  Here we show in simulations of the Haldane model that pulse propagation in
disordered topological insulators is robust throughout the central portion of
the band gap where localized modes do not arise. Since transmission is robust
in topological insulators, the essential field variable is the phase of the
transmitted field, or, equivalently, its spectral derivative, which is the
transmission time. Except near resonances with bulk localized modes that couple
the upper and lower edges of a topological insulator, the transmission time in
a topological insulator is proportional to the density of states and to the
energy excited within the sample. The average transmission time is enhanced in
disordered TIs near the band edge and slightly suppressed in the center of the
band gap. The variance of the transmission time at the band edge for a random
ensemble with moderate disorder is dominated by fluctuations at resonances with
localized states, and initially scales quadratically. When modes are absent,
such as in the center of the band gap, the transmission time self-averages and
its variance scales linearly. This leads to significant sample-to-sample
fluctuations in the transmission time. However, because the transmission time
is the sum of contributions from the continuum edge mode, which stretches
across the band gap, and far-off-resonance modes near the band edge, there are
no sharp features in the spectrum of transmission time in the center of the
band gap. As a result, ultrashort, broadband pulses are faithfully transmitted
in the center of the band gap of topological insulators with moderate disorder
and bent paths. This allows for robust signal propagation in complex
topological metawaveguides for applications in high-speed optoelectronics and
telecommunications.
