We holographically study the entanglement between two CFTs in a thermofield double state at nonzero chemical potential. In the bulk, this entanglement corresponds to entanglement between the two exterior regions of a Reissner-Nordstrom AdS black hole. We will make use of two probes: thermo-mutual information and two-point correlators of scalar operators. In particular, in the zero-temperature limit the entropy density of the black hole remains finite, while neutral correlators and the mutual information of finite regions vanish, implying that these are not good probes of entanglement at zero temperature. However, the correlators of electrically charged scalar operators can be made to remain finite. We comment on the time evolutions of these quantities and other possible applications.