Interplay of topology and electron-electron interactions in Rarita-Schwinger-Weyl semimetals

Abstract

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 four-fold 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 ${\mathbb{Z}}_2$-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.

4+ pages and supplemental material, published version

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• Linear response in planar Hall and thermal Hall setups for Rarita-Schwinger-Weyl semimetals
• Band geometry from position-momentum duality at topological band crossings
• Andreev bound states in superconductor-barrier-superconductor junctions of Rarita-Schwinger-Weyl semimetals
• Reflections of topological properties in the planar-Hall response for semimetals carrying pseudospin-1 quantum numbers
• Chiral Vortical Effect in Extended Rarita-Schwinger Field Theory and Chiral Anomaly
• Novel criticality of Dirac fermions from lattice symmetry breaking
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• Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions
• Spin density wave order in interacting type-I and type-II Weyl semimetals
• Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals
• p-wave superconductivity and the axi-planar phase of triple-point fermions
• Three-dimensional time reversal invariant topological superconductivity in doped chiral topological semimetals
• Chiral separation effect for spin 3/2 fermions
• Correlated interaction effects in three-dimensional semi-Dirac semimetal
• Geometric semimetals and their simulation in synthetic matter
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• Correlated second-order Dirac semimetals with Coulomb interactions
• Nature of Andreev bound states in Josephson junctions of triple-point semimetals
• Distinguishing features of longitudinal magnetoconductivity for a Rarita-Schwinger-Weyl node
• Persistent fermionic entanglement under decoherence