$$\testit{d}$$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals
Abstract
In this work, we uncover the properties of complex tensor ($$\textit{d}$$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$$\frac{3}{2}$$ fermions at a fourfold linear band-crossing point. Although the general theory of $$\textit{d}$$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$$\frac{3}{2}$$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $$\textit{d}$$-wave superconductors where the $$\textit{d}$$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.
- Authors:
-
[1];
[1]
- Simon Fraser Univ., Burnaby, BC (Canada)
- Univ. of Maryland, College Park, MD (United States)
- Publication Date:
- Research Org.:
- Univ. of Maryland, College Park, MD (United States); Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); German Research Foundation (DFG); US Army Research Office (ARO); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); US Army Research Laboratory (USARL); Natural Sciences and Engineering Research Council of Canada (NSERC)
- OSTI Identifier:
- 1803528
- Grant/Contract Number:
- SC0019040; SC0019449; SC0020312; LI 3628/1-1
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 18; 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; Materials Science; Physics
Citation Formats
Link, Julia M., Boettcher, Igor, and Herbut, Igor F. $\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals. United States: N. p., 2020.
Web. doi:10.1103/physrevb.101.184503.
Link, Julia M., Boettcher, Igor, & Herbut, Igor F. $\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals. United States. https://doi.org/10.1103/physrevb.101.184503
Link, Julia M., Boettcher, Igor, and Herbut, Igor F. Mon .
"$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals". United States. https://doi.org/10.1103/physrevb.101.184503. https://www.osti.gov/servlets/purl/1803528.
@article{osti_1803528,
title = {$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals},
author = {Link, Julia M. and Boettcher, Igor and Herbut, Igor F.},
abstractNote = {In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.},
doi = {10.1103/physrevb.101.184503},
journal = {Physical Review. B},
number = 18,
volume = 101,
place = {United States},
year = {Mon May 04 00:00:00 EDT 2020},
month = {Mon May 04 00:00:00 EDT 2020}
}
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