We derive the polarizability of an electron system in (i) the superconducting phase, with
d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the
d-density-wave (dDW) state, characterized by a
d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-
Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azimuthal modulation, consistent with the
d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector $\mathbf{Q}=(\ensuremath{\pi},\ensuremath{\pi})$, albeit imperfect, due to a nonzero value of the hopping ratio ${t}^{\ensuremath{'}}∕t$ in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the $(\mathbf{q},\ensuremath{\omega})$ dependence of the retarded polarizability.
One of the most prominent problems in high temperature superconductivity is the nature of the pseudogap phase in underdoped regimes; particularly important is the role of phase fluctuations. The Gutzwiller-projected BCS Hamiltonian is a useful model for high temperature superconductivity due to an exact mapping to the Heisenberg model at half filling and generally a very close connection to the t-J model at moderate doping. We develop the dynamical mean field theory for the d-wave BCS Hamiltonian with on-site repulsive interaction,
U, physically imposing the partial Gutzwiller projection. For results, two pseudogap energy scales are identified: one associated with the bare pairing gap for the singlet formation and the other with the local phase coherence. The real superconducting gap determined from sharp coherence peaks in the density of states shows strong renormalization from the bare value due to
U.
Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale $\ensuremath{\xi}$ via a momentum dependent external self-energy ${\ensuremath{\Sigma}}_{\mathbf{k}}$. This external self-energy describes nonlocal dynamical correlations induced by the short-ranged collective spin density wave--like antiferromagnetic spin (or the charge density wave--like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with a finite correlation length. This generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with the nearest and the next nearest neighbor hopping. The effective single impurity problem in this generalized $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ is solved by the numerical renormalization group. Both types of the strongly correlated metals, namely: (i) The doped Mott insulator and (ii) the case of the bandwidth $W\ensuremath{\lesssim}U$ (
U---value of the local Coulomb interaction) are considered. The densities of states, the spectral functions, and the angle resolved photoemission spectra calculated within the $\mathrm{DMFT}+{\ensuremath{\Sigma}}_{\mathbf{k}}$ show a pseudogap formation near the Fermi level of the quasiparticle band.
We conclusively show that a pseudogap state can arise at
T>Tc, for reasonable pairing interaction strength, from order parameter fluctuations in a two-dimensional minimal model of
d-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest-neighbor interaction and establish our result using a combination of a cluster-based Monte Carlo method for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\ensuremath{\sim}160\ifmmode\times\else\texttimes\fi{}160$ allows two major conclusions: (i) at
T<Tc, despite the presence of thermal phase fluctuations, the superconductor has only nodal Fermi points while all non-nodal points on the normal state Fermi surface show a two-peak spectral function with a dip at $\ensuremath{\omega}=0$, and (ii) for
T>Tc, the Fermi points develop into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature
T∗>Tc. We show the variation of
Tc and
T∗ with coupling strength and provide detailed spectral results at a coupling where ${T}^{*}\ensuremath{\sim}1.5{T}_{c}$.
It is generally believed that in a 2D metal, whose ground state is antiferromagnetically ordered with
Q=(π,π), thermal (static) magnetic fluctuations give rise to precursor behavior above
TN, in which the spectral function of a hot fermion (the one for which
k and
k+Q are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of
T>TN and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following [Y.M. Vilk and A.-M. S. Tremblay, J. Phys. I France
7 1309 (1997)] that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion, but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, like, e.g., Eliashberg theory for magnetically-mediated superconductivity. We also analyze the potential pseudogap behavior at
T=0. We argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.