Specific Heat Evidence on the Normal State Pseudogap

Lorama, J.W.; Mirza, K. A.; Cooper, J. R.; Tallon, J. L.

doi:10.1016/s0022-3697(98)00180-2

Cited by 152 publications

(124 citation statements)

References 7 publications

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“…Moreover, it is at p c where other fundamental properties such as the superconducting condensation energy and quasiparticle lifetime, change abruptly, the resistivity follows its unusual linear temperature dependence to the lowest temperature and the pseudogap extrapolates to zero. 10,11 These features all indicate that the quantum transition identified here is connected with the fundamental physical properties of HTS.…”

supporting

confidence: 51%

“…This suppression in the underdoped region can also be directly linked to the strong reduction in entropy and condensation energy associated with the pseudogap. 11 It is therefore evident here that the onset of short-range magnetic correlations at the critical point p c coincides with a change in the superconducting ground state properties in HTS. It separates the phase diagram into two distinct regions: ͑i͒ below p c where T g , T f increase rapidly with underdoping and the superfluid density is rapidly suppressed, and ͑ii͒ above p c where T g , T f →0 and the superfluid density is almost constant, indicating a transition from weak to strong superconductivity, respectively.…”

mentioning

confidence: 61%

“…9 Many fundamental physical quantities such as the superconducting condensation energy, 10,11 the superfluid density, 12,13 and the quasiparticle weight, 10,14 show abrupt changes as p→p c . While compelling in their totality, 10,11 none of the results can be considered as evidence of a quantum transition. In particular there is no evidence for an associated order parameter and slowing down of the relevant fluctuations.…”

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confidence: 98%

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Evidence for a generic quantum transition in high-Tccuprates

Tallon²,

et al. 2002

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We study the low-energy spin fluctuations and superfluid density of a series of pure and Zn-substituted high-T c superconductors ͑HTS͒ using the muon spin relaxation and ac-susceptibility techniques. At a critical doping state, p c , we find ͑i͒ simultaneous abrupt changes in the magnetic spectrum and in the superconducting ground state and ͑ii͒ that the slowing down of spin fluctuations becomes singular at Tϭ0. These results provide experimental evidence for a quantum transition that separates the superconducting phase diagram of HTS into two distinct ground states. DOI: 10.1103/PhysRevB.66.064501 PACS number͑s͒: 74.72.Ϫh, 74.25.Ha, 75.40.Ϫs, 76.75.ϩi Quantum phase transitions occur at zero temperature at a critical electron density separating distinct ground states. Near a quantum critical point, electrons in metals are highly correlated and the diverging fluctuations may induce unconventional superconductivity. [1][2][3][4][5][6][7][8] For example, in certain heavy fermion compounds a ''bubble'' of superconductivity occurs around the quantum critical point at which itinerant antiferromagnetism is suppressed by applied pressure. 9 The search for an underlying quantum phase transition in high-T c superconductors ͑HTS͒ is motivated by the potential for quantum fluctuations to bind electronic carriers into superconducting Cooper pairs and also to cause the celebrated linear temperature dependence of their electrical resistivity. [1][2][3][4][5][6][7][8]10 HTS exhibit a common generic phase diagram in which the superconducting transition temperature, T c , rises to a maximum at an optimal doping of approximately 0.16 holes per planar copper atom and then falls to zero on the overdoped side. In addition the underdoped normal state exhibits correlations, which introduce a gap in the density of states that strongly affects all physical properties. There is no phase transition associated with the opening of this gap and so it is called a pseudogap. Analysis of specific heat data, for example, suggests that the pseudogap energy decreases with doping and falls to zero at a critical doping of p c Ӎ0.19, just beyond optimal doping, 10,11 a behavior rather analogous to the quantum-critical heavy-fermion materials. 9 Many fundamental physical quantities such as the superconducting condensation energy, 10,11 the superfluid density, 12,13 and the quasiparticle weight, 10,14 show abrupt changes as p→p c . While compelling in their totality, 10,11 none of the results can be considered as evidence of a quantum transition. In particular there is no evidence for an associated order parameter and slowing down of the relevant fluctuations. With this in mind we examined the evolution with doping of the low-energy spin fluctuation spectrum using muon spin relaxation ( SR) combined with low-field ac-susceptibility measurements of the superfluid density.The samples studied were: ͑i͒ La 2Ϫx Sr x Cu 1Ϫy Zn y O 4 ͑LSCO͒ (xϭ0.03-0.24 and yϭ0, 0.01, and 0.02͒. Samples were synthesized using solid-state reaction and where necessary follow...

