Robust band of critical states in T 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.