It is now well-established that fractional quasiparticles,
with quantum numbers that are non-integer multiples of the electron's,
can arise as collective excitations of a many-body electronic system.
The canonical example of this phenomenon is the fractional quantum
Hall state, discovered thirty years ago in a two-dimensional electron
gas in strong normal magnetic field and at very low temperatures. It
hosts quasiparticles that carry a fraction of the electron's charge.
Thanks to the special topology of two dimensions, they are also
endowed with fractional statistics; that is, they are neither bosons
nor fermions, but something in between, known as anyons. The ground
state is strongly interacting in the sense that it cannot be
constructed from single-particle wave functions. By contrast, in an
integer quantum Hall state the quasiparticles are the ordinary
(integral) electrons and holes and the ground state is weakly
interacting. More recent developments have revealed other systems in
which nontrivial topological properties result in fractionalization,
such as topological insulators and superconductors, and certain
defects in graphene. However, accessing the fractional quasiparticles
in these systems has proved to be difficult.
In this talk, I will briefly review these developments, and in
particular discuss a proposal for creating anyons (and fractional
charge) in a weakly interacting system which allows for easier access
and manipulation. The system is a layered structure of a
two-dimensional electron gas in an integer quantum Hall state and a
type-II superconductor with an artificial array of pinning site (e.g.
holes). A reasonable estimate of system parameters shows that it could
be made in the lab with today's technology. The anyons may be accessed
by established techniques for manipulating superconducting vortices
or, alternatively, through an all-electric circuit. I will discuss
experiments that can detect the fractional charge and statistics of
the quasiparticles, and conclude by sketching extensions of the
proposal.
References:
1) Weeks, Rosenberg, Seradjeh, Franz, Nature Phys. 3, 796 (2007),
2) Rosenberg, Seradjeh, Weeks, Franz, Phys. Rev. B 79, 205102 (2009).