366
S. Tchoumakov et al.
5 Conclusion
Over a wide range of doping, we find that the s−wave critical temperature for a
Luttinger semimetal with screened Coulomb repulsion is T c /T F ≈ 4.4 × 10 −4 .
T c /T F is small but may be an explanation for the superconductivity of YPtBi, a
candidate Luttinger semimetal, where experiments report T c /T F ≈ (1 − 8) × 10 −4 .
Previous theoretical works on YPtBi, with phonon-based pairing, estimate a critical
temperature at least one order of magnitude smaller than in experiments [15, 18].
We quantitatively show the origins of superconductivity, in relation to the plasmon
[9] and Kohn–Luttinger [4] mechanisms of superconductivity. We also analyze
the Eliashberg equation of j = 3/2 fermions [15, 16] and propose that an
unconventional order parameter, with J = L = S = 1, may turn the repulsive
contribution of the screened Coulomb potential to attractive. This reminds a recent
discussion on graphene, where the Berry curvature promotes the = 1 component
of a repulsive interaction to attractive [19]. A more involved study would be required
to determine the dominant superconducting channel.
Acknowledgments This project is funded by a grant from Fondation Courtois, a Discovery
Grant from NSERC, a Canada Research Chair, and a “Établissement de nouveaux chercheurs
et de nouvelles chercheuses universitaires” grant from FRQNT. This research was enabled in
part by support provided by Calcul Québec (www.calculquebec.ca) and Compute Canada (www.
computecanada.ca).
Bibliography
1. W.L. McMillan, Transition temperature of strong-coupled superconductors. Phys. Rev. 167(2),
331–334 (1968). doi:10.1103/PhysRev.167.331
2. Y. Takada, Theory of superconductivity in polar semiconductors and its application to N-type semiconducting SrTiO3. J. Phys. Soc. Jpn. 49(4), 1267–1275 (1980).
doi:10.1143/JPSJ.49.1267
3. J. Ruhman, P.A. Lee, Superconductivity at very low density: the case of strontium titanate.
Phys. Rev. B 94(22), 224515 (2016). doi:10.1103/PhysRevB.94.224515
4. W. Kohn, J.M. Luttinger, New mechanism for superconductivity. Phys. Rev. Lett. 15(12), 524–
526 (1965). doi:10.1103/PhysRevLett.15.524
5. S. Tchoumakov, L.J. Godbout, W. Wictzak-Krempa, Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals. Arxiv:1910.04189.
https://arxiv.org/abs/1910.04189
6. P.B. Allen, R.C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed.
Phys. Rev. B 12(3), 905–922 (1975). doi:10.1103/PhysRevB.12.905
7. J.M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: general theory.
Phys. Rev. 102(4), 1030–1041 (1956). doi:10.1103/PhysRev.102.1030
8. S. Tchoumakov, W. Witczak-Krempa, Dielectric and electronic properties of three-dimensional
Luttinger semimetals with a quadratic band touching. Phys. Rev. B 100(7), 075104 (2019).
doi:10.1103/PhysRevB.100.075104
9. Y. Takada, Plasmon mechanism of superconductivity in the multivalley electron gas. J. Phys.
Soc. Jpn. 61, 238–253 (1992). doi:10.1143/JPSJ.61.238
S. Tchoumakov et al.
5 Conclusion
Over a wide range of doping, we find that the s−wave critical temperature for a
Luttinger semimetal with screened Coulomb repulsion is T c /T F ≈ 4.4 × 10 −4 .
T c /T F is small but may be an explanation for the superconductivity of YPtBi, a
candidate Luttinger semimetal, where experiments report T c /T F ≈ (1 − 8) × 10 −4 .
Previous theoretical works on YPtBi, with phonon-based pairing, estimate a critical
temperature at least one order of magnitude smaller than in experiments [15, 18].
We quantitatively show the origins of superconductivity, in relation to the plasmon
[9] and Kohn–Luttinger [4] mechanisms of superconductivity. We also analyze
the Eliashberg equation of j = 3/2 fermions [15, 16] and propose that an
unconventional order parameter, with J = L = S = 1, may turn the repulsive
contribution of the screened Coulomb potential to attractive. This reminds a recent
discussion on graphene, where the Berry curvature promotes the = 1 component
of a repulsive interaction to attractive [19]. A more involved study would be required
to determine the dominant superconducting channel.
Acknowledgments This project is funded by a grant from Fondation Courtois, a Discovery
Grant from NSERC, a Canada Research Chair, and a “Établissement de nouveaux chercheurs
et de nouvelles chercheuses universitaires” grant from FRQNT. This research was enabled in
part by support provided by Calcul Québec (www.calculquebec.ca) and Compute Canada (www.
computecanada.ca).
Bibliography
1. W.L. McMillan, Transition temperature of strong-coupled superconductors. Phys. Rev. 167(2),
331–334 (1968). doi:10.1103/PhysRev.167.331
2. Y. Takada, Theory of superconductivity in polar semiconductors and its application to N-type semiconducting SrTiO3. J. Phys. Soc. Jpn. 49(4), 1267–1275 (1980).
doi:10.1143/JPSJ.49.1267
3. J. Ruhman, P.A. Lee, Superconductivity at very low density: the case of strontium titanate.
Phys. Rev. B 94(22), 224515 (2016). doi:10.1103/PhysRevB.94.224515
4. W. Kohn, J.M. Luttinger, New mechanism for superconductivity. Phys. Rev. Lett. 15(12), 524–
526 (1965). doi:10.1103/PhysRevLett.15.524
5. S. Tchoumakov, L.J. Godbout, W. Wictzak-Krempa, Superconductivity from Coulomb repulsion in three-dimensional quadratic band touching Luttinger semimetals. Arxiv:1910.04189.
https://arxiv.org/abs/1910.04189
6. P.B. Allen, R.C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed.
Phys. Rev. B 12(3), 905–922 (1975). doi:10.1103/PhysRevB.12.905
7. J.M. Luttinger, Quantum theory of cyclotron resonance in semiconductors: general theory.
Phys. Rev. 102(4), 1030–1041 (1956). doi:10.1103/PhysRev.102.1030
8. S. Tchoumakov, W. Witczak-Krempa, Dielectric and electronic properties of three-dimensional
Luttinger semimetals with a quadratic band touching. Phys. Rev. B 100(7), 075104 (2019).
doi:10.1103/PhysRevB.100.075104
9. Y. Takada, Plasmon mechanism of superconductivity in the multivalley electron gas. J. Phys.
Soc. Jpn. 61, 238–253 (1992). doi:10.1143/JPSJ.61.238