  Few-site Kitaev chains are promising for realizing Majorana zero modes
without topological protection but fully nonlocal, which are known as poor
man's Majorana modes. While several signatures have already been reported both
theoretically and experimentally, it still remains unknown what is the nature
of superconducting correlations in the presence of poor man's Majorana modes.
In this work, we study few-site Kitaev chains and demonstrate that they host
pair correlations with distinct symmetries, entirely determined by the
underlying quantum numbers. In particular, we find that a two-site Kitaev chain
hosts local (odd-frequency) and nonlocal (odd- and even-frequency) pair
correlations, both spin polarized and highly tunable by the system parameters.
Interestingly, the odd-frequency pair correlations exhibit a divergent
behaviour around zero frequency when the nonlocal $p$-wave pair potential and
electron tunneling are of the same order, an effect that can be controlled by
the onsite energies. Since a divergent odd-frequency pairing is directly
connected to the intrinsic spatial nonlocality of Majorana zero modes in
topological superconductors, the divergent odd-frequency pairing here reflects
the intrinsic Majorana nonlocality of poor man's Majorana modes but without any
relation to topology. Our findings could help understanding the emergent pair
correlations in few-site Kitaev chains.
