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Pseudogap and the specific heat respulsive hubbard model

Ana Claudia Lausmann

Published Aug 15, 2014• 0 citations
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Abstract

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

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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
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.
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.
In the present work the Roth s two-pole approximation (Phys. Rev. 184, 451 (1969)) has been used to investigate the role of d− p hybridization in the normal and superconducting states of an extended d− p Hubbard model. Superconductivity with singlet dx2−y2 -wave pairing is treated by following Beenen and Edwards formalism (Phys. Rev. B 52, 13636 (1995)). In the first part of this work, the effects of the hybridization on the superconductivity, in the hole-doped regime, have been studied treating Roth s band shift within two different approximations. In the first one, the band shift has been calculated in the limit U →¥ (U is the Coulomb interaction), with zero temperature and without consider the superconducting effects. These regards, are restrict to the band shift. In the other parts of the problem, U, the temperature and the superconducting effects have been considered finites. In the second approximation, the Coulomb interaction, the temperature and the superconductivity have been considered in the calculation of some relevant correlation functions present in the Roth s band shift. The obtained results show that the hybridization acts in the sense of to suppresses the superconductivity. Also, it has been verified that the first approximation overstimates the effects of the hybridization on the superconductivity. In the second part of these work, hoppings to second-nearest-neighbors have been included in the model with the purpose of reproduces adequately the asymetries (mainly those related with the Fermi surface, band structure and phase diagram) between the hole- and electron-doped systems. Particularly, it is shown that the crossover from hole-like to electronlike Fermi surface is deeply affected by the d − p hybridization in the hole doping case. It has been verified that the effect of the hybridization is most pronounced around the saddle-points, where the superconducting gap is maximum in the particular case of dx2−y2 -wave symmetry. As a consequence, the critical temperature Tc is directly affected by the hibridization. Moreover, the obtained results suggest that in the hole doped regime, the hybridization may act on the transport properties of the system due to the sign changes of the Hall coefficient when the crossover of the Fermi surface occurs. In the electron doped case, the crossover in the Fermi surface is not verified. Nevertheless, as the hybridization suppresses the density of states near the Fermi level, the superconductivity is affected. The topology of the Fermi surface in the hole and electron doping regime agree with recent experimental ARPES results for La2−xSrxCuO4 (hole doping) and Nd2−xCexCuO4 (electron doping).
Recent experiments on cuprates show that as a function of doping, the normal-state specific heat sharply peaks at the doping ${\ensuremath{\delta}}^{*}$, where the pseudogap ends at low temperature. This finding is taken as the thermodynamic signature of a quantum critical point, whose nature has not yet been identified. Here we present calculations for the two-dimensional Hubbard model in the doped Mott insulator regime, which indicate that the specific heat anomaly can arise from the finite-temperature critical end point of a first-order transition between a pseudogap phase with dominant singlet correlations and a metal. As a function of doping at the temperature of the end point, the specific heat diverges. Upon increasing temperature, the peak becomes broader. The diverging correlation length is associated with uniform density fluctuations. No broken symmetries are needed. These anomalies also occur at half-filling as a function of interaction strength, and are relevant for organic superconductors and ultracold atoms.
Anomalous properties of the normal state of a strongly correlated electron system described by an attractive extended Hubbard model are investigated. The equations of motion of the Green’s functions are calculated with the two-pole approximation which gives rise to quasiparticle renormalized bands. The two-pole approximation leads to a set of correlation functions. In particular, the antiferromagnetic correlation function plays an important role as a source of anomalies in the normal state of the model. The uniform static magnetic susceptibility as a function of occupation n T and temperature is calculated. At low temperatures, the susceptibility presents a peak for n T ≃ 0.80. The results suggest that it is the onset of short-range antiferromagnetic correlations, which could be a mechanism for the pseudogap. The Fermi surface, defined by the spectral function , is presented for different dopings. It has been observed that above n T ≃ 0.80 the ordinary Fermi surface evolves to a hole pocket with pseudogaps near the antinodal points (0,π) and (π,0).
Quasiparticle bands of the two-dimensional Hubbard model are calculated using the Roth two-pole approximation to the one-particle Green's function. Excellent agreement is obtained with recent Monte Carlo calculations, including an anomalous volume of the Fermi surface near half-filling, which can possibly be explained in terms of a breakdown of Fermi liquid theory. The calculated bands are very flat around the (\ensuremath{\pi},0) points of the Brillouin zone in agreement with photoemission measurements of cuprate superconductors. With doping there is a shift in spectral weight from the upper band to the lower band. The Roth method is extended to deal with superconductivity within a four-pole approximation allowing electron-hole mixing. It is shown that triplet p-wave pairing never occurs. A self-consistent solution with singlet ${\mathit{d}}_{{\mathit{x}}^{2}\mathrm{\ensuremath{-}}{\mathit{y}}^{2}}$-wave pairing is found and optimal doping occurs when the van Hove singularity, corresponding to the flat band part, lies at the Fermi level. Nearest-neighbor antiferromagnetic correlations play an important role in flattening the bands near the Fermi level and in favoring superconductivity. However, the mechanism for superconductivity is a local one, in contrast to spin-fluctuation exchange models. For reasonable values of the hopping parameter the transition temperature Tc{\mathit{T}}_{\mathit{c}}Tc​ is in the range 10--100 K. The optimum doping ${\mathrm{\ensuremath{\delta}}}_{\mathit{c}}$ lies between 0.14 and 0.25, depending on the ratio U/t. The gap equation has a BCS-like form and 2${\mathrm{\ensuremath{\Delta}}}_{\mathrm{max}}$/kTc{\mathit{kT}}_{\mathit{c}}kTc​\ensuremath{\simeq}4.