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arXiv:1211.3123 · Physical Review B

Energetics of superconductivity in the two-dimensional Hubbard model

Emanuel Gull, Andrew J. Millis

Published Dec 17, 2012• 86 citations
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Abstract

The energetics of the interplay between superconductivity and the pseudogap in high-temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. Two regimes of superconductivity are found: a weak-coupling/large-doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong-coupling regime in which superconductivity is associated with an increase in potential energy and a decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal-state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However, the absence, in the strongly correlated but nonsuperconducting state, of discernibly nonlinear response to an applied pairing field suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.

DOI
10.1103/physrevb.86.241106

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The energetics of the interplay between superconductivity and the pseudogap in high-temperature superconductivity is examined using the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. Two regimes of superconductivity are found: a weak-coupling/large-doping regime in which the onset of superconductivity causes a reduction in potential energy and an increase in kinetic energy, and a strong-coupling regime in which superconductivity is associated with an increase in potential energy and a decrease in kinetic energy. The crossover between the two regimes is found to coincide with the boundary of the normal-state pseudogap, providing further evidence of the unconventional nature of superconductivity in the pseudogap regime. However, the absence, in the strongly correlated but nonsuperconducting state, of discernibly nonlinear response to an applied pairing field suggests that resonating valence bond physics is not the origin of the kinetic-energy driven superconductivity.
In conventional superconductors described by the Bardeen-Cooper-Schrieffer (BCS) Theory, the transition from the normal to the superconducting state is accompanied by a reduction in the potential energy and an increase in the kinetic energy. On the other hand, in high-temperature superconductors the potential and the kinetic energies present an unconventional behavior that may be strongly related to the pseudogap phenomena. In this work, the kinetic and potential energies in the superconducting state of the two-dimensional Hubbard model were analyzed. The model is investigated using the Green’s function method within a n-pole approximation, which allows superconductivity with dx2�����y2-wave pairing. In the present scenario, a pseudogap emerges near the anti-nodal points in the Fermi surface, when the strong coupling regime is reached. The results show that in the low doping region, the system enters the strong coupling regime and the opening of a pseudogap is followed by a decrease in the kinetic energy and an increase in the potential energy. A phase diagram of Coulomb interaction U versus the occupation nT is also presented. This phase diagram shows clearly that the pseudogap regime coincides with the strong coupling regime in which the kinetic and potential energies present an unconventional behavior. The analysis of the density of states and the chemical potential showed that the unconventional behavior of the potential and kinetic energies occurs due to the pseudogap emergence in the high occupancy region. It was also observed that the pseudogap emergence, when the occupancy increases, is preceded by a change in the Fermi surface topology, which characterizes a Lifshitz transition. Both the pseudogap and the Lifshitz transition are affected by the next-nearest neighbor hopping t2 (of the Hubbard model). This result is in accordance with recent theoretical and experimental results for the Hubbard model and the cuprates.
Abstract We investigate the interplay between the pseudogap state and d-wave superconductivity in the two-dimensional doped Hubbard model by employing an eight-site cluster dynamical mean-field theory method. By tuning electron hopping parameters, the strong-coupling pseudogap in the two-dimensional Hubbard model can be either enhanced or suppressed in the doped Mott insulator regime. We find that in underdoped cases, the closing of pseudogap leads to a significant enhancement of superconductivity, indicating competition between the two in the underdoped regime. In contrast, at large dopings, suppressing the pseudogap is accompanied by a concurrent decrease in the superconducting transition temperature T c, which can be attributed to a reduction in antiferromagnetic correlations behind both the pseudogap and superconductivity. We elucidate this evolving relationship between pseudogap and superconductivity across different doping regimes.
Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.
Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy, indicating that the transition is driven by a pairing potential. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the Dynamical Cluster Approximation we study the nature of superconductivity in a microscopic model of the cuprates, the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional, spin-charge separated state, consistent with the RVB model of high-temperature superconductors.
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature Tc(d), the maximum of the condensation energy as a function of doping, the correlation between maximum Tc(D) and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.
Pairing occurs in conventional superconductors through a reduction of the electronic potential energy accompanied by an increase in kinetic energy. In the underdoped cuprates, optical experiments show that pairing is driven by a reduction of the electronic kinetic energy. Using the dynamical cluster approximation we study superconductivity in the two-dimensional Hubbard model. We find that pairing is indeed driven by the kinetic energy and that superconductivity evolves from an unconventional state with partial spin-charge separation, to a superconducting state with quasiparticle excitations.