Driving topological insulators out of equilibrium: deviations from periodicity

The behaviour of topological systems driven out of equilibrium has been
a very fascinating area of research; for, not only the external perturbation
can significantly manipulate the properties of such materials, but, given
the right conditions, it may also create topological phases in materials where
there were none, to begin with. In this context, we study the response of a
two-dimensional topological system to an external time-dependent perturbation.
In particular, we try to understand how the conductivity of this system varies
when subject to an external drive. While it is possible to analyze the effect of a
periodic drive, by employing Floquet theory, the same cannot be said about a
perturbation that breaks time periodicity. This is especially useful in the context
of pump-probe measurements which are used to experimentally probe
topological materials. In this work, we study the conductivity - both longitudinal
and transverse - of a two-dimensional TI to an external time-dependent
perturbation in the form of a short pulse (i.e. a 'periodic' drive with a Gaussian
envelope) and compare it with the response of the same system to a
Floquet (i.e., periodic) drive.