A milestone in graphene research was the 2005 discovery of an
integer quantum Hall effect. In contrast to its manifestation
in conventional two-dimensional (2D) electron systems, such
as in semiconductor heterostructures, the graphene quantum
Hall effect reflects the "ultra-relativistic" character of
the underlying carriers, via a particular sequence of plateaus
in the transverse Hall resistance.
In view of the fractional cousin of the integer quantum Hall
effect in 2D electron systems, one may thus naturally ask the
question about a fractional quantum Hall effect in graphene.
Does it also reflect the ultra-relativistic character of the
charge carriers? To what extent is it different from the
fractional quantum Hall effect in (non-relativistic)
semiconductor heterostructures? Many of these questions remain
open from an experimental point of view, although some
fractional states have recently been observed in transport
and spectroscopic measurements.
This talk aims at a theoretical perspective on the fractional
quantum Hall effect in graphene, namely in view of its
multi-component character due to the fourfold spin-valley
degeneracy, which gives rise to an internal SU(4) symmetry
and that is approximately respected by the underlying
electron-electron interactions. This theoretical perspective
will be confronted with recent experimental advances.