Instability of a tilted vortex line in magnetically coupled layered superconductors

We calculate the line tension of a tilted stack of magnetically coupled two-dimensional pancake vortices held at the ends and show that the line tension becomes negative at an angle of 52°. We further calculate the tilt modulus at arbitrary angle θ and show that it becomes negative starting at the same angle 52° for long wavelengths. A structure for the vortex line is given, which is shown to have a lower energy.