Floquet Topological Insulator in Graphene

Graphene supports a number of remarkable electronic properties, some
of which make it a candidate for certain microelectronic applications.   
The challenge, however, of opening a gap in its electronic spectrum has limited its use for basic
circuit elements such as transistors.  In this talk I will review recent work
in which an analog of such a gapped spectrum is induced by a time-dependent potential.
The resulting system turns out to have electronic structure with non-trivial
topology, and is an example of a "Floquet Topological Insulator." It supports
surprising fundamental behaviors -- including a quantized Hall effect with
no magnetic field -- but there are fundamental challenges to predicting its
electronic behavior in settings where it can be measured.   I will present
results of numerical calculations in which we meet some of these challenges, and
show what should be found in the simplest possible measurement geometry, a
two-terminal conductor.  I will discuss the features of the results that demonstrate
the unusual topology of the electronic structure, as well as surprising properties
that are unique to the time-dependent nature of the system.