*
National Institute for Materials Science, Tsukuba 305-0047, Japan
It is now well established that the Abrikosov vortex lattice in type II superconductors melts via a thermodynamic first-order transition. However, much less consensus has been reached on the possible phases and melting process of interlayer Josephson vortex lattice, despite of considerable experimental and theoretical efforts. In the present work, we tackle this unsolved issue by using the density functional theory (DFT).
The DFT has been formulated by Ramakrishnan and Yussouff for general freezing phenomena
[1,2]. In DFT the free energy of a system is described by spatial variations of particle density in terms of the so-called direct pair correlation function (DPCF) of particles in the liquid state.
The DPCF depends on the density, temperature, and particle-particle interactions, and can be evaluated by for example the HNC approximation. A lattice order appears when the density wave characterized by non-vanishing Fourier components at the corresponding reciprocal lattice vectors takes lower free energy than uniform liquid. For pancake vortices, both the first-order nature of the vortex liquid freezing and quantitative aspects (e.g. Lindemann number) have been successfully captured by DFT at the clean limit [3].
As it is hard to evaluate the DPCF accurately in the presence of finite interlayer Josephson couplings, we will not try to draw the melting line in the H-T phase diagram. Instead, we adopt the DPCF and the layer pinning strength as parameters to explore the possible freezing processes. This approach turns out to be fruitful, and we have obtained several interesting results [4]: (i) At the dense limit of Josephson vortices (m=1), the freezing from liquid to lattice switches from first order to continuous at a tricritical point upon increasing pinning potential;
(ii) A smectic phase with more vortex lines in every other layers (period m=2) and intra-layer liquid correlations is observed at strong layer pinning. When the smectic phase is present, the freezing of vortex liquid is two-step, a second-order liquid-smectic and a first-order smectic-lattice transition; (iii) A direct, first-order liquid-lattice transition preempts the smectic order with m equal to and above 3.
Adopting the physical parameters available by experiments, we find that the m=2 smectic is possible for YBCO at high magnetic fields, while no smectic order is expected for BSCCO.
This work is a collaboration with M. B. Luo and Y. Q. Ma.
[1] T. V. Ramakrishnan and M. Yussouff, Phys. Rev. B, 19 , 2775 (1979).
[2] T. V. Ramakrishnan, Phys. Rev. Lett. 48 , 541 (1982).
[3] S. Sengupta et al ., Phys. Rev. Lett. 67 , 3444 (1991).
[4] X. Hu et al ., cond-mat/0406180.
*Hu.Xiao@nims.go.jp