Strongly correlated superconductivity: A plaquette dynamical mean-field theory study

Abstract

We use cluster Dynamical Mean Field Theory to study the simplest models of correlated electrons, the Hubbard model and the t-J model. We use a plaquette embedded in a medium as a reference frame to compute and interpret the physical properties of these models. We study various observables such as electronic lifetimes, one electron spectra, optical conductivities, superconducting stiffness, and the spin response in both the normal and the superconducting state in terms of correlation functions of the embedded cluster. We find that the shortest electron lifetime occurs near optimal doping where the superconducting critical temperature is maximal. A second critical doping connected to the change of topology of the Fermi surface is also identified. The mean field theory provides a simple physical picture of three doping regimes, the underdoped, the overdoped and the optimally doped regime in terms of the physics of the quantum plaquette impurity model. We compare the plaquette Dynamical Mean Field Theory results with earlier resonating valence bond mean field theories, noting the improved description of the momentum space anisotropy of the normal state properties and the doping dependence of the coefficient of the linear temperature dependence of the superfluid density in the superconducting state.

Plaquette valence bond theory of high-temperature superconductivity

“…We think that this critical point of the plaquette has crucial importance for the physics of the strong-coupling d x 2 −y 2 -wave superconductivity. The importance of these three many-body states of the plaquette CDMFT has been discussed first for the t-J model [19]. In that case an additional triplet state in the N = 4 sector appeared without formation of the single quantum critical point.…”

“…Since the first plaquette CDMFT calculation of d x 2 −y 2 -wave superconducting order together with antiferromagnetic fluctuations [16], there have been many calculations for different cluster sizes and geometries based on continuous-time quantum Monte Carlo (CTQMC) or exact diagonalization solvers [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. Unfortunately, the basic qualitative feature of the many-body states in the plaquette were hidden in the computational details.…”

Cluster extended dynamical mean-field approach and unconventional superconductivity

“…After that, δ σσ (r i − r j ) is then constructed using the translation invariance of the lattice. Two major differences between these self-consistent equations and those in CDMFT [31] are the explicit appearance of the order parameter and the fact that the intersite magnetic interaction is driving the superconducting pairing.…”

“…When the Weiss fields are neglected, these cluster schemes are no longer self-consistent and reduce to cluster perturbation theory (CPT), which approximates lattice quantities by expanding about the isolated cluster limit [30]. A main advantage of dynamical cluster theories is the ability to account for various types of order not possible within DMFT [31]. For example, a four-site cluster can treat a d-wave superconducting order parameter as well as stripe charge or spin order.…”

Dynamical mean field theory of the repulsive BCS+Umodel

“…The basic idea is to incorporate the superconducting order parameter via the Nambu spinor formalism [12]. A more recent development is to combine the Nambu spinor formalism with the cellular dynamical mean field theory (CDMFT), which enlarges the DMFT impurity from a single site to a cluster [14,16,32]. An important advantage of this approach is the flexibility to allow non-local pairing such as d-wave pairing now that electrons can be paired with those in the other sites within the cluster.…”