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Microscopic models for heavy-fermion materials often assume a local, i.e.,momentum-independent, hybridization between the conduction band and thelocal-moment f electrons. Motivated by recent experiments, we considersituations where this neglect of momentum dependence is inappropriate, namelywhen the hybridization function has nodes in momentum space. We explore thethermodynamic and optical properties of the highly anisotropic heavy Fermiliquid, resulting from Kondo screening in a higher angular-momentum channel.The dichotomy in momentum space has interesting consequences: While e.g. thelow-temperature specific heat is dominated by heavy quasiparticles, theelectrical conductivity at intermediate temperatures is carried by unhybridizedlight electrons. We then discuss aspects of the competition between Kondoeffect and ordering phenomena induced by inter-moment exchange: We propose thatthe strong momentum-space anisotropy plays a vital role in selecting competingphases. Explicit results are obtained for the interplay of unconventionalhybridization with unconventional, magnetically mediated, superconductivity,utilizing variants of large-N mean-field theory. We make connections to recentexperiments on CeCoIn5 and other heavy-fermion materials.

Heavy-fermion metals with hybridization nodes: Unconventional Fermi liquids and competing phases