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Infrared fixed points of higher-spin fermions in topological semimetals

TitleInfrared fixed points of higher-spin fermions in topological semimetals
Publication TypeJournal Article
Year of Publication2020
AuthorsI. Boettcher
JournalPhys. Rev. B
Volume102
Pagination155104
Date PublishedOCT 5
Type of ArticleArticle
ISSN2469-9950
Abstract

We determine the fate of interacting fermions described by the Hamiltonian H = p . J in three-dimensional topological semimetals with linear band crossing, where p is momentum and J are the spin- j matrices for half-integer pseudospin j >= 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 p . J are unstable for j >= 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 O(3) symmetric fixed point composed of equal chirality Weyl fermions is stable for j <= 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 0(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.

DOI10.1103/PhysRevB.102.155104