Asymmetry of Critical Exponents in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">YBa</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cu</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>7</mml:mn><mml:mo>−<

Charalambous, M.; Riou, O.; Gandit, P.; Billon, B.; Léjay, P.; Chaussy, J.; Hardy, W. N.; Bonn, D. A.; Liang, Ruixing

doi:10.1103/physrevlett.83.2042

Cited by 13 publications

(20 citation statements)

References 22 publications

(22 reference statements)

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“…[12]. For this reason, deviations from 3D-XY critical behavior around T P do not signal the failure of 3D-XY universality, as previously claimed [12], but reflect a mere finite size effect at work. Indeed, from Fig.…”

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confidence: 51%

“…A finite size scaling analysis [14] reveals inhomogeneities with a characteristic length scale ranging from 300 to 400Å, in the YBa 2 Cu 3 O 7−δ samples YBCO3, UBC2 and UBC1 of Ref. [12]. For this reason, deviations from 3D-XY critical behavior around T P do not signal the failure of 3D-XY universality, as previously claimed [12], but reflect a mere finite size effect at work.…”

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confidence: 73%

“…To quantify this point we show in Fig. 1 the measured heat coefficient of YBa 2 Cu 3 O 7−δ [12] around the peak. The rounding and the shape of the specific heat coefficient clearly exhibit the characteristic behavior of a system in confined dimensions, i.e., rod or cube shaped inhomogeneities [13].…”

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confidence: 99%

“…As usual, in the above expression ± refer to t = T /T c −1 > 0 and t < 0, respectively. The critical amplitudes [12]). The two arrows mark T c ≈ 92.12K and T P ≈ 91.98K, respectively.…”

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confidence: 99%

“…These properties include the Specific heat coefficient C/T [mJ/(gK 2 )] versus log 10 |t| for YBa 2 Cu 3 O 7−δ (sample YBCO3, [12]) for T c = 92.12K. specific heat, magnetic torque, diamagnetic susceptibility, melting line, etc.…”

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confidence: 99%

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D-XY critical behavior in cuprate superconductors

Schneider¹,

Singer²

2000

Physica C: Superconductivity

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We outline the universal and finite temperature critical properties of the 3D-XY model, extended to anisotropic extreme type-II superconductors, as well as the universal quantum critical properties in 2D. On this basis we review: (i) the mounting evidence for 3D-XY behavior in optimally doped cuprate superconductors and the 3D to 2D crossover in the underdoped regime; (ii) the finite size limitations imposed by inhomogeneities; (iii) the experimental evidence for a 2D-XY quantum critical point in the underdoped limit, where the superconductor to insulator transition occurs; (iv) the emerging implications and constraints for microscopic models.The starting point of the phenomenological theory of superconductivity is the GinzburgLandau HamiltonianD is the dimensionality of the system, the complex scalar Ψ (R) is the order parameter, M the effective mass of the pair and A the vector potential. The pair carries a non-zero charge in addition to its mass. The charge (Φ 0 = hc/2e) couples the order parameter to the electromagnetic field via the first term in H. If Ψ and A are treated as classical fields, the relative probability P of finding a given configuration [Ψ, Ψ * , A] is thenThe free energy F follows fromwhere the partition function on the right hand side corresponds to an integral over all possible realizations of the vector potential A, the order parameter Ψ and its complex conjugate Ψ * . Setting e = 0, the free energy reduces to that for a normal to neutral superfluid transition, which is one of the best understood continuous phase transitions with unparalleled agreement between theory, simulations and experiment [1]. In extreme type-II superconductors, however, the coupling to vector potential fluctuations appears to be weak [2], but nonetheless these fluctuations drive the system -very close to criticality -to a charged critical point [3,4]. In any case, inhomogeneities prevent cuprate superconductors from entering this regime, due to the associated finite size effect. For these reasons, the neglect of vectorpotential fluctuations appears to be a reasonable starting point. In this case the vectorpotential in Hamiltonian Eq. (1) can be replaced by its most probable value. The critical properties at finite temperature are then those of the 3D-XY model, reminiscent to the lamda transition in superfluid helium, but extended to take the effective mass anisotropy into account [5,6]. The universal properties of the 3D-XY universality class are characterized by a set of critical exponents, describing the asymptotic behavior of the correlation length ξ ± i , magnetic penetration depth λ i , specific heat A ± , etc., in terms ofwhere 3ν = 2 − α. As usual, in the above expression ± refer to t = T /T c −1 > 0 and t < 0, respectively. The critical amplitudes ξ ± i,0 , λ 2 i,0 , A ± , etc., are nonuniversal, but there are universal critical

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confidence: 51%

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confidence: 73%

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confidence: 99%

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confidence: 99%

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confidence: 99%

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