equations with explicit momentum-dependent kernels. In order to facilitate the numerical procedure to solve these equations, correlations are treated within the Gutzwiller approximation (i.e., mean-field-slave boson approximation). Our results strongly support the view thatd-wave symmetry is the most important feature of the superconducting state in the copper oxides. A possible extension beyond the mean field approximation is also presented.

We address the problem of anisotropic superconductivity in the two-dimensional Hubbard model. The Eliashberg equations have been generalized to the case which accounts for the anisotropy of the order parameter. Strong local correlations are treated within the mean field slave boson approximation. The superconducting transition temperatureTc is evaluated as a function of the occupation number. Our results indicate that thed-wave state is the most likely channel for superconductivity for small concentration of holes. We have also derived an approximate analytical formula forTc valid for any value of the occupation number. In addition, the influence of strong correlations on the electron-phonon coupling function is also discussed.