  We have found that single-crystal films can be grown on (0001) Al2O3
substrates through the golden relation of a perfect lattice-matching ratio
between the a-axis lattice constants of MgB2 and Al2O3. Selected area electron
diffraction patterns evidently indicate hexagonal MgB2 film with a 30 degrees
in-plane rotation with respect to the Al2O3 substrate. The films grown on Al2O3
show a zero-resistance transition temperature of 39.6 K with a transition width
of 0.1 K. The critical current density at zero field is comparable to the
depairing critical current density and rapidly decreases with increasing
applied field due to the lack of pinning sites, as observed for high-quality
MgB2 single crystals.
