We propose a model for the intrinsic quantum criticality of $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$, in which a vortex in momentum space gives rise to a new type of Fermi surface singularity. The unquenched angular momentum of the $|J=7/2,m_J=\pm 5/2⟩$ Yb $4f$ states generates a momentum-space line defect in the hybridization between $4f$ and conduction electrons, leading to a quasi-two-dimensional Fermi surface with a $k_{\perp }^4$ dispersion and a singular density of states proportional to $E^{-1/2}$. We discuss the implications of this line node in momentum space for our current understanding of quantum criticality and its interplay with topology.

• Received 11 August 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.176404