  We investigate disorder-driven topological phase transitions in quantized
electric quadrupole insulators. We show that chiral symmetry can protect the
quantization of the quadrupole moment $q_{xy}$, such that the higher-order
topological invariant is well-defined even when disorder has broken all
crystalline symmetries. Moreover, nonvanishing $q_{xy}$ and consequent corner
modes can be induced from a trivial insulating phase by disorder that preserves
chiral symmetry. The critical points of such topological phase transitions are
marked by the occurrence of extended boundary states even in the presence of
strong disorder. We provide a systematic characterization of these
disorder-driven topological phase transitions from both bulk and boundary
descriptions.

Mesoscale and Nanoscale Physics