We investigate the competing Fermi surface instabilities in the kagome tight-binding model. Specifically, we consider on-site and short-range Hubbard interactions in the vicinity of van Hove filling of the dispersive kagome bands where the fermiology promotes the joint effect of enlarged density of states and nesting. The sublattice interference mechanism devised by Kiesel and Thomale [Phys. Rev. B 86, 121105 (2012)] allows us to explain the intricate interplay between ferromagnetic fluctuations and other ordering tendencies. On the basis of the functional renormalization group used to obtain an adequate low-energy theory description, we discover finite angular momentum spin and charge density wave order, a twofold degenerate d-wave Pomeranchuk instability, and f-wave superconductivity away from van Hove filling. Together, this makes the kagome Hubbard model the prototypical scenario for several unconventional Fermi surface instabilities.

The band structure of graphene exhibits van Hove singularities (VHS) at doping x = ±1/8 away from the Dirac point. Near the VHS, interactions effects, enhanced due to the large density of states, can give rise to various many-body phases at experimentally accessible temperatures. We study the competition between different many-body instabilities in graphene using functional renormalization group (FRG). We predict a rich phase diagram, which, depending on long range hopping as well as screening strength and absolute scale of the Coulomb interaction, contains a d + id-wave superconducting (SC) phase, or a spin density wave phase at the VHS. The d + id state is expected to exhibit quantized charge and spin Hall response, as well as Majorana modes bound to vortices. In the vicinity of the VHS, we find singlet d + id-wave as well as triplet f -wave SC phases.

We study the electronic phases of the kagome Hubbard model (KHM) in the weak-coupling limit around Van Hove filling. Through an analytic renormalization group analysis, we find that there exists a sublattice interference mechanism where the kagome sublattice structure affects the character of the Fermi surface instabilities. It leads to major suppression of T c for d + id superconductivity in the KHM and causes an anomalous increase of T c upon addition of longer-range Hubbard interactions. We conjecture that the suppression of conventional Fermi liquid instabilities makes the KHM a prototype candidate for hosting exotic electronic states of matter at intermediate coupling.

Since its discovery, the superconducting phase in water-intercalated sodium cobaltates Na(x)CoO2·yH2O (x∼0.3, y∼1.3) has posed fundamental challenges in terms of experimental investigation and theoretical understanding. By a combined cluster calculation and renormalization group approach, we find an anisotropic chiral d+id-wave state as a consequence of multiorbital effects, Fermi surface topology, and magnetic fluctuations. It naturally explains the singlet property and close-to-nodal gap features of the superconducting phase as indicated by experiments.

One central challenge in high-Tc superconductivity (SC) is to derive a detailed understanding for the specific role of the Cu-d x 2 −y 2 and O-px,y orbital degrees of freedom. In most theoretical studies an effective one-band Hubbard (1BH) or t-J model has been used. Here, the physics is that of doping into a Mott-insulator, whereas the actual high-Tc cuprates are doped charge-transfer insulators. To shed light on the related question, where the material-dependent physics enters, we compare the competing magnetic and superconducting phases in the ground state, the single-and two-particle excitations and, in particular, the pairing interaction and its dynamics in the three-band Hubbard (3BH) and 1BH-models. Using a cluster embedding scheme, i.e. the variational cluster approach (VCA), we find which frequencies are relevant for pairing in the two models as a function of interaction strength and doping: in the 3BH-models the interaction in the low-to optimal-doping regime is dominated by retarded pairing due to low-energy spin fluctuations with surprisingly little influence of inter-band (p-d charge) fluctuations. On the other hand, in the 1BH-model, in addition a part comes from "high-energy" excited states (Hubbard band), which may be identified with a non-retarded contribution. We find these differences between a charge-transfer and a Mott insulator to be renormalized away for the ground-state phase diagram of the 3BH-and 1BH-models, which are in close overall agreement, i.e. are "universal". On the other hand, we expect the differences -and thus, the material dependence to show up in the "non-universal" finite-T phase diagram (Tc-values).