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Evidence for a generic quantum transition in high-Tccuprates

Tallon²,

et al. 2002

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“…The condensation energy is known experimentally from specific heat measurements for YBa 2 Cu 3 O 6.95 (YBCO) to be ∼3 K per formula unit 15,16 (f.u.). Within the t-J model, the change in magnetic exchange energy can be calculated from the nearest-neighbour spin correlations [3][4][5] between the normal (N) and superconducting (S) states:…”

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Magnetic energy change available to superconducting condensation in optimally doped YBa2Cu3O6.95

et al. 2006

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U nderstanding the magnetic excitations in high-temperature (high-T c ) copper-oxide superconductors is important because they may mediate the electron pairing for superconductivity 1,2 . By determining the wavevector ( Q) and energy (hω) dependence of the magnetic excitations, it is possible to calculate the change in the exchange energy available to the superconducting condensation energy 3-5 . For the high-T c superconductor YBa 2 Cu 3 O 6+x , the most prominent feature in the magnetic excitations is the resonance 6-12 . Suggestions that the resonance contributes a major part of the superconducting condensation 4,13 have not gained acceptance because the resonance is only a small portion of the total magnetic scattering 12-14 . Here, we report an extensive mapping of magnetic excitations for YBa 2 Cu 3 O 6.95 (T c ∼ 93 K). Absolute intensity measurements of the full spectra allow us to estimate the change in the magnetic exchange energy between the normal and superconducting states, which is about 15 times larger than the superconducting condensation energy 15,16 -more than enough to provide the driving force for high-T c superconductivity in YBa 2 Cu 3 O 6.95 .If magnetic excitations are mediating electron pairing in the high-T c copper oxides, it is expected that the change in magnetic exchange energy will provide enough energy for superconducting condensation. The condensation energy is known experimentally from specific heat measurements for YBa 2 Cu 3 O 6.95 (YBCO) to be ∼3 K per formula unit 15,16 (f.u.). Within the t-J model, the change in magnetic exchange energy can be calculated from the nearest-neighbour spin correlations 3-5 between the normal (N) and superconducting (S) states:where J is the exchange interaction, and S i and S j are the electron spin operators at nearest-neighbour Cu sites i and j in the CuO 2 plane, respectively. Instead of estimating the magnetic resonance's contribution to the superconducting condensation 4,13 , here we seek to calculate E ex from the entire observable magnetic excitation spectrum. In general, a complete determination of the magnetic excitation spectrum is difficult as spin fluctuations can spread over a large wavevector and energy range. YBCO has two CuO 2 planes per unit cell (bilayer) and therefore the magnetic excitations have odd (acoustic) or even (optical) symmetry with respect to the neighbouring planes (Fig. 1). For optimally doped YBCO, the magnetic excitation spectrum is dominated by a resonance mode centred at 41 meV in the acoustic channel 6,7 , and a mapping of the acoustic and optical magnetic excitations should allow an estimation of E ex . Figure 1 summarizes the key conclusions of our work. The optical and acoustic spin fluctuations can be separated by their differences in q z dependence (Fig. 1b). The total magnetic response χ (Q, ω) can then be written as342Å is the spacing between the nearest-neighbour CuO 2 planes along the c axis. To probe the entire magnetic spectra in optical and acoustic channels of YBCO, we used the multi-angle posit...

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“…The reported values for this two constants depend strongly on the conditions of each experiment [17] and on the theoretical method used to relate the different parts of the total specific heat. Thirdly, there is a "jump" in the constant pressure specific heat [21] C p at T c (at zero magnetic field and evolving into a "peak" at finite magnetic field), ∆C p /T c , attributable to the C es component, indicating a second order phase transition which in turn becomes a smooth maximum as doping decreases [22]. Finally, as the "upturn" in the specific heat at very low temperatures is suppressed, a cubic term ßT 3 is also observed [23].…”

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Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson–Fermion model

Salas

Fortes

Solís

et al. 2016

Physica C: Superconductivity and its Applications

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We adapt the Boson-Fermion superconductivity model to include layered systems such as underdoped cuprate superconductors. These systems are represented by an infinite layered structure containing a mixture of paired and unpaired fermions. The former, which stand for the superconducting carriers, are considered as noninteracting zero spin composite-bosons with a linear energymomentum dispersion relation in the CuO2 planes where superconduction is predominant, coexisting with the unpaired fermions in a pattern of stacked slabs. The inter-slab, penetrable, infinite planes are generated by a Dirac comb potential, while paired and unpaired electrons (or holes) are free to move parallel to the planes. Composite-bosons condense at a critical temperature at which they exhibit a jump in their specific heat. These two values are assumed to be equal to the superconducting critical temperature Tc and the specific heat jump reported for YBa2Cu3O6.80 to fix our model parameters namely, the plane impenetrability and the fraction of superconducting charge carriers. We then calculate the isochoric and isobaric electronic specific heats for temperatures lower than Tc of both, the composite-bosons and the unpaired fermions, which matches recent experimental curves. From the latter, we extract the linear coefficient (γn) at Tc, as well as the quadratic (αT 2 ) term for low temperatures. We also calculate the lattice specific heat from the ARPES phonon spectrum, and add it to the electronic part, reproducing the experimental total specific heat at and below Tc within a 5% error range, from which the cubic (ßT 3 ) term for low temperatures is obtained. In addition, we show that this model reproduces the cuprates mass anisotropies.

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Specific Heat Evidence on the Normal State Pseudogap

Cited by 152 publications

References 7 publications

Evidence for a generic quantum transition in high-Tccuprates

Evidence for a generic quantum transition in high-Tccuprates

Magnetic energy change available to superconducting condensation in optimally doped YBa2Cu3O6.95

Specific heat of underdoped cuprate superconductors from a phenomenological layered Boson–Fermion model

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