Influence of a Van Hove singularity on the electronic specific heat of high-Tc superconductors

Dorbolo, Stéphane; Houssa, Michel; Ausloos, Marcel

doi:10.1016/0921-4534(96)00353-x

Cited by 14 publications

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References 24 publications

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“…An experimental check of Refs. [1] or [2] is proposed here. The study of the influence of the doping rate and the effects of a magnetic field is more interesting work in our opinion than to use the best band structure with two transfer integrals, as opposed to employing phenomenological parameters as we did.…”

Section: (5)mentioning

confidence: 99%

“…It will be an interesting check of the Bok and Bouvier comment [1] with respect to our work [2] whether the exponent is equal to 2 or 5/3. Finally, we agree that the real electronic band structure is indeed quite complicated.…”

Section: (5)mentioning

confidence: 99%

“…Typically for the fit used in Ref. [2], the physical parameters should be t = 0.40 eV, hence independent of t' [9] as can be easily checked.…”

Section: (5)mentioning

confidence: 99%

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Answer to comment on the paper of S. Dorbolo et al., Physica C 267 (1996) 24–30 entitled: Influence of Van Hove singularity on the electronic specific heat of high-Tc superconductors

Dorbolo

1997

Physica C: Superconductivity

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In their comment [1], J. Bok and J. Bouvier mentioned the lack of validity of work starting with the specific heat formula Eq. (1) in our paper [2]. They discussed two other points i.e. the variation of the physical parameters as well as the electronic band structure. Even though their points are well taken, we show that our conclusions are still valid from a qualitative point of view.In thermodynamics, the specific heat can be considered as the first derivative of the entropy, the first derivative of the internal energy or the second derivative of the free energy [3]. In Ref. [4], G. Rickayzen starts from the entropy S in order to compute the electronic specific heat co= ~)v=where fk is the Fermi-Dirac distribution function and E k is the quasiparticle spectrum:We computed the electronic specific heat C e from* E-mail: dorbolo@gw.unipc.ulg.ac.be.with U the internal energy. It is claimed in Eq.(1) that the last equality in Eq. (2) is invalid. In fact, the quasiparticle spectrum is defined bywhere u k and v k are the coefficients of the linear combination of creation and destruction operators of quasiparticles [5]. Therefore, after taking the temperature derivative of U in Eq. (3), Eq. (1) is found again. The difference between Eq. (2) and the r.h.s of Eq. (1) is Ek(OEk/OT)fk. This term becomes the most important one close to T~ when the gap varies strongly. Using Eq.(1), a few modifications to our previous results occur but the main qualitative conclusions are exactly obtained.In Fig. 1, we compare the electronic specific heat calculated with Eq. (2) and Eq. (1) for the same set of physical parameters A(0) = 20 meV and m* = 8 m 0. At low temperature, both results are quite similar. A linear contribution is observed. As expected, the deviation is more important when the temperature lies close to T~.The specific heat singularity at T¢ observed in many systems, though quantitatively different from each other, can still be explained with a quasiparticle spectrum containing a d-wave gap parameter for reasonable values of the physical parameters i.e.

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Section: (5)mentioning

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Answer to comment on the paper of S. Dorbolo et al., Physica C 267 (1996) 24–30 entitled: Influence of Van Hove singularity on the electronic specific heat of high-Tc superconductors

Dorbolo

1997

Physica C: Superconductivity

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“…24. On the other hand, in a previous work, 25 we have studied the influence of a logarithmic VHS in the electronic density of states on the mean-field electronic specific heat C e,m f of a strictly two-dimensional ͑2D͒ superconductor. We have shown that experimental data on a YBa 2 Cu 3 O 7Ϫx single crystal 26 were in good agreement with an energy spectrum containing VHS and a d-wave gap parameter, especially in the low-temperature range.…”

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confidence: 99%

Electronic specific heat of superconductors with Van Hove singularities: Effects of a magnetic field and thermal fluctuations

Dorbolo

Ausloos

Houssa³

1998

Phys. Rev. B

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The mean-field electronic specific heat of a superconductor in the presence of a magnetic field is calculated. We consider an energy spectrum presenting saddle points in the band structure. They correspond to Van Hove singularities in the density of states. We use a three-dimensional band structure by introducing a coupling energy between the CuO 2 planes. Both s-wave and d-wave energy-gap-parameter cases are investigated. It is noticed that the specific-heat jump should increase or decrease with the field, respectively. It is found that the d-wave model seems to be qualitatively and quantitatively more realistic. The influence of a magnetic field on the jump of the electronic specific heat of various high-T c superconductors such as YBa 2 Cu 3 O 7Ϫx , HgBa 2 Ca 2 Cu 3 O 8 , and Tl 2 Ba 2 CuO 6ϩ␦ near T c is compared to mean-field results. Fluctuations are extracted and analyzed. It is pointed out that the mean-field background should be extracted before analyzing the fluctuations. Critical fluctuation regimes, Gaussian, lowest Landau level, and XY regimes as well as the effective dimensionality of the systems are obtained. The field regimes are given on the T c line.

