Melting of a flux-line fluid confined byCuO2planes: Lindemann-criterion failure

The strong pinning of flux lines by ${\mathrm{CuO}}_2$ planes in high-${\mathit{T}}_{\mathit{c}}$ superconductors effectively eliminates one of the two components of the flux-line displacement field when the magnetic field is aligned parallel to the planes. It is argued that in this geometry the Abrikosov flux-line lattice is stable for any finite density of the system. The crystalline order parameter vanishes and the Lindemann ratio diverges continuously as H→${\mathit{H}}_{\mathrm{c}1\mathrm{}}^{+}$.