I do not say that charge density is not important for your study, but my suggestion is to first check if there is any effect of gating on the transmission spectrum, as it is likely to be more sensitive to the applied gate voltage than the charge density. If there is no effect on the transmission, it would then mean that there is something wrong with the calculation setup. The charge density might not be a good quantity for this check because the gate-induced changes in the density can be rather small to be visible on the graph you have posted.