Robust band of critical states in time-reversal symmetry-broken fermionic systems with lattice selective disorder

We analyze the localization properties of two-dimensional systems based on partite lattices with a basis. Contrary to standard results, we find that a band of critical states emerges for systems in the unitary class A preserving spin symmetry when disorder is unevenly distributed over the basis atoms. The critical metal arises when the less disordered sublattice is connected and has time-reversal symmetry broken. The unexpected robustness to disorder presented here is an appealing result which can be measured in optical lattices.