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arXiv:1607.02517 · Physical review. B./Physical review. B

Antagonistic effects of nearest-neighbor repulsion on the superconducting pairing dynamics in the doped Mott insulator regime

Alexis Reymbaut, M. Charlebois, Marco Fellous-Asiani, Lorenzo Fratino, P. Sémon, G. Sordi, A.–M. S. Tremblay

Published Oct 27, 2016• 28 citations
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Abstract

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 $U=9t$ and nearest-neighbor repulsion $V=0,2t,4t$. In the underdoped regime, $V$ increases the CDMFT superconducting transition temperature ${T}_{c}^{d}$ even though it decreases the superconducting order parameter at low temperature for all dopings. However, in the overdoped regime $V$ decreases ${T}_{c}^{d}$. 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 $V$ 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 $V$ and on the persistence of $d$-wave superconductivity over extended-$s$ or $s+d$ wave.

DOI
10.1103/physrevb.94.155146

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The nearest-neighbor superexchange-mediated mechanism for dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ 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=4t2/(U\ensuremath−V)J=4{t}^{2}/(U\ensuremath{-}V)J=4t2/(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.
Many theoretical approaches find ddd-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where UUU is the on-site repulsion and W=8tW=8tW=8t the bandwidth) pairing is controlled by the exchange energy J=4t2/UJ=4{t}^{2}/UJ=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion VVV will destroy superconductivity when it becomes larger than JJJ, a condition that is easily satisfied in cuprates, for example. Using cellular dynamical mean-field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing at strong coupling is preserved, even when $V\ensuremath{\gg}J$, as long as $V\ensuremath{\lesssim}U/2$. While at weak coupling VVV always reduces the spin fluctuations and hence ddd-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by VVV increases binding at low frequency while the pair-breaking effect of VVV is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect ddd-wave superconductivity from VVV.
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Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of ddd-wave pairing when a nearest-neighbor Coulomb repulsion VVV is present in addition to the on-site Coulomb repulsion UUU. We find that ddd-wave pairing and the superconducting transition temperature Tc{T}_{c}Tc​ are only weakly suppressed as long as VVV does not exceed U/2U/2U/2. This stability is traced to the strongly retarded nature of pairing that allows the ddd-wave pairs to minimize the repulsive effect of VVV. When VVV approaches U/2U/2U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of ddd-wave pairing and Tc{T}_{c}Tc​ than for smaller VVV.
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