Neutrinophilic two Higgs doublet model with $U(1)$ global symmetry

We propose a neutrinophilic two-Higgs-doublet model, where the vacuum expectation value (VEV) of the second Higgs doublet is only induced at one-loop level via several neutral fermions. Thus, the masses of active neutrinos arising from the Higgs doublets are naturally small via such a tiny VEV. We discuss various phenomenology of the model, including the neutrino masses and oscillations, bounds on non-unitarity, lepton-flavor violations, the oblique parameters, the muon anomalous magnetic moment, the GeV-scale sterile neutrino candidate arising from the tiny VEV, and collider signatures. We finally discuss the possibility of detecting the sterile neutrino suggested in the experiment of Future Circular Collider (FCC).