  In literature ladder operators of different nature exist. The most famous are
those obeying canonical (anti-) commutation relations, but they are not the
only ones. In our knowledge, all ladder operators have a common feature: the
lowering operators annihilate a non zero vector, the {\em vacuum}. This is
connected to the fact that operators of these kind are often used in
factorizing some positive operators, or some operators which are { bounded from
below}. This is the case, of course, of the harmonic oscillator, but not only.
In this paper we discuss what happens when considering lowering operators with
no vacua. In particular, after a general analysis of this situation, we propose
a possible construction of coherent states, and we apply our construction to
graphene.
