Non-Hermitian Disorder-induced Topological Insulators

Recent studies of disorder or non-Hermiticity induced topological insulators
inject new ingredients for engineering topological matter. Here we consider
the effect of purely non-Hermitian disorders, a combination of these two
ingredients, in a 1D chiral symmetric lattice with disordered gain and loss.
Topological states can be induced by increasing gain-loss disorder strength
with topological invariant carried by localized states in the complex bulk spectra,
the system reveals richer phase diagrams and distinct topological states
compared to Hermitian disorder systems.
The non-Hermitian critical behavior is characterized by the biorthogonal
localization length of zero energy edge modes, which diverges at the
critical transition point and establishes the bulk-edge correspondence.
Furthermore, we show that the bulk topology may be experimentally accessed
by measuring the biorthogonal chiral displacement, which
converges to the winding number through time-averaging and can be extracted
from proper Ramsey-interference sequences. We propose a feasible scheme to implement
and probe such non-Hermitian disorder driven topological insulators using
photons in coupled micro-cavities.