Magnetic Field Induced Phase Transitions in YBa2Cu4O8

The c-axis resistivity measurements in YBa2Cu4O8 from Hussey et al. for magnetic field orientations along the c-axis as well as within the ab-plane are analyzed and interpreted using the scaling theory for static and dynamic classical critical phenomena. We identify a superconductor to normal conductor transition for both field orientations as well as a normal conductor to insulator transition at a critical field Hc ‖ a with dynamical critical exponent z = 1, leading to a multicritical point where superconducting, normal conducting and insulating phases coexist. PACS. 74.25.Dw superconductivity phase diagrams – 74.25.Fy superconductivity transport properties Recently it has been demonstrated, that the doping tuned superconductor to insulator (SI) transition in cuprates can be understood in terms of quantum critical phenomena in two dimensions [1,2]. Zero temperature magnetic field driven SI transitions have also been observed in ultrathin Bi films, and successfully interpreted in terms of the scaling theory of quantum critical phenomena [3]. Nevertheless, three important questions concerning the physics of insulating and superconducting cuprates remain open. One is the nature and dimensionality of the normal state revealed when superconductivity is supressed by a magnetic field [4,5,6,7] and the second is the role of disorder. The third issue concerns the dynamical universality classes of SI and superconductor to normal state (SN) transitions at finite temperatures. We address these three issues through an analysis and interpretation of recent out-of-plane resistivity measurements ρc of YBa2Cu4O8 in magnetic fields by Hussey et al. [7], using the scaling theory of static and dynamic classical critical phenomena. Since this material is stoichiometric and, therefore, can be synthesized with negligible disorder, we consider the pure case. As shown below, the experimental data for ρc(T,H ‖ c) are consistent with a magnetic field tuned SN transition, while the data for ρc(T,H ‖ a) provide strong evidence for a multicritical point at the critical field, Hc ‖ a, b, where the superconducting, normal conducting and insulating phases coexist. Moreover, the existence of the critical field, where the NI transition occurs, allows us to determine the dynamical universality class of this transition uniquely: z = 1. We attribute the occurrence of the multicritical point to the comparatively small anisotropy in the correlation lengths, rendering the critical field for the NI transition to accessible values. For this reason we expect the multicritical point and the associated NI transition to be generic for Correspondence to: e-mail: [email protected] sufficiently clean and homogeneous cuprates with moderate anisotropy. The appropriate approach to uncover the phase diagram from conductivity measurements is the scaling theory of classical dynamic critical phenomena [8]. We now sketch the essential predictions of this theory in terms of a dimensional analysis. A defining characteristic of a superconductor is its broken U(1) or gauge symmetry, which is reflected in the order parameter Ψ . Gauge invariance then implies the following identification for the gradient operator i∇Ψ −→ i∇Ψ + 2π Φ0 A. (1) The basic scaling argument, which amounts to a dimensional analysis, states that the two terms on the right hand side must have the same scaling dimension, (Length) ≡ L. The dimensionality of the magnetic and electric field are then expressed as H = ∇× A ∝ L, E = ∂A ∂t ∝ (Lt). (2) In a superconductor the order parameter Ψ is a complex scalar, Ψ = Re(Ψ) + iIm(Ψ), corresponding to a vector with two components. Consequently, the dimensionality of the order parameter is n = 2. Based upon the dimensional statement ξ = ξ 0 |ǫ| −ν ∝ L, ǫ = T − Tc Tc , (3) where ± = sign(ǫ), we obtain in D dimensions for the free energy density the scaling form f = F/(V kBT ) ∝ L −D ∝ (ξ), (4) 2 T. Schneider, J. M. Singer: Magnetic Field Induced Phase Transitions in YBa2Cu4O8 and for H 6= 0 f = (ξ)G(Z), Z = H(ξ) Φ0 , (5) due to Eq. (2). G is an universal scaling function of its argument Z. An extension to 3D anisotropic materials, such as cuprates, is straightforward [9]: f = ( ξ x ξ ± y ξ ± z )−1 G(Z), (6) where the indices x, y, z denote the corresponding crystallographic b, a, c-axes of the cuprates, and H = H(0, sin δ, cos δ) : Z = (ξ x ) 2