Classification of gapless Z2 spin liquids in three-dimensional Kitaev models

Frustrated quantum magnets can harbor unconventional spin-liquid ground states in which the elementary magnetic moments fractionalize into new emergent degrees of freedom. While the fractionalization of quantum numbers is one of the recurring themes in modern condensed matter physics, it often remains a challenge to devise a controlled analytical framework tracking this phenomenon. A notable exception is the exactly solvable Kitaev model, in which spin degrees of freedom fractionalize into Majorana fermions and a Z(2) gauge field. Here, we discuss the physics of fractionalization in three-dimensional Kitaev models and demonstrate that the itinerant Majorana fermions generically form a (semi) metal which, depending on the underlying lattice structure, exhibits Majorana Fermi surfaces, nodal lines, or topologically protected Weyl nodes. We show that the nature of these Majorana metals can be deduced from an elementary symmetry analysis of the projective time-reversal and inversion symmetries for a given lattice. This allows us to comprehensively classify the gapless spin liquids of Kitaev models for the most elementary tricoordinated lattices in three dimensions. We further expand this classification by addressing the effects of time-reversal symmetry breaking and additional interactions.