  We report the structural and optical properties of molecular beam epitaxy
(MBE) grown 2-dimensional (2D) material molybdenum diselenide (MoSe2) on
graphite, CaF2 and epitaxial graphene. Extensive characterizations reveal that
2H- MoSe2 grows by van-der-Waals epitaxy on all 3 substrates with a preferred
crystallographic orientation and a Mo:Se ratio of 1:2. Photoluminescence at
room temperature (~1.56 eV) is observed in monolayer MoSe2 on both CaF2 and
epitaxial graphene. The band edge absorption is very sharp, <60 meV over 3
decades. Overcoming the observed small grains by promoting mobility of Mo atoms
would make MBE a powerful technique to achieve high quality 2D materials and
heterostructures.
