D. F. Agterberg

Superconductivity without inversion symmetry: MnSi versus CePt3Si.

Superconductivity in materials without spatial inversion symmetry is studied. We show that in contrast to common belief, spin-triplet pairing is not entirely excluded in such systems. Moreover, paramagnetic limiting is analyzed for both spin-singlet and -triplet pairing. The lack of inversion symmetry reduces the effect of the paramagnetic limiting for spin-singlet pairing. These results are applied to MnSi and CePt3Si.

S-wave spin-triplet order in superconductors without inversion symmetry: Li2Pd3B and Li2Pt3B.

We investigate the order parameter of noncentrosymmetric superconductors Li2Pd3B and Li2Pt3B via the behavior of the penetration depth lambda(T). The low-temperature penetration depth shows BCS-like behavior in Li2Pd3B, while in Li2Pt3B it follows a linear temperature dependence. We propose that broken inversion symmetry and the accompanying antisymmetric spin-orbit coupling, which admix spin-singlet and spin-triplet pairing, are responsible for this behavior. The triplet contribution is weak in Li2Pd3B, leading to a wholly open but anisotropic gap. The significantly larger spin-orbit coupling in Li2Pt3B allows the spin-triplet component to be larger in Li2Pt3B, producing line nodes in the energy gap as evidenced by the linear temperature dependence of lambda(T). The experimental data are in quantitative agreement with theory.

Spin susceptibility in superconductors without inversion symmetry

In materials without spatial inversion symmetry, the spin degeneracy of the conduction electrons can be lifted by an antisymmetric spin–orbit coupling. We discuss the influence of this spin–orbit coupling on the spin susceptibility of such superconductors, with a particular emphasis on the recently discovered heavy Fermion superconductor CePt3Si. We find that, for this compound (with tetragonal crystal symmetry) irrespective of the pairing symmetry, the stable superconducting phases would give a very weak change of the spin susceptibility for fields along the c-axis and an intermediate reduction for fields in the basal plane. We also comment on the consequences for the paramagnetic limiting in this material.

Helical vortex phase in the noncentrosymmetric CePt3Si.

We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that the upper critical field for a field along the c axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that, to get good agreement between theory and recent experimental measurements of H(c2), this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that the Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order.

Superconductivity and spin-orbit coupling in non-centrosymmetric materials: A review

In non-centrosymmetric superconductors, where the crystal structure lacks a centre of inversion, parity is no longer a good quantum number and an electronic antisymmetric spin-orbit coupling (ASOC) is allowed to exist by symmetry. If this ASOC is sufficiently large, it has profound consequences on the superconducting state. For example, it generally leads to a superconducting pairing state which is a mixture of spin-singlet and spin-triplet components. The possibility of such novel pairing states, as well as the potential for observing a variety of unusual behaviors, led to intensive theoretical and experimental investigations. Here we review the experimental and theoretical results for superconducting systems lacking inversion symmetry. Firstly we give a conceptual overview of the key theoretical results. We then review the experimental properties of both strongly and weakly correlated bulk materials, as well as two dimensional systems. Here the focus is on evaluating the effects of ASOC on the superconducting properties and the extent to which there is evidence for singlet-triplet mixing. This is followed by a more detailed overview of theoretical aspects of non-centrosymmetric superconductivity. This includes the effects of the ASOC on the pairing symmetry and the superconducting magnetic response, magneto-electric effects, superconducting finite momentum pairing states, and the potential for non-centrosymmetric superconductors to display topological superconductivity.

Dislocations and vortices in pair-density-wave superconductors

Unconventional superconductors often host two or more competing states at low temperatures. Line defects seemingly have a role in the relative stability of coexisting density waves that oscillate in space.

Order parameter and vortices in the superconducting Q phase of CeCoIn5.

Recently, it has been reported that the low-temperature high-magnetic field superconducting phase in CeCoIn(5) (Q phase), has spin-density wave (SDW) order that only exists within this phase. This indicates that the SDW order is the result of the development of pair density wave (PDW) order in the superconducting phase that coexists with d-wave superconductivity. Here we develop a phenomenological theory for these coexisting orders. This provides selection rules for the PDW order and further shows that the detailed structure of this order is highly constrained. We then apply our theory to the vortex phase. This reveals vortex phases in which the d-wave vortex cores exhibit charge density wave order and further reveals that the SDW order provides detailed information about the vortex phase.

Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates.

We analyze incommensurate charge-density-wave (CDW) and pair-density-wave (PDW) orders with transferred momenta (±Q,0)/(0,±Q) in underdoped cuprates within the spin-fermion model. Both orders appear due to an exchange of spin fluctuations before magnetic order develops. We argue that the ordered state with the lowest energy has nonzero CDW and PDW components with the same momentum. Such a state breaks C_{4} lattice rotational symmetry, time-reversal symmetry, and mirror symmetries. We argue that the feedback from CDW/PDW order on fermionic dispersion is consistent with ARPES data. We discuss the interplay between the CDW/PDW order and d_{x^{2}-y^{2}} superconductivity and make specific predictions for experiments.

Pairing of j = 3 / 2 Fermions in Half-Heusler Superconductors

We theoretically consider the superconductivity of the topological half-Heusler semimetals YPtBi and LuPtBi. We show that pairing occurs between j=3/2 fermion states, which leads to qualitative differences from the conventional theory of pairing between j=1/2 states. In particular, this permits Cooper pairs with quintet or septet total angular momentum, in addition to the usual singlet and triplet states. Purely on-site interactions can generate s-wave quintet time-reversal symmetry-breaking states with topologically nontrivial point or line nodes. These local s-wave quintet pairs reveal themselves as d-wave states in momentum space. Furthermore, due to the broken inversion symmetry in these materials, the s-wave singlet state can mix with a p-wave septet state, again with topologically stable line nodes. Our analysis lays the foundation for understanding the unconventional superconductivity of the half-Heuslers.

Checkerboard order in vortex cores from pair-density-wave superconductivity

We consider competing pair-density-wave (PDW) and