Infrared fixed points of higher-spin fermions in topological semimetals

Abstract

We determine the fate of interacting fermions described by the Hamiltonian $H=\text{p}\cdot \text{J}$ in three-dimensional topological semimetals with linear band crossing, where $\text{p}$ is momentum and $\text{J}$ are the spin-$j$ matrices for half-integer pseudospin $j\ge 3/2$. While weak short-range interactions are irrelevant at the crossing point due to the vanishing density of states, weak long-range Coulomb interactions lead to a renormalization of the band structure. Using a self-consistent perturbative renormalization group approach, we show that band crossings of the type $\text{p}\cdot \text{J}$ are unstable for $j\le 7/2$. Instead, through an intriguing interplay between cubic crystal symmetry, band topology, and interaction effects, the system is attracted to a variety of infrared fixed points. We also unravel several other properties of higher-spin fermions for general $j$, such as the relation between fermion self-energy and free energy, or the vanishing of the renormalized charge. An $\text{O}(3)$ symmetric fixed point composed of equal chirality Weyl fermions is stable for $j\le 7/2$ and very likely so for all $j$. We then explore the rich fixed point structure for $j=5/2$ in detail. We find additional attractive fixed points with enhanced $\text{O}(3)$ symmetry that host both emergent Weyl or massless Dirac fermions, and identify a puzzling, infrared stable, anisotropic fixed point without enhanced symmetry in close analogy to the known case of $j=3/2$.

13+11 pages, published version

References in corpus (14)

• Multiple types of topological fermions in transition metal silicides
• Discovery of topological chiral crystals with helicoid arc states
• New classes of chiral topological nodes with non-contractible surface Fermi arcs in CoSi
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
• Topological Mott insulator in three-dimensional systems with quadratic band touching
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• A New Type of Quantum Criticality in the Pyrochlore Iridates
• Inflated nodes and surface states in superconducting half-Heusler compounds
• Anisotropy induces non-Fermi-liquid behavior and nematic magnetic order in three-dimensional Luttinger semimetals
• Observation of multiple types of topological fermions in PdBiSe
• Pseudospin 3/2 Fermions, Type-II Weyl Semimetals and Critical Weyl Semimetals in Tricolor Cubic Lattice
• Majorana surface modes of nodal topological pairings in spin-$\frac{3}{2}$ semi-metals
• Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals

Cited by in corpus (2)

• p-wave superconductivity and the axi-planar phase of triple-point fermions
• Transport properties of the pseudospin-3/2 Dirac-Weyl fermions in the double-barrier-modulated two-dimensional system