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arXiv:cond-mat/0508205 · Physical Review B

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

S. S. Kancharla, Bumsoo Kyung, David Sénéchal, Marcello Civelli, Massimo Capone, Gabriel Kotliar, A.–M. S. Tremblay

Published May 23, 2008• 184 citations
arXivHTMLPDF

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 toward 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 two-dimensional 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 ${t}^{\ensuremath{'}}$, 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 ${t}^{\ensuremath{''}}$ 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 ${T}_{c}∕{T}_{c}^{\mathit{max}}$ 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 Bardeen--Cooper--Schrieffer approach. At strong coupling, $d$-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.

DOI
10.1103/physrevb.77.184516

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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 toward a quantitative theory of the competition between antiferromagnetism and ddd-wave superconductivity in the cuprates, we use cellular dynamical mean-field theory to compute zero-temperature properties of the two-dimensional square lattice Hubbard model. The ddd-wave order parameter is found to scale like the superexchange coupling JJJ for on-site interaction UUU 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\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′, 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\ensuremath′′{t}^{\ensuremath{''}}t\ensuremath′′ 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∕Tcmax{T}_{c}∕{T}_{c}^{\mathit{max}}Tc​∕Tcmax​ 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 ddd-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard Bardeen--Cooper--Schrieffer approach. At strong coupling, ddd-wave superconductivity and antiferromagnetism naturally appear as two equally important competing instabilities of the normal phase of the same underlying Hamiltonian.
Using variational cluster perturbation theory we study the competition between ddd-wave superconductivity (dSCd\mathrm{SC}dSC) and antiferromagnetism (AF) in the $t\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}{t}^{\ensuremath{'}\ensuremath{'}}\mathrm{\text{\ensuremath{-}}}U$ Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of dSCd\mathrm{SC}dSC that should be observable in photoemission experiments.
The competition between ddd-wave superconductivity (SC) and antiferromagnetism (AF) in the high-Tc{T}_{c}Tc​ cuprates is investigated by studying the hole- and electron-doped two-dimensional Hubbard model with a recently proposed variational quantum-cluster theory. The approach is shown to provide a thermodynamically consistent determination of the particle number, provided that an overall shift of the on-site energies is treated as a variational parameter. The consequences for the single-particle excitation spectra and for the phase diagram are explored. By comparing the single-particle spectra with quantum Monte Carlo and experimental data, we verify that the low-energy excitations in a strongly correlated electronic system are described appropriately. The cluster calculations also reproduce the overall ground-state phase diagram of the high-temperature superconductors. In particular, they include salient features such as the enhanced robustness of the antiferromagnetic state as a function of electron doping and the tendency towards phase separation into a mixed antiferromagnetic-superconducting phase at low doping and a pure superconducting phase at high (both hole and electron) doping.
Cooperation and competition between the antiferromagnetic, ddd-wave superconducting, and Mott-insulating states are explored for the two-dimensional Hubbard model including nearest and next-nearest-neighbor hoppings at zero temperature. Using the variational cluster approach with clusters of different shapes and sizes up to 10 sites, it is found that the doping-driven transition from a phase with microscopic coexistence of antiferromagnetism and superconductivity to a purely superconducting phase is discontinuous for strong interaction and accompanied by phase separation. At half-filling the system is in an antiferromagnetic Mott-insulating state with vanishing charge compressibility. Upon decreasing the interaction strength UUU below a certain critical value of roughly ${U}_{c}\ensuremath{\sim}4$ (in units of the nearest-neighbor hopping), however, the filling-dependent magnetic transition changes its character and becomes continuous. Phase separation or, more carefully, the tendency towards the formation of inhomogeneous states disappears. This critical value is in contrast to previous studies, where a much larger value was obtained. Moreover, we find that the system at half-filling undergoes the Mott transition from an insulator to a state with a finite charge compressibility at essentially the same value. The weakly correlated state at half-filling exhibits superconductivity microscopically admixed to the antiferromagnetic order. This scenario suggests a close relation between phase separation and the Mott-insulator physics.
Abstract The spectral properties of the doped t – t ’ Hubbard model, using parameters typical for high-temperature cuprate superconductors, and the mechanism of d-wave pairing remain among the longstanding problems of many-body fermionic materials. We used a strong-coupling Green’s function expansion around a correlated reference system, namely a particle-hole-symmetric undoped Hubbard lattice with t′=0{t}^{{\prime} }=0t′=0 t ′ = 0 , which can be treated numerically exactly using sign-problem-free lattice Quantum Monte Carlo calculations. This reference system exhibits a large antiferromagnetic Mott-Hubbard-Slater gap in the electronic spectrum. We investigate how the Mott-like spectrum is reconstructed under finite doping and nonzero t′{t}^{{\prime} }t′ t ′ using a dual-fermion-inspired perturbation expansion. For a large next-nearest-neighbor hopping t′=−0.3t{t}^{{\prime} }=-0.3tt′=−0.3t t ′ = − 0.3 t , characteristic of cuprate families with T c around 100 K, the electronic spectral function reveals a strongly renormalized flat-band feature with a pseudogap near the antinodal point. The superconducting response of this system to a small dx2−y2{d}_{{x}^{2}-{y}^{2}}dx2−y2​ d x 2 − y 2 -like external field shows a pseudogap at the antinodal point in the normal part of the Nambu Green’s function, associated with “bad-fermion” behavior in the normal phase. At the same time, the anomalous Green’s function exhibits a d-wave-like structure with zero response at the nodal point of the Brillouin zone.
The nearest-neighbor superexchange-mediated mechanism for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity in the one-band Hubbard model faces the challenge that nearest-neighbor Coulomb repulsion can be larger than superexchange. To answer this question, we use cellular dynamical mean-field theory (CDMFT) with a continuous-time quantum Monte Carlo solver to determine the superconducting phase diagram as a function of temperature and doping for on-site repulsion U=9tU=9tU=9t and nearest-neighbor repulsion V=0,2t,4tV=0,2t,4tV=0,2t,4t. In the underdoped regime, VVV increases the CDMFT superconducting transition temperature Tcd{T}_{c}^{d}Tcd​ even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime VVV decreases Tcd{T}_{c}^{d}Tcd​. We gain insight into these paradoxical results through a detailed study of the frequency dependence of the anomalous spectral function, extracted at finite temperature via the MaxEntAux method for analytic continuation. A systematic study of dynamical positive and negative contributions to pairing reveals that even though VVV has a high-frequency depairing contribution, it also has a low frequency pairing contribution since it can reinforce superexchange through $J=4{t}^{2}/(U\ensuremath{-}V)$. Retardation is thus crucial to understanding pairing in doped Mott insulators, as suggested by previous zero-temperature studies. We also comment on the tendency to charge order for large VVV and on the persistence of ddd-wave superconductivity over extended-sss or s+ds+ds+d wave.
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