Spin-Peierls Instability of Three-Dimensional Spin Liquids with Majorana Fermi Surfaces

摘要

Three-dimensional (3D) variants of the Kitaev model can harbor gapless spinliquids with a Majorana Fermi surface on certain tricoordinated latticestructures such as the recently introduced hyperoctagon lattice. Here weinvestigate Fermi surface instabilities arising from additional spin exchangeterms (such as a Heisenberg coupling) which introduce interactions between theemergent Majorana fermion degrees of freedom. We show that independent of thesign and structure of the interactions, the Majorana surface is alwaysunstable. Generically the system spontaneously doubles its unit cell atexponentially small temperatures and forms a spin liquid with line nodes.Depending on the microscopics further symmetries of the system can be broken atthis transition. These spin-Peierls instabilities of a 3D spin liquid areclosely related to BCS instabilities of fermions.