We study, for the first time, the effects of strong short-range electron-electron interactions in generic Rarita-Schwinger-Weyl semimetals hosting spin-3/2\ electrons with linear dispersion at a fourfold band crossing point. The emergence of this novel quasiparticle, which is absent in high-energy physics, has recently been confirmed experimentally in the solid state. We combine symmetry considerations and a perturbative renormalization group analysis to discern three interacting phases that are prone to emerge in the strongly correlated regime: The chiral topological semimetal breaks a\ Z2\ symmetry and features four Weyl nodes of monopole charge\ +1\ located at vertices of a tetrahedron in momentum space. The\ s-wave superconducting state opens a Majorana mass gap for the fermions and is the leading superconducting instability. The Weyl semimetal phase removes the fourfold degeneracy and creates two Weyl nodes with either equal or opposite chirality depending on the anisotropy of the band structure. We find that symmetry breaking occurs at weaker coupling if the total monopole charge remains constant across the transition.

}, doi = {10.1103/PhysRevLett.124.127602}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.124.127602}, author = {Boettcher, Igor} } @article {ISI:000483803100006, title = {Ground state of the three-dimensional BCS d-wave superconductor}, journal = {Phys. Rev. B}, volume = {100}, number = {10}, year = {2019}, month = {SEP 4}, pages = {104503}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave (l = 2) superconductor at weak coupling. It is a noninert state, invariant under the symmetry C-2 only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg-Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.100.104503}, author = {Herbut, Igor F. and Boettcher, Igor and Mandal, Subrata} } @article {ISI:000462898900011, title = {Optical response of Luttinger semimetals in the normal and superconducting states}, journal = {Phys. Rev. B}, volume = {99}, number = {12}, year = {2019}, month = {MAR 25}, pages = {125146}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {We investigate the optical response properties of three-dimensional Luttinger semimetals with the Fermi energy close to a quadratic band touching point. In particular, in order to address recent experiments on the spectroscopy of pyrochlore iridates and half-Heusler superconductors, we derive expressions for the optical conductivity in both the normal and general superconducting states in the linear response regime within the random phase approximation. The response functions can be decomposed into contributions from intraband and interband transitions, the latter comprising a genuine signature of the quadratic band touching point. We demonstrate the importance of interband transitions in the optical response in the normal state both in the homogeneous and quasistatic limit. Our analysis reveals a factorization property of the homogeneous conductivity in the spatially anisotropic case and the divergence of the conductivity for strong spatial anisotropy. In the quasistatic limit, the response is dominated by interband transitions and significantly different from systems with a single parabolic band. As an applications of the formalism in the superconducting state we compute the optical conductivity and superfluid density for the s-wave singlet superconducting case for both finite and vanishing chemical potential.}, issn = {2469-9950}, doi = {10.1103/PhysRevB.99.125146}, author = {Boettcher, Igor} }