  We study (fermionic) spectral functions in two holographic models, the
Gubser-Rocha-linear axion model and the linear axion model, where translational
symmetry is broken by axion fields linear to the boundary coordinates
($\psi_{I}=\beta \delta_{Ii} x^{i}$). Here, $\beta$ corresponds to the strength
of momentum relaxation. The spectral function is computed by the fermionic
Green's function of the bulk Dirac equation, where a fermion mass, $m$, and a
dipole coupling, $p$, are introduced as input parameters. By classifying the
shape of spectral functions, we construct complete phase diagrams in
($m,p,\beta$) space for both models. We find that two phase diagrams are
similar even though their background geometries are different. We also find
that the effect of momentum relaxation on the (spectral function) phases of two
models are similar even though the effect of momentum relaxation on the DC
conductivities of two models are very different. We suspect that this is
because holographic fermion does not back-react to geometry in our framework.
