Instabilities at [110] Surfaces of d_{x^2-y^2} Superconductors

We compare different scenarios for the low temperature splitting of the zero-energy peak in the local density of states at (110) surfaces of d_{x^2-y^2}-wave superconductors, observed by Covington et al. (Phys.Rev.Lett.79 (1997), 277). Using a tight binding model in the Bogolyubov-de Gennes treatment we find a surface phase transition towards a time-reversal symmetry breaking surface state carrying spontaneous currents and an s+id-wave state. Alternatively, we show that electron correlation leads to a surface phase transition towards a magnetic state corresponding to a local spin density wave state.Comment: 4 pages, 5 figure

Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t=-0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder.Comment: 8 pages, to appear in European Physical Journal

Theory of reduced singlet pairing without the underlying state of charge stripes in the high-temperature superconductor YBa_2Cu_3O_6.45

Recently, a strongly enhanced xy anisotropy of magnetic excitations was observed in YBa_2Cu_3O_y (YBCO_y) with y=6.45 and Tc=35 K [Science 319, 597 (2008)]. Unlike the observation in YBCO_6.6 and YBCO_6.85, the anisotropy grows to be pronounced at lower temperature and at lower energy, and is not suppressed by the onset of superconductivity. We propose that the effect of singlet pairing is substantially reduced in YBCO_6.45. This reduction concomitantly enhances an order competing with singlet pairing, a strong tendency of the so-called d-wave Pomeranchuk instability, leading to the magnetic excitations observed experimentally.Comment: 11 pages, 4 figures, published versio

Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

We calculate the Landau interaction function f(k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.Comment: 10 pages, 16 figure

Orbital Dependence of Quasiparticle Lifetimes in Sr2RuO4

Using a phenomenological Hamiltonian, we investigate the quasiparticle lifetimes and dispersions in the three low energy bands, gamma, beta, and alpha of Sr2RuO4. Couplings in the Hamiltonian are fixed so as to produce the mass renormalization as measured in magneto-oscillation experiments. We thus find reasonable agreement in all bands between our computed lifetimes and those measured in ARPES experiments by Kidd et al. [1] and Ingle et al. [2]. In comparing computed to measured quasiparticle dispersions, we however find good agreement in the alpha-band alone.Comment: 7 pages, 5 figure

Superconductivity in the attractive Hubbard model: functional renormalization group analysis

We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous propagators and anomalous effective interactions. In addition to the anomalous interactions arising already in the reduced BCS model, effective interactions with three incoming legs and one outgoing leg (and vice versa) occur. We accomplish their integration into the usual diagrammatic formalism by introducing a Nambu matrix for the effective interactions. From a random-phase approximation generalized through use of this matrix we conclude that the impact of the 3+1 effective interactions is limited, especially considering the effective interactions important for the determination of the order parameter. The exact hierarchy of flow equations for one-particle irreducible vertex functions is truncated on the two-particle level, with higher-order self-energy corrections included in a scheme proposed by Katanin. Using a parametrization of effective interactions by patches in momentum space, the flow equations can be integrated numerically to the lowest scales without encountering divergences. Momentum-shell as well as interaction-flow cutoff functions are used, including a small external field or a large external field and a counterterm, respectively. Both approaches produce momentum-resolved order parameter values directly from the microscopic model. The size of the superconducting gap is in reasonable agreement with expectations from other studies.Comment: 22 pages, 16 figures, references added, some changes in the introductio

Renormalization Group Study of the Electron-phonon Interaction in the High Tc Cuprates

We generalize the numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high Tc cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interaction are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interaction will trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.Comment: 4 pages, 3 figures, references added, added more details about others' previous studie

Competition of Fermi surface symmetry breaking and superconductivity

We analyze a mean-field model of electrons on a square lattice with two types of interaction: forward scattering favoring a d-wave Pomeranchuk instability and a BCS pairing interaction driving d-wave superconductivity. Tuning the interaction parameters a rich variety of phase diagrams is obtained. If the BCS interaction is not too strong, Fermi surface symmetry breaking is stabilized around van Hove filling, and coexists with superconductivity at low temperatures. For pure forward scattering Fermi surface symmetry breaking occurs typically via a first order transition at low temperatures. The presence of superconductivity reduces the first order character of this transition and, if strong enough, can turn it into a continuous one. This gives rise to a quantum critical point within the superconducting phase. The superconducting gap tends to suppress Fermi surface symmetry breaking. For a relatively strong BCS interaction, Fermi surface symmetry breaking can be limited to intermediate temperatures, or can be suppressed completely by pairing.Comment: 14 pages, 10 figure

Truncated unity functional renormalization group for multiband systems with spin-orbit coupling

Although the functional renormalization group (fRG) is by now a well-established method for investigating correlated electron systems, it is still undergoing significant technical and conceptual improvements. In particular, the motivation to optimally exploit the parallelism of modern computing platforms has recently led to the development of the "truncated-unity" functional renormalization group (TU-fRG). Here, we review this fRG variant, and we provide its extension to multiband systems with spin-orbit coupling. Furthermore, we discuss some aspects of the implementation and outline opportunities and challenges ahead for predicting the ground-state ordering and emergent energy scales for a wide class of quantum materials.Comment: consistent with published version in Frontiers in Physics (2018