Abstract We explore the interplay between nematicity (spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band (PFB) models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the T c dome. There, a plausible s x 2 + y 2 − d x 2 − y 2 − d x y -wave symmetry, in place of the conventional d x 2 − y 2 -wave, governs the nematicity-enhanced pairing with a sharp rise in the T c dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing interaction is shown to become stronger with more compact pairs in real space than when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the PFBs with many-body interactions.
Abstract We explore the interplay between nematicity (spontaneous breaking of the sixfold rotational symmetry), superconductivity, and non-Fermi liquid behavior in partially flat-band (PFB) models on the triangular lattice. A key result is that the nematicity (Pomeranchuk instability), which is driven by many-body effect and stronger in flat-band systems, enhances superconducting transition temperature in a systematic manner on the T c dome. There, a plausible s x 2 + y 2 − d x 2 − y 2 − d x y -wave symmetry, in place of the conventional d x 2 − y 2 -wave, governs the nematicity-enhanced pairing with a sharp rise in the T c dome on the filling axis. When the sixfold symmetry is spontaneously broken, the pairing interaction is shown to become stronger with more compact pairs in real space than when the symmetry is enforced. These are accompanied by a non-Fermi character of electrons in the PFBs with many-body interactions.
Interactions in Fermi systems can induce a "Pomeranchuk instability" leading to orientational symmetry breaking, that is, nematic order. In a metallic system close to such an instability the Fermi surface is easily deformed by anisotropic perturbations, and exhibits enhanced collective fluctuations. We discuss electrons on a square lattice near a Pomeranchuk instability with d-wave symmetry. The strong response of such a system to a small orthorhombic perturbation can explain naturally the large in-plane anisotropy of electronic and magnetic properties observed in detwinned YBCO crystals. Fluctuations in a quantum critical regime near the instability provide a mechanism for non-Fermi liquid behavior. They lead to a singular forward scattering interaction, which destroys fermionic quasi-particles on the whole Fermi surface except at "cold spots" on the Brillouin zone diagonal. The decay rate for DC transport is linear in temperature except at the cold spots, where conventional Fermi liquid behavior survives. In clean systems this gives rise to a T 3/2 temperature dependence of the DC resistivity, as observed in some overdoped cuprates. In the presence of disorder, the resistivity is linear in T at low temperatures.
Interplay of Pomeranchuk instability (spontaneous symmetry breaking of the Fermi surface) and d-wave superconductivity is studied for the repulsive Hubbard model on the square lattice with the dynamical mean-field theory combined with the fluctuation exchange approximation (FLEX+DMFT). We show that the fourfold symmetric Fermi surface becomes unstable against a spontaneous distortion into twofold near the van Hove filling, where the symmetry of superconductivity coexisting with the Pomeranchuk-distorted Fermi surface is modified from the d-wave pairing to the (d+s) wave. By systematically shifting the position of van Hove filling with varied second- and third-neighbor hoppings, we find that the transition temperature TcPI for the Pomeranchuk instability is more sensitively affected by the position of van Hove filling than the superconducting TcSC. This implies that the filling region for strong Pomeranchuk instability and that for the TcSC dome can be separated, and that Pomeranchuk instability can appear even if the peak of TcPI is lower than the peak of TcSC. An interesting finding is that the Fermi surface distortion can enhance the superconducting TcSC in the overdoped regime, which is explained with a perturbational picture for small distortions.
