  Superconducting nanowires used in single-photon detectors have been realized
on amorphous or poly-crystalline films. Here, we report the use of
single-crystalline NbN thin films for superconducting nanowire single-photon
detectors (SNSPDs). Grown by molecular beam epitaxy (MBE) at high temperature
on nearly lattice-matched AlN-on-sapphire substrates, the NbN films exhibit
high degree of uniformity and homogeneity. Even with relatively thick films,
the fabricated nanowire detectors show saturated internal efficiency at near-IR
wavelengths, demonstrating the potential of MBE-grown NbN for realizing large
arrays of on-chip SNSPDs and their integration with AlN-based $\chi^{(2)}$
quantum photonic circuits.
