# Special Condensed Matter Seminar

Hamiltonian Theory of Fractional Chern Bands

http://pantheon.yale.edu/~rshankar/

It has been known for some time that a system with a filled band will
have an integer quantum Hall conductance equal to its Chern number, a
toplogical index associated with the band. While this is true for a
system in a magnetic field with filled Landau Levels, even a system in
zero external field can exhibit the QHE if its band has a Chern number.
I review this issue and discuss a more recent question of whether a
partially filled Chern band can exhibit the Fractional QHE. I describe
the work done with Ganpathy Murthy in which we show how composite
fermions, which were so useful in explaining the usual FQHE, can be
introduced here and with equal success by adapting our Hamiltonian
Theory of CFs developed for the FQHE in the continuum.