Oscillatory Melting Temperature of the Vortex Smectic Phase in Layered Superconductors

We report on transport measurements of $\mathrm{YBa}{}_2\mathrm{Cu}{}_3\mathrm{O}{}_{7-\delta }$ single crystals with different oxygen contents in the geometry $B$, $J\Vert \mathrm{ab}\left(J\perp B\right)$. Our data show that the vortices become confined between the Cu-O planes below a well-defined temperature at which the effective size $2\xi$ of the vortex core is approximately equal to the period of the Cu-O layers. This confinement strongly increases the vortex liquid freezing temperature. A new melting line is found separating a vortex liquid and a smectic phase, which shows an oscillatory field dependence reflecting differences between commensurate and incommensurate smectic states.