Electronic instability, layer selectivity and Fermi arcs in La$_3$Ni$_2$O$_7$

Using advanced dynamical mean-field theory on a realistic level we study the normal-state correlated electronic structure of the high-pressure superconductor La$_3$Ni$_2$O$_7$ and compare the features of the conventional bilayer (2222) Ruddelsden-Popper crystal structure with those of a newly-identified monolayer-trilayer (1313) alternation. Both structural cases display Ni-$d_{z^2}$ flat-band character at low-energy, which drives an electronic instability with a wave vector ${\bf q_{\rm I}}=(0.25,0.25,q_z)$ at ambient pressure, in line with recent experimental findings. The 1313 electronic structure exhibits significant layer selectivity, rendering especially the monolayer part to be Mott-critical. At high pressure, this layer selectivity weakens and the 1313 fermiology displays arcs reminiscent to those of high-$T_c$ cuprates. In contrast to dominant inter-site self-energy effects in the latter systems, here the Fermi arcs are the result of the multiorbital and multilayer interplay within a correlated flat-band scenario.