  We investigate the photoluminescence of interlayer excitons in
heterostructures consisting of monolayer MoSe2 and WSe2 at low temperatures.
Surprisingly, we find a doublet structure for such interlayer excitons. Both
peaks exhibit long photoluminescence lifetimes of several ten nanoseconds up to
100 ns at low temperatures, which verifies the interlayer nature of both. The
peak energy and linewidth of both show unusual temperature and power
dependences. In particular, we observe a blue-shift of their emission energy
for increasing excitation powers. At a low excitation power and low
temperatures, the energetically higher peak shows several spikes. We explain
the findings by two sorts of interlayer excitons; one that is indirect in real
space but direct in reciprocal space, and the other one being indirect in both
spaces. Our results provide fundamental insights into long-lived interlayer
states in van der Waals heterostructures with possible bosonic many-body
interactions
