Adding a second Kondo channel to heavy fermion materials reveals new exotic symmetry breaking phases associated with the development of Kondo coherence. In this paper, we review two such phases, the hastatic order associated with non-Kramers doublet ground states, where the two-channel nature of the Kondo coupling is guaranteed by virtual valence fluctuations to an excited Kramers doublet, and composite pair superconductivity, where the two channels differ by charge 2e and can be thought of as virtual valence fluctuations to a pseudo-isospin doublet. The similarities and differences between these two orders will be discussed, along with possible realizations in actinide and rare earth materials like URu2Si2 and NpPd5Al2.
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