Crystalline Kitaev spin liquids

Frustrated magnetic systems exhibit many fascinating phases. Prime among them are quantum spin liquids, where the magnetic moments do not order even at zero temperature. A subclass of quantum spin liquids called Kitaev spin liquids are particularly interesting, because they are exactly solvable, can be realized in certain materials, and show a large variety of gapless and gapped phases. Here we show that nonsymmorphic symmetries can enrich spin liquid phases, such that the low-energy spinon degrees of freedom form three-dimensional Dirac cones or nodal chains. In addition, we suggest a realization of such Kitaev spin liquids in metal-organic frameworks.