  We clarify the mechanism for negative differential conductivity in
holographic conductors. Negative differential conductivity is a phenomenon in
which the electric field decreses with the increase of the current. This
phenomenon is widely observed in strongly correlated insulators, and it has
been known that some models of AdS/CFT correspondence (holographic conductors)
reproduces this behaviour. We study the mechanism for negative differential
conductivity in holographic conductors by analyzing the lifetime of the bound
states of the charge carriers. We find that when the system exhibits negative
differential conductivity, the lifetime of the bound states grows as the
electric field increases. This suggests that the negative differential
conductivity in this system is realized by the supression of the ionization of
the bound states that supplies the free carriers.
