We make a non-perturbative analysis of the strong interaction between gapless nodal fermions and nematic order parameter in two-dimensional
dx2−y2 superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor
N is smaller than a threshold
Nc. Such gap generation leads to an additional
is-wave Cooper pairing instability, and induces a fully gapped
dx2−y2+is superconducting dome in the vicinity of nematic quantum critical point. The opening of dynamical gap has important consequences, including saturation of fermion velocity renormalization, weak confinement of fermions, and suppression of observable quantities.
Abstract The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropic s-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap
Δ(θ,ωm) Δ ( θ , ω m ) and show that its angular dependence strongly varies below
Tc T c . We show that this variation is a signature of QC pairing and comes about because there are multiple s-wave pairing instabilities with closely spaced transition temperatures
Tc,n T c , n . Taken alone, each instability would produce a gap
Δ(θ,ωm) Δ ( θ , ω m ) that changes sign
8n 8 n times along the Fermi surface. We show that the equilibrium gap
Δ(θ,ωm) Δ ( θ , ω m ) is a superposition of multiple components that are nonlinearly induced below the actual
Tc=Tc,0 T c = T c , 0 , and get resonantly enhanced at
T=Tc,n < Tc T = T c , n < T c . This gives rise to strong temperature variation of the angular dependence of
Δ(θ,ωm) Δ ( θ , ω m ) . This variation progressively disappears away from a QC point.
The
d-wave high-temperature cuprate superconductor may exhibit a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effects on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization-group analysis shows that random mass and random gauge field are both irrelevant and, thus, do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.
At the nematic quantum critical point that exists in the -wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of the renormalization group approach and show that, the fermion damping rate vanishes more rapidly than the energy ω and the quasiparticle residue in the limit . The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid theory than a marginal Fermi liquid. We also investigate the interplay of quantum nematic critical fluctuation and gauge-potential-like disorder, and find that the effective disorder strength flows to the strong coupling regime at low energies. Therefore, even an arbitrarily weak disorder can drive the system to become a disorder controlled diffusive state. Based on these theoretical results, we are able to understand a number of interesting experimental facts observed in curpate superconductors.
Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x(2)-y(2)) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x(2)-y(2))+is and d(x(2)-y(2))+id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0,1) essentially undamped.
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.