Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

Abstract

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism and d-wave superconductivity in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the twodimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t ′ , the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t ′′ improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs Tc/T max c phase diagram of the cuprates is universal. The calculated angle-resolved photoemission spectrum displays the observed electron-hole asymmetry. The tendency to homogeneous coexistence of the superconducting and antiferromagnetic order parameters is stronger than observed in most experiments but consistent with many theoretical results and with experiments in some layered high-temperature superconductors. Clearly, our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BardeenCooper-Schrieffer approach. At strong coupling, d-wave superconductivity and antiferromagnetism appear naturally as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.

Dynamical mean-field theory study of stripe order and d -wave superconductivity in the two-dimensional Hubbard model

“…The uniform solution is similar to those in earlier work [53,54], although we did not study exactly the same parameters. The plaquette-DMFT energy is in reasonable agreement with recent numerical results [78], although the differences between methods are generally larger than, e.g., differences in the energies of different wavelength stripe states.…”

“…Thus, on the one hand, we extend the single-site real-space DMFT calculations [62,63,65,66] to include d-wave superconductivity and, on the other, we extend the uniform plaquette DMFT approximation [52][53][54][55]57,58] to include the striped order. We find a wide region of coexistence between striped order and spatially modulated d-wave superconductivity, and analyze the behavior of the superconducting order parameter in the striped states.…”

“…It has been used to gain insight to the Mott transition both in the Hubbard model [49] and in real materials [50]. Since the initial realization [52] that the plaquette DMFT (meaning cellular DMFT [51] with a 2 × 2 cluster) can describe d-wave superconductivity, this approximation has been employed to study the competition and coexistence of superconductivity and magnetic order in the ground state [53,54], the effect of nearest-neighbor repulsion [55,56], and finite temperature energetics and critical temperatures of the superconductivity [57,58]. This approximation in its basic form cannot produce a striped state, since the 2 × 2 unit cell does not allow modulation of the magnetization across the lattice.…”

Effective theory of Fermi pockets in fluctuating antiferromagnets

“…In a recent paper 37 with others, we argued that there were 2 generic possibilities: (i ) In the first case, there was a direct transition at a single critical g = g c to a Fermi liquid metal with a large Fermi surface. This transition has been examined in previous work 38 , and is directly expressed in terms of fluctuations of the O(3) order parameter n a ; the T > 0 crossovers above g = g c have also been described [27][28][29][30][31] .…”

Bosons in high-temperature superconductors: an experimental survey

“…Earlier cluster dynamical mean-filed computations by Haule et al (2007) had already produced a phase diagram for the d-wave order parameter which follows the dome behaviour as a function of doping seen for the value of the critical temperature T c . Additional work by Kancharla et al (2008) gives more details on the competition between superconductivity and antiferromagnetism in doped Mott insulators. These results provide in part, a motivation for the experimental investigation of possible boson effects in the high T c oxides as will be reviewed here.…”