Chapter 6
p-Wave Superconductivity and d-Vector
Representation
Jean-Pascal Brison
Abstract Since the mid-80s, new classes of superconductors have been discovered
in which the origin of superconductivity cannot be attributed to the electron–ion
interactions at the heart of conventional superconductivity. Most of these unconventional superconductors are strongly correlated electron systems, and identifying
(or even more difficult, predicting) the precise superconducting state has been, and
sometimes remains, an actual challenge. However, in most cases, it has been demonstrated that in these materials the spin state of the Cooper pairs is a singlet state,
often associated with a ‘d-wave’ or ‘s + /−’ orbital state. For a few systems, a spintriplet state is strongly suspected, like in superfluid
3 He; this leads to a much more
complex superconducting order parameter. This was long supposed to be the case for
the d-electron system Sr 2 RuO 4 , and is very likely realized in some uranium-based
( f -electron) ‘heavy fermions’ like UPt 3 (with multiple superconducting phases) or
UGe 2 (with coexisting ferromagnetic order). Beyond the interest for these materials,
p-wave superconductivity is presently quite fashionable for its topological properties
and the prediction that it could host Majorana-like low energy excitations, seen as
a route towards robust (topologically protected) qubits. The aim of these notes is to
make students and experimentalists more familiar with the d-vector representation
used to describe p-wave (spin triplet) superconductivity. The interest of this formalism will be illustrated on some systems where p-wave superconductivity is the prime
suspect.
6.1 Introduction
The purpose of these notes is only to cover some aspects of spin-triplet superconductors, not so commonly covered in the excellent textbooks available on superconductivity, in general, and unconventional superconductors, in particular. Among
J.-P. Brison (B)
CEA, IRIG, Pheliqs, Université Grenoble Alpes, 17 avenue des Martyrs, 38054 Grenoble Cedex
09, France
e-mail: jean-pascal.brison@cea.fr
© The Author(s) 2021
H. Bulou et al. (eds.), Magnetism and Accelerator-Based Light Sources,
Springer Proceedings in Physics 262,
https://doi.org/10.1007/978-3-030-64623-3_6
165
p-Wave Superconductivity and d-Vector
Representation
Jean-Pascal Brison
Abstract Since the mid-80s, new classes of superconductors have been discovered
in which the origin of superconductivity cannot be attributed to the electron–ion
interactions at the heart of conventional superconductivity. Most of these unconventional superconductors are strongly correlated electron systems, and identifying
(or even more difficult, predicting) the precise superconducting state has been, and
sometimes remains, an actual challenge. However, in most cases, it has been demonstrated that in these materials the spin state of the Cooper pairs is a singlet state,
often associated with a ‘d-wave’ or ‘s + /−’ orbital state. For a few systems, a spintriplet state is strongly suspected, like in superfluid
3 He; this leads to a much more
complex superconducting order parameter. This was long supposed to be the case for
the d-electron system Sr 2 RuO 4 , and is very likely realized in some uranium-based
( f -electron) ‘heavy fermions’ like UPt 3 (with multiple superconducting phases) or
UGe 2 (with coexisting ferromagnetic order). Beyond the interest for these materials,
p-wave superconductivity is presently quite fashionable for its topological properties
and the prediction that it could host Majorana-like low energy excitations, seen as
a route towards robust (topologically protected) qubits. The aim of these notes is to
make students and experimentalists more familiar with the d-vector representation
used to describe p-wave (spin triplet) superconductivity. The interest of this formalism will be illustrated on some systems where p-wave superconductivity is the prime
suspect.
6.1 Introduction
The purpose of these notes is only to cover some aspects of spin-triplet superconductors, not so commonly covered in the excellent textbooks available on superconductivity, in general, and unconventional superconductors, in particular. Among
J.-P. Brison (B)
CEA, IRIG, Pheliqs, Université Grenoble Alpes, 17 avenue des Martyrs, 38054 Grenoble Cedex
09, France
e-mail: jean-pascal.brison@cea.fr
© The Author(s) 2021
H. Bulou et al. (eds.), Magnetism and Accelerator-Based Light Sources,
Springer Proceedings in Physics 262,
https://doi.org/10.1007/978-3-030-64623-3_6
165