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“…The use of a van Hove singularity vHs in the density of states DOS near or at the Fermi surface makes the standard BCS model more suitable for the high-T c cuprates 6,7,8 . The singularity in the density o f states known as the van Hove singularity arises wherever the group velocity v anishes and where there is a locally at region of the frequency as a function of the wavevector k. The critical points where these singularities are observed may be saddle points.…”

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BCS superconductivity in the van Hove scenario in s and d waves

Ghosh¹

1999

Braz. J. Phys.

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The e ect of including a van Hove singularity in the density of state of a renormalized BCS equation in s and d waves and its appropriateness in describing some properties of high-Tc cuprates in the weak-coupling region are studied in two space dimensions. The speci c heat and knight shift as a function of temperature exhibit scaling below the critical temperature in d wave. We also study the jump in the speci c heat at the critical temperature Tc in s and d waves, which can have v alues signi cantly higher than the standard BCS values and which increases with Tc, as experimentally observed in many d-wave high-Tc materials. The experimental results on the speci c heat and knight shift of the Y-123 system are compared with the theoretical predictions.The discovery of high-T c cuprates 1 with many unusual properties both above and below the critical temperature T c presents a serious question on the applicability of the Bardeen-Cooper-Schrie er BCS theory of superconductivity 2 , 3 at high temperatures. The high-T c materials have many u n usual properties, such as, an anomalously large C and 0 =T c and small isotope e ect, where C is the jump in speci c heat at T c and 0 is the zero-temperature BCS gap.Despite much e ort, the normal state of the high-T c cuprates has not been satisfactorily understood yet and there are controversies about the appropriate microscopic Hamiltonian and pairing mechanism 4, 5 . The use of a van Hove singularity vHs in the density of states DOS near or at the Fermi surface makes the standard BCS model more suitable for the high-T c cuprates 6, 7, 8 . The singularity in the density o f states known as the van Hove singularity arises wherever the group velocity v anishes and where there is a locally at region of the frequency as a function of the wavevector k. The critical points where these singularities are observed may be saddle points. In high T c compounds there have been evidences of saddle points which yield a logarithmic divergence. Moreover recent experiments 9, 1 0 h a ve given evidences of an extended saddle point singularity which corresponds to a power law behavior 7 . The use of a vHs in the DOS can simulate di erent non-Fermi liquid type properties of both the normal and superconducting states 6, 7 . Some experiments also suggest a peak in the DOS associated with a vHs near the Fermi level 11, 9 , 1 2 . There have been attempts to explain many anomalous features of the high-T c cuprates using a vHs in the DOS 6, 7 : such as the large values of C and 0 =T c , anomalous isotope e ect, pressure coe cient o f T c , temperature variation of speci c heat C s T and knight shift etc. Virtually, in all these applications an s-wave i n teraction has been employed.However, there are evidences that some of the high-T c cuprates have singlet d-wave Cooper pairs and the gap parameter has d x 2 ,y 2 symmetry in two dimensions 5 . Recent measurements of the penetration depth T 11, 9 , 12 and superconducting speci c heat at different temperatures T 11, 9, 12 and related theoretical analyse...

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Influence of a Van Hove singularity on the electronic specific heat of high-Tc superconductors

Cited by 14 publications

References 24 publications

Answer to comment on the paper of S. Dorbolo et al., Physica C 267 (1996) 24–30 entitled: Influence of Van Hove singularity on the electronic specific heat of high-Tc superconductors

Answer to comment on the paper of S. Dorbolo et al., Physica C 267 (1996) 24–30 entitled: Influence of Van Hove singularity on the electronic specific heat of high-Tc superconductors

Electronic specific heat of superconductors with Van Hove singularities: Effects of a magnetic field and thermal fluctuations

BCS superconductivity in the van Hove scenario in s and d waves

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