Interplay of Coulomb Repulsion and
Spin–Orbit Coupling in Superconducting
3D Quadratic Band Touching Luttinger
Semimetals
Serguei Tchoumakov, Louis J. Godbout, and William Witczak-Krempa
Abstract We investigate the superconductivity of 3D Luttinger semimetals, such
as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various
pairing mechanisms have already been considered for these semimetals, such as
from polar phonons modes, and in this work we explore pairing from the screened
electron–electron Coulomb repulsion.
In these materials, the small Fermi energy and the spin–orbit coupling strongly
influence how charge fluctuations can mediate pairing. We find the superconducting
critical temperature as a function of doping for an s−wave order parameter, and
determine its sensitivity to changes in the dielectric permittivity. Also, we discuss
how order parameters other than s−wave may lead to a larger critical temperature,
due to spin–orbit coupling.
Keywords Superconductivity · Luttinger semimetals · Coulomb repulsion ·
Critical temperature · Eliashberg equation · Spin–orbit
1 Introduction
In regular metals, Coulomb repulsion is commonly believed to compete against the
superconducting pairing between electrons. For example, in the electron-phonon
mechanism of superconductivity with electron-phonon coupling g, the critical
temperature below which an electron gas becomes superconducting is [1]
S. Tchoumakov · L. J. Godbout
Département de Physique, Université de Montréal, Montréal, QC, Canada
e-mail: serguei.tchoumakov@umontreal.ca; louis.godbout.2@umontreal.ca
W. Witczak-Krempa ()
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: w.witczak-krempa@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_34
359
Spin–Orbit Coupling in Superconducting
3D Quadratic Band Touching Luttinger
Semimetals
Serguei Tchoumakov, Louis J. Godbout, and William Witczak-Krempa
Abstract We investigate the superconductivity of 3D Luttinger semimetals, such
as YPtBi, where Cooper pairs are constituted of spin-3/2 quasiparticles. Various
pairing mechanisms have already been considered for these semimetals, such as
from polar phonons modes, and in this work we explore pairing from the screened
electron–electron Coulomb repulsion.
In these materials, the small Fermi energy and the spin–orbit coupling strongly
influence how charge fluctuations can mediate pairing. We find the superconducting
critical temperature as a function of doping for an s−wave order parameter, and
determine its sensitivity to changes in the dielectric permittivity. Also, we discuss
how order parameters other than s−wave may lead to a larger critical temperature,
due to spin–orbit coupling.
Keywords Superconductivity · Luttinger semimetals · Coulomb repulsion ·
Critical temperature · Eliashberg equation · Spin–orbit
1 Introduction
In regular metals, Coulomb repulsion is commonly believed to compete against the
superconducting pairing between electrons. For example, in the electron-phonon
mechanism of superconductivity with electron-phonon coupling g, the critical
temperature below which an electron gas becomes superconducting is [1]
S. Tchoumakov · L. J. Godbout
Département de Physique, Université de Montréal, Montréal, QC, Canada
e-mail: serguei.tchoumakov@umontreal.ca; louis.godbout.2@umontreal.ca
W. Witczak-Krempa ()
Département de physique, Université de Montréal, Montréal, QC, Canada
Centre de Recherches Mathématiques, Université de Montréal, Montréal, QC, Canada
e-mail: w.witczak-krempa@umontreal.ca
© Springer Nature Switzerland AG 2021
M. B. Paranjape et al. (eds.), Quantum Theory and Symmetries, CRM Series in
Mathematical Physics, https://doi.org/10.1007/978-3-030-55777-5_34
359