Holographic Fermions in Striped Phases

We examine the fermionic response in a holographic model of a low temperature striped phase, working for concreteness with the setup we studied in [Cremonini:2016rbd,Cremonini:2017usb], in which a U(1) symmetry and translational invariance are broken spontaneously at the same time. We include an ionic lattice that breaks translational symmetry explicitly in the UV of the theory. Thus, this construction realizes spontaneous crystallization on top of a background lattice. We solve the Dirac equation for a probe fermion in the associated background geometry using numerical techniques, and explore the interplay between spontaneous and explicit breaking of translations. We note that in our model the breaking of the U(1) symmetry doesn't play a role in the analysis of the fermionic spectral function. We investigate under which conditions a Fermi surface can form and focus in particular on how the ionic lattice affects its structure. When the ionic lattice becomes sufficiently strong the spectral weight peaks broaden, denoting a gradual disappearance of the Fermi surface along the symmetry breaking direction. This phenomenon occurs even in the absence of spontaneously generated stripes. The resulting Fermi surface appears to consist of detached segments reminiscent of Fermi arcs.