Amorphous and polycrystalline routes towards a chiral spin liquid

We show that a chiral spin liquid spontaneously emerges in partially amorphous, polycrystalline, or ion-irradiated Kitaev materials. In these systems, time-reversal symmetry is broken spontaneously due to a non-zero density of plaquettes with an odd number of edges, $n_{odd}$. This mechanism opens a sizeable gap, at small $n_{odd}$ compatible with that of typical amorphous materials and polycrystals, and which can alternatively be induced by ion-irradiation. We find that the gap is proportional to $n_{odd}$, saturating at $n_{odd}\sim 40\%$. Using exact diagonalization, we find that the chiral spin liquid is approximately as stable to Heisenberg interactions as Kitaev's honeycomb spin liquid model. Our results open up a significant number of non-crystalline systems where chiral spin liquids can emerge without external magnetic fields.