<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
Julia M. Link, Igor Boettcher, Igor F. Herbut
Abstract
Quasiparticles appearing in Dirac or Weyl semimetals connect relativistic physics at high energies to ongoing studies of novel condensed matter states. Recently, the standard model of emergent particles in solids got a new entry with the observation in several candidate compounds, such as PdBiSe, of the spin-$\frac{3}{2}$ Rarita-Schwinger-Weyl fermion. In this work, the authors explore the uncharted territory of possible unconventional superconductivity in these materials. They find that for small carrier densities the $d$-wave order parameter forms the uniaxial nematic state known from liquid crystals, while at a higher chemical potential it yields the exotic `cyclic state' which breaks time-reversal symmetry without showing any magnetization. Surprisingly, the latter phase also features sixteen small Bogoliubov-Fermi surfaces.