While many-body effects in flat-band systems are receiving renewed hot interest in condensed-matter physics for superconducting and topological properties as well as for magnetism, studies have primarily been restricted to multiband systems (with coexisting flat and dispersive bands). Here we focus on one-band systems where a band is ``partially flat,'' comprising flat and dispersive portions in k space to reveal whether intriguing correlation effects can already arise on the simplest possible one-band level. For that, the two-dimensional repulsive Hubbard model is studied for two models having different flat areas in an intermediate-coupling regime with the dynamical mean-field theory combined with the fluctuation exchange approximation. We have a crossover from ferromagnetic to antiferromagnetic spin fluctuations as the band filling is varied and this triggers, for the model with a wider flat portion, a triplet-pair superconductivity favored over an unusually wide filling region, which is taken over by a sharply growing singlet pairing. For the model with a narrower flat portion, TC against filling exhibits an unusual double-peaked TC dome, associated with different numbers of nodes in the gap function having remarkably extended pairs in real space. We identify these as a manifestation of the physics outside the conventional nesting physics where only the pair scattering across the Fermi surface in designated (hot) spots is relevant. Another correlation effect arising from the flattened band is found in a non-Fermi-liquid behavior as detected in the momentum distribution function, frequency dependence of the self-energy, and spectral function. These indicate that unusual correlation physics can indeed occur in flat-band systems.
Strong interaction between fermions may lead to a novel quantum ground state where the rotational symmetry is spontaneously broken while the translational symmetry is still preserved. Such a 'nematic' Fermi liquid has a spontaneously deformed Fermi surface and supports a gapless Goldstone mode associated with the broken rotational symmetry. We consider a nematic Fermi liquid of fermions carrying two internal quantum numbers that, for example, may represent the layer degree of freedom of a bilayer system. It is found that the effective interaction mediated by a collective mode gives rise to a pairing instability of the underlying fermions under certain conditions, leading to the conclusion that the nematic order could be useful for superconductivity.
While it is over 30 years since the high-T c superconductor was discovered, the cuprates have attracted great interests in many scientific fields.Understanding high-T c is one of the most challenging issues in the condensed matter theory.The mechanism of the superconductivity in these materials is still not fully understood, and continues to be discussed intensely.Specifically, the two-dimensional repulsive Hubbard model, which is a representative model for the cuprates, still has many questions, and many analytical and numerical methods have been proposed for studying the superconductivity, magnetism and other instabilities.In the present thesis, we propose to combine the non-perturbative dynamical mean field theory (DMFT) with the perturbative diagrammatic expansion techniques to treat the local correlation effects ("Mott physics") and momentum dependent pairing interaction (that produces the d-wave pairing superconductivity) to explore the superconductivity and various instabilities in the Hubbard model.First, we formulate the combination of the fluctuation exchange (FLEX) approximation and DMFT in a self-consistent manner in terms of the Luttinger-Ward functional for superconducting phases.The resultant phase diagram exhibits a clear T c dome structure against the band filling as observed experimentally, while in the ordinary FLEX, T c almost monotonically increases toward the half-filling.We trace the origin of the T c -dome back to a combined effect of the filling dependence of the local vertex correction and the filling dependence of the pairing interaction.As another effect inherent in the strongly correlated systems, we study a phase transition for the Pomeranchuk instability, where the four-fold rotational symmetry in the electronic structure on the tetragonal lattice is spontaneously broken into two-fold due to an interaction effect.We find that the Pomeranchuk instability is remarkably more sensitive to the Fermi surface warping than the superconducting T c dome.An interesting question is the effect of the distorted Fermi surface due to the Pomeranchuk instability on the superconductivity, and we have revealed that the gap function is slightly changed from ordinary d-wave pairing to (d+s)-wave.Furthermore, we find that the Fermi surface distortion can enhance the superconducting T c in frustrated systems.i Finally, we consider the extension of the DMFT vertex to study the vertex correction effect on nonlocal self-energy and the pairing interaction.For this purpose, we employ the DΓA (dynamical vertex approximation) formalism, which is extended here to accommodate superconducting phases.For the Hubbard model we obtain the T c -dome due to a combined effect as in the FLEX+DMFT case, but the transition temperature is reduced by the vertex correction.We also find that the pairing interaction is strongly screened by the vertex correction effect.ii
Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin [Formula: see text] itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting [Formula: see text] enclosing the nematic quantum critical point. For temperatures above [Formula: see text], we see strikingly non-Fermi liquid behavior, including a "nodal-antinodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low-frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.