Positive curvature of the thermodynamic transition line in the isotropic superconductor (K,Ba)BiO₃

    The H-T phase diagram of high-T_c oxides has been the focus of intense theoretical and experimental works during the past decade. One of the most striking phenomenon which has been observed is the existence of a melting line T_m(H) above which the vortex lattice melts into a liquid of entangled lines.This melting has very fundamental consequences on the physics of vortices as the free motion of the flux lines in the liquid state gives rise to a large dissipation which renders the system useless for applications. Similarly, the presence of strong thermal fluctuations also renders the determination of H_c2 difficult from thermodynamic measurements. It is still unclear whether this upper critical field still exists as a transition line (or is just some smooth crossover) and what is the "true" (i.e. thermodynamic) superconducting phase transition line. In order to shed light on this transition, it was important to perform thermodynamic measurements on a high-T_c oxide presenting only small thermal fluctuations. We have presented in [1] specific heat, magneto-tunnelling, reversible magnetization and transport measurements on high quality (K,Ba)BiO₃ single crystals for which the Ginzburg number G_i is only ~ 10^-4 (due to its perfectly isotropic structure (i.e. cubic), a lower T_c ~ 31 K and a coherence length of the order of 30 Å). Despite those small thermal fluctuations, we have previously shown that the magneto-transport data can be well described by the vortex-glass scaling formalism thus suggesting that the vortex solid melts into a liquid at high temperature through a second order phase transition. In the following, the vortex-glass transition field H_vg is defined as the field for which R ® 0. On the other hand, magnetotunnelling measurements have shown that the superconducting gap D closes above some characteristic field HDand the corresponding HD (T) line was in reasonable agreement with the classical Werthamer-Helfang-Hohenberg (WHH) theory for the upper critical field [2]. The physical image emerging from those measurements was then that of a liquid phase existing for H_vg < H < HD~ H_c2. We however show here that the magnetic field H_Cp is smaller than HDand presents a strong positive curvature thus pointing towards a very peculiar nature for the thermodynamic superconducting transition. This is a totally unexpected feature as in conventional superconductors the specific heat anomaly enables to define the upper critical field and thus is expected to vary it linearly with T close to T_c.
    As pointed out above, those specific heat measurements are in striking contrast with our previous magneto-tunnelling [2] data which suggested than the upper critical field (defined as the field HDfor which the superconducting gap is completely closed) present a classical WHH dependence. We have thus performed similar magneto-tunnelling measurements on the sample which has been used for the specific heat experiments (more details about the experimental procedure can be found in [2]. The corresponding points, together with the field H_vg have been reported on Fig. 3. As shown, in agreement with our previous data, the curvature is much less pronounced for HDand surprisingly H_vg < H_Cp < HD.

Figure 3: H-Tphase diagram of the (K,Ba)BiO₃ system. Squares (H_Cp(T)): onset on the specific heat anomaly, circles H_vg(T): "vortex-glass transition" line deduced from transport measurements (R ® 0), triangles: HD(T) defined as the line for which the superconducting gap measures by tunnelling spectroscopy vanishes.

[1] S. Blanchard, T. Klein, J. Marcus, I. Joumard, T. Sulpice, P. Szabó, P. Samuely, A.G.M. Jansen, C. Marcenat, Phys. Rev. Lett. 88 (2002), 177201.
[2] P. Samuely, P. Szabó et al., Europhys. Lett.41 (1998), 207.

P. Szabó, P. Samuely
S. Blanchard, T. Klein, J. Marcus, I.Joumard (LEPES CNRS Grenoble), C. Marcenat (Commissariat ŕ l'Energie Atomique, Grenoble)