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We have found that single-crystal films can be grown on (0001) Al2O3substrates through the golden relation of a perfect lattice-matching ratiobetween the a-axis lattice constants of MgB2 and Al2O3. Selected area electrondiffraction patterns evidently indicate hexagonal MgB2 film with a 30 degreesin-plane rotation with respect to the Al2O3 substrate. The films grown on Al2O3show a zero-resistance transition temperature of 39.6 K with a transition widthof 0.1 K. The critical current density at zero field is comparable to thedepairing critical current density and rapidly decreases with increasingapplied field due to the lack of pinning sites, as observed for high-qualityMgB2 single crystals.

Perfect Domain-Lattice Matching Between MgB2 and Al2O3: Single-Crystal MgB2 Thin Films Grown on Sapphire