  Topological states were initially discovered in solid state systems and have
generated widespread interest in many areas of physics. The advances in cold
atoms create novel settings for studying topological states that would be quite
unrealistic in solid state systems. One example is that the constituents of
quantum gases can be various types of bosons, fermions, and their mixtures.
This paper explores interaction-induced topological states in two-dimensional
Bose-Fermi mixture. We propose a class of topological states which have no
fractionalized excitations but possess maximally chiral edge states. For
previously known topological states, these two features can only be found
simultaneously in the integer quantum Hall states of fermions and the $E_{8}$
state of bosons. The existences of some proposed states in certain continuum
and lattice models are corroborated by exact diagonalization and density matrix
renormalization group calculations. This paper suggests that Bose-Fermi mixture
is a very appealing platform for studying topological states.
