Abstract:
We compare predictions of the mean-field theory of superconductivity for nearly antiferromagnetic and nearly ferromagnetic metals for cubic and tetragonal lattices. The calculations are based on the parametrization of an effective interaction arising from the exchange of magnetic fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, the robustness of magnetic pairing increases gradually as one goes from a cubic structure to a more and more anisotropic tetragonal structure either on the border of antiferromagnetism or ferromagnetism.

Abstract:
We conpare predictions of the mean-field theory of supercnductivity for metallic systems on the border of a density instability for cubic and tetragonal lattices. The calculations are based on a parametrisation of an effective interaction arising from the exchange of density fluctuations and assume that a single band is relevant for superconductivity. The results show that for comparable model parameters, desnity fluctuation mediated pairing is more robust in quasi-two dimensions than in three dimensions, and that the robustness of pairing increases gradually as one goes from a cubic to a more and more anisotropic tetragonal structure. We also find that the robustness of density fluctuation mediated pairing can depend sensitively on the incipient ordering wavevector. We discuss the similarities and differences between the mean-field theories of superconductivity for density and magnetically mediated pairing.

Abstract:
We compare predictions of the mean-field theory of superconductivity for nearly antiferromagnetic and nearly ferromagnetic metals in two dimensions. The calculations are based on a parametrization of the effective interaction arising from the exchange of magnetic fluctuations. The Eliashberg equations for the transition temperature are solved including the full momentum dependence of the self-energy. The results show that for comparable parameters d-wave singlet pairing in nearly antiferromagnetic metals is generally much stronger than p-wave triplet pairing in nearly ferromagnetic metals in quasi two dimensions. The relevance to the layered materials, and in particular Sr2RuO4 that exhibits p-wave triplet pairing, is discussed.

Abstract:
We present detailed electronic structure calculations for CaFe2As2. We investigate in particular the `collapsed' tetragonal and orthorhombic regions of the temperature-pressure phase diagram and find properties that distinguish CaFe2As2 from other Fe-pnictide compounds. In contrast to the tetragonal phase of other Fe-pnictides the electronic structure in the `collapsed' tetragonal phase of CaFe2As2 is found to be strongly 3D. We discuss the influence of these properties on the formation of superconductivity and in particular we find evidence that both magnetic and lattice interactions may be important to the formation of superconductivity. We also find that the Local Spin Density Approximation is able to accurately predict the ordering moment in the low temperature orthorhombic phase.

Abstract:
We introduce a simple but powerful zero temperature Stoner model to explain the unusual phase diagram of the ferromagnetic superconductor, UGe2. Triplet superconductivity is driven in the ferromagnetic phase by tuning the majority spin Fermi level through one of two peaks in the paramagnetic density of states (DOS). Each peak is associated with a metamagnetic jump in magnetisation. The twin peak DOS may be derived from a tight-binding, quasi-one-dimensional bandstructure, inspired by previous bandstructure calculations.

Abstract:
We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi surface section comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as nuclear magnetic resonance and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.

Abstract:
Using density functional theory we investigate the evolution of the magnetic ground state of NbFe$_{2}$ due to doping by Nb-excess and Fe-excess. We find that non-rigid-band effects, due to the contribution of Fe-\textit{d} states to the density of states at the Fermi level are crucial to the evolution of the magnetic phase diagram. Furthermore, the influence of disorder is important to the development of ferromagnetism upon Nb doping. These findings give a framework in which to understand the evolution of the magnetic ground state in the temperature-doping phase diagram. We investigate the magnetic instabilities in NbFe$_{2}$. We find that explicit calculation of the Lindhard function, $\chi_{0}(\mathbf{q})$, indicates that the primary instability is to finite $\mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energy calculations indicate that $\mathbf{q}=0$ antiferromagnetism is the ground state. We discuss the influence of competing $\mathbf{q}=0$ and finite $\mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior in this material.

Abstract:
Density functional theory methods are applied to investigate the properties of the new superconductor $\beta$-YbAlB$_4$ and its polymorph $\alpha$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $\beta$-YbAlB$_4$ and $\alpha$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $\beta$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $\beta$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.

Abstract:
A renormalization group treatment of metamagnetic quantum criticality in metals is presented. In clean systems the universality class is found to be of the overdamped, conserving (dynamical exponent z=3) Ising type. Detailed results are obtained for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity and specific heat near the transition. An application of the theory is made to Sr3Ru2O7, which appears to exhibit a metamagnetic critical end-point at a very low temperature and a field of order 5-7T.

Abstract:
We present the first study of a magnetic quantum phase transition in the itinerant-electron ferromagnet Ni3Al at high pressures. Electrical resistivity measurements in a diamond anvil cell at hydrostatic pressures up to 100 kbar and temperatures as low as 50 mK indicate that the Curie temperature collapses towards absolute zero at a critical pressure pc=82(2) kbar. Over wide ranges in pressure and temperature, both in the ferromagnetic and paramagnetic states, the temperature variation of the resistivity is found to deviate from the conventional Fermi-liquid form. We consider the extent to which this deviation can be understood in terms of a mean-field model of enhanced spin fluctuations on the border of ferromagnetism in three dimensions.