Theory of topological glass transitions in amorphous topological matter

Amorphous systems have recently been identified as promising platforms for topological matter. In this work we introduce a scaling theory of amorphous topological phase transitions in two dimensional systems. We investigate the universal behaviour of a density-driven Chern and Z₂ glass transitions by carrying out a finite-size scaling analysis of topological invariants averaged over random geometries. We find that the universal properties of continuum problems can be captured by studying random geometries generated by percolation lattices. Strikingly, our results show that even for short-range hopping the topological phase may persists down to the classical site percolation threshold. Furthermore, our theory suggests that the value of the critical exponent describing the diverging localization length near the critical density is close to that of the exponent of the correlation length of the critical percolation cluster. Our theory supports the conclusion that density-driven amorphous topological transitions have their unique properties not shared by disordered systems and occupy separate universality classes.