Order fractionalization and the two channel Kondo lattice

The symmetric two-
channel Kondo lattice, involving two separate conduction electron seas, inter-
acting with a lattice of local moments, provides an idealized model for the
novel cubic heavy electron superconductors, PrX₂Al₂₀, (X=Ti, Va) and UBe₁₃.
There are many indications that two-channel Kondo lattice is unstable to the
development of broken channel symmetry, in which the Kondo effect develops
selectively in one channel giving rise to a \channel magnetization" We study
this novel phase using the large N expansion. One of the remarkable features
of the resulting mean-field theory, is the emergence of a two-component spinor
describing the channel magnetization, suggesting the possibility of order frac-
tionalization. Using the large N expansion, we show that the long-wavelength
physics of the two-channel Kondo lattice is described by the principle chiral
model, in which the skyrmion density of the channel magnetization couples to
the difference of the electromagnetic and internal gauge fields. We will discuss
the implications of these results for the order fractionalization conjecture and
possible observable consequences.