D-XY critical behavior in cuprate superconductors

Abstract

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

Diamagnetism, Nernst signal, and finite-size effects in superconductors above the transition temperatureTc

“…Noting that in cuprate and amorphous conventional superconductors the spatial extent of the homogeneous domains is limited, 8,[16][17][18][19][20][21][22] we explored the applicability of the 0D-model, neglecting thermal fluctuations, to describe the isothermal magnetization and Nernst signal curves above T c . Sufficiently above T c we observed that for both models, the full 0D-model and its Gaussian version, describe the essential features of the curves, including the temperature dependence of the minimum in the magnetization and maximum in the Nernst signal curves at H m , rather well.…”

“…[2][3][4][5][6][7] On the other hand, there is considerable evidence that cuprate and amorphous conventional superconductors are homogeneous over a limited spatial domain only. 8,[16][17][18][19][20][21][22] In this case, the growth of the correlation lengths is limited by approaching the transition temperature T c because it cannot exceed the respective extent of the homogenous domains. Within a two dimensional superconductor, consisting of a stack of superconducting layers with insulating spacing sheets in between, the adoption of this scenario where the magnetization stems from homogeneous domains with limited extent only would result in an effective 0D-superconductor.…”

Genetic identification of two sibling species ofLutzomyia longipalpis(Diptera: Psychodidae) that produce distinct male sex pheromones in Sobral, Ceará State, Brazil

“…Allele frequencies were calculated for each locus separately and the extent of intra-and intersample genetic diversity was estimated using: (i) number of alleles (N a ) per locus; (ii) the observed heterozygosity (H O ); and (iii) expected heterozygosity 1 1 2 1 3 4 1 3 4 (H E ); H O and H E were calculated for each locus, both individually for each sample and across all samples, using the program populations Version 1.2.28 (Langella 2002). Every sample (males and females separately) was then tested (1000 iterations) for deviation from Hardy-Weinberg equilibrium (HWE) across each locus using a modification of the Guo & Thompson (1992) Markov-chain random walk algorithm available in arlequin Version 2.000 (Schneider et al 2000). The statistical significance of deviations from Hardy-Weinberg expectations was adjusted by a sequential Bonferroni correction (Rice 1989) to maintain a type-I error rate of α = 0.05 within each sample.…”

Lieb-Robinson bounds on the speed of information propagation

“…We also indicate whether the function A max (λ) is increasing or decreasing in each interval. From the table we see that the function A max (λ) is minimized for λ = λ (123) (23) . Thus we have…”

“…This model is well understood and is studied mainly in connection with quantum phase transitions. This model is also of practical interest, for example, in understanding the isolator-superconductor phase transition in cuprate type II superconductors [23]. At zero temperature the system exhibits two phases, one with an energy gap and another which is gapless.…”