Nonsymmorphic band sticking in a topological superconductor

Abstract

Single-crystal x-ray diffraction recently identified the space group of the weakly correlated yet exotic time reversal symmetry (TRS) breaking superconductor $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ to be nonsymmorphic $Cmcm$. This symmetry causes band sticking on a zone face pierced by four Fermi surfaces, leading to two nodal Fermi lines and a nodal Fermi loop on that zone face ${k}_{z}=\frac{\ensuremath{\pi}}{c}$. These line singularities are examples of perfectly flat (in energy and in geometry) nodal structures that lie precisely at a single energy, with that energy being the Fermi level ${E}_{F}$, even under variation of the carrier density. Projections onto surfaces perpendicular to that zone face produce collapsed drumhead state regions of zero area on the edges of the surface Brillouin zone. Although small by most measures, spin-orbit coupling splits the line and loop degeneracies on the Fermi surfaces (FSs) in the normal state except at two symmetry-related Dirac points, which topologically are locally dispersionless in one direction (zero velocity and infinite mass) while linear in the other two directions. The band sticking and distinctive Fermi surface placed Dirac points are most impactful in establishing $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ as a topological superconductor in the bulk, with the degenerate FSs providing a natural platform for the superconducting order-parameter symmetry necessary for describing this TRS breaking superconductor. Unlike most other crystal symmetries, spin-orbit coupling leaves intact a nodal line piercing the FS, resulting in Dirac points situated at ${E}_{F}$ lying along nodal lines. Additionally, the degeneracy exactly at the Fermi energy is central in placing $\mathrm{La}\mathrm{Ni}{\mathrm{Ga}}_{2}$ precisely at a Lifshitz FS instability, independent of band filling and protected by $Cmcm$ symmetry. The eight-band low-energy Bogoliubov--de Gennes quasiparticle spectrum is presented along one dispersive direction for varying strengths of TRS breaking. We include a discussion of energetics of gauge symmetry and magnetic order resulting from TRS breaking, incorporating information from experimental data. These results suggest a scenario where TRS breaking rather than gauge-symmetry breaking (superconductivity) might be the driving order parameter.