The work in this thesis is centred around exploring the transport properties induced by periodically driving topologically non-trivial systems. In particular, it focuses upon the signatures associated with Majorana modes in 1D topological superconductors and their adiabatic manipulations, in anticipation of the next generation of experiments pursuing the realization and control of such excitations, which have been stipulated as the potential building blocks of robust quantum computation.
We examine two distinct ways by which external driving can influence a system's
topology. Firstly, we focus upon systems for which the modulation results in the
emergence of additional topological phases, not present in their static counterparts, the classification of which is not well defined by the usual topological invariants associated with the energy spectrum of the bulk system. For such systems, transport properties are vital in identifying non-trivial topological regimes and, with this motivation, we examine the relationship between driven scattering matrix topological invariants and conductance signatures.
Secondly, we determine the transport statistics associated with the adiabatic
manipulation of topological excitations appearing in static systems, with a specific focus upon a Majorana braiding protocol. In this way, we demonstrate that the topological protection of the operation is reflected in geometric contributions to the heat transport induced by the driving. In addition to providing potential experiential signatures of such manipulations, this analysis also sheds light on the influence of periodic driving upon
exchange fluctuation theorems, that govern the thermodynamics of non-equilibrium quantum systems, and also the performance of such protected operations as nanoscale thermal machines.