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Pseudogap and kinetic energy of unconventional superconductors described by a two-dimensional Hubbard model

Giordano Paulo da Motta

Published Mar 30, 2020• 0 citations
OpenAlex

Abstract

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.

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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.
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 this work the specific heat of a two-dimensional Hubbard model, suitable to discuss high- T c superconductors (HTSC), is studied taking into account hopping to first ( t ) and second ( t 2 ) nearest neighbors. Experimental results for the specific heat of HTSC's, for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green's function method within a n-pole approximation. The specific heat is calculated on the pseudogap and on the superconducting regions. In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations become sufficiently strong. The specific heat jump coefficient Δγ decreases when the total occupation per site ( n T ) reaches a given value. Such behavior of Δγ indicates the presence of a pseudogap in the regime of high occupation.
The specific heat and the condensation energy of a two-dimensional Hubbard model, suitable to discuss high Tc superconductors (HTSTC), is studied taking into account hopping to first (t) and second (t2) nearest neighbors. Results for the Hubbard model show that the specific heat as a function of the temperature C(T) presents a two peaks structure (DUFFY; MOREO, 1997). The low temperature peak has been associated with spin fluctuation while the high temperature peak is related to charge fluctuation. Experimental results for the specific heat of HTSC s (LORAM et al., 2001), for instance, the YBCO and LSCO, indicate a close relation between the pseudogap and the specific heat. In the present work, we investigate the specific heat by the Green s function method within the n-pole approximation proposed by L. Roth (ROTH, 1969). The specific heat is calculated on the pseudogap and on the superconducting regions. Superconductivity with dx2−y2- wave pairing is considered following the procedure proposed by Beenen and Edwards (BEENEN; EDWARDS, 1995). The analytical expressions for the specific heat and for the condensation energy have been obtained following the formalism presented in reference (KISHORE; JOSHI, 1971). In the present scenario, the pseudogap emerges when the antiferromagnetic (AF) fluctuations (present in the Roth s band shift) become strongly sufficient to push down the region of the nodal point (π,π) on the renormalized quasi-particle bands. We observed that above a given total occupation nT , the specific heat decreases signaling the pseudogap presence. The effects of the antiferromagnetic fluctuations on the condensation energy and on superconductivity are also investigated.x
A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes ttt (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (UUU, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.
Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two-dimensional Hubbard model with next-nearest-neighbor hopping (${t}^{\ensuremath{'}}$), chemical potential, and temperature as control parameters. At ${t}^{\ensuremath{'}}\ensuremath{\le}0$, we identify a line of Lifshitz transition points associated with a change in the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects and becomes more singular when ${t}^{\ensuremath{'}}$ becomes more negative. The resulting temperature dependence on the bare ddd-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at ${t}^{\ensuremath{'}}\ensuremath{\le}0$ extends our understanding of the quantum critical region in the phase diagram and shines lights on future investigations of the nature of the quantum critical point in the two-dimensional Hubbard model.
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.