Infrared fixed points of higher-spin fermions in topological semimetals
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 O ( 3 ) symmetrymore »
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States); Univ. of Maryland, College Park, MD (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1684620
- Grant/Contract Number:
- SC0019449; SC0019040; SC0020312
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 102; Journal Issue: 15; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Topological materials; Semimetals; Spin; Effective field theory; Renormalization group
Citation Formats
Boettcher, Igor. Infrared fixed points of higher-spin fermions in topological semimetals. United States: N. p., 2020.
Web. doi:10.1103/physrevb.102.155104.
Boettcher, Igor. Infrared fixed points of higher-spin fermions in topological semimetals. United States. https://doi.org/10.1103/physrevb.102.155104
Boettcher, Igor. Mon .
"Infrared fixed points of higher-spin fermions in topological semimetals". United States. https://doi.org/10.1103/physrevb.102.155104. https://www.osti.gov/servlets/purl/1684620.
@article{osti_1684620,
title = {Infrared fixed points of higher-spin fermions in topological semimetals},
author = {Boettcher, Igor},
abstractNote = {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 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.},
doi = {10.1103/physrevb.102.155104},
journal = {Physical Review. B},
number = 15,
volume = 102,
place = {United States},
year = {Mon Oct 05 00:00:00 EDT 2020},
month = {Mon Oct 05 00:00:00 EDT 2020}
}
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