One vanishing minor in the neutrino mass matrix

We study a specific texture of the neutrino mass matrix, namely the models with one $2\times 2$ subdeterminant equal to zero. We carry out a complete phenomenological analysis with all possible relevant correlations. Every pattern of the six possible ones is found able to accommodate the experimental data, with three cases allowing also for non-invertible mass matrices. We present symmetry realizations for all the models.