  In this work, we study the hidden-strange molecular states composed of a
baryon and a vector meson in a coupled-channel $N\rho-N\omega-N\phi-\Lambda
K^*-\Sigma K^*$ interaction. With the help of the effective Lagrangians which
coupling constants are determined by the SU(3) symmetry, the interaction is
constructed and inserted into the quasipotential Bethe-Salpeter equation to
search for poles in the complex plane, which correspond to molecular states.
Two poles are found with a spin parity $3/2^-$ near the $N\rho$ and the $\Sigma
K^*$ thresholds, which can be related to the $N(1700)$ and the $N(2100)$,
respectively. No pole near the $N\phi$ threshold can be found if direct
interaction between a nucleon and $\phi$ meson is neglected according to the
OZI rule. After introducing the QCD van der Waals force between a nucleon and
$\phi$ meson, a narrow state can be produced near the $N\phi$ threshold.
Inclusion of the QCD van der Waals force changes the line shape of the
invariant mass spectrum in the $N\phi$ channel leading to a worse agreement
with the present low-precision data. Future experiments at BelleII, JLab, and
other facilities will be very helpful to clarify the existence of these
possible hidden-strange molecular states.
