No abstract

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.

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.

We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that 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 Hc2, 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 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. PACS numbers:The recently discovered heavy fermion superconductor CePt 3 Si 1 has triggered many experimental and theoretical studies 2,3,4,5,6,7,8,9 . There are two features which have caused this attention: the absence of inversion symmetry; and the comparatively high upper critical magnetic field (H c2 ). Broken inversion symmetry (parity) has a pronounced effect on the quasiparticle states through the splitting of the two spin degenerate bands. This influences the superconducting phase, which usually relies on the formation of pairs of electrons in degenerate quasiparticle states with opposite momentum. The availability of such quasiparticle states is usually guaranteed by time reversal and inversion symmetries (parity) 10,11 . It is relatively easy to remove time reversal symmetry, e.g. by a magnetic field, and the physical consequences of this have been well studied. However, parity is not so straightforwardly manipulated by external fields. Superconductivity in materials without inversion center therefore provides a unique opportunity in this respect.The large H c2 ≈ 4T in CePt 3 Si 1,8 implies that the Zeeman splitting must be non-negligible below T c = 0.75K (the estimated paramagnetic limit is at H P ≈ 1.2 T). In a magnetic field, this superconductor has to form Cooper pairs under rather odd circumstances. In particular, it is no longer guaranteed that a state with momentum k at the Fermi surface has a degenerate partner at −k. The state k would rather pair with a degenerate state −k + q and in this way generate an inhomogeneous superconducting phase. We argue below that recent H c2 measurements 8 suggest that this is the case in CePt 3 Si. These measurements show that, while the upper critical field is basically isotropic close to T c , a small anisotropy appears at lower temperature 8 (H c c2 /H ab c2 = 1.18 at T = 0). The apparent absence of a paramagnetic limit in CePt 3 Si can be explained by lack of inversion symmetry even if the pairing has s-wave symmetry 2,12,13 . However, these works indicate that suppression of paramagnetism is very anisotropic and the application of this theory to CePt 3 Si would indicate no paramagnetic suppression for the field along the c-axis, but a suppression fo...

It is commonly believed that in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: the gap is nodeless, it has point nodes, or it has line nodes. Here, we show that for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories; instead it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a Z2 invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing; since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these Z2-protected Fermi surfaces to be ubiquitous.

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.

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.

With the ground breaking work of the Fulde, Ferell, Larkin, and Ovchinnikov (FFLO), it was realized that superconducting order can also break translational invariance; leading to a phase in which the Cooper pairs develop a coherent periodic spatially oscillating structure. Such pair density wave (PDW) superconductivity has become relevant in a diverse range of systems, including cuprates, organic superconductors, heavy fermion superconductors, cold atoms, and high density quark matter. Here we show that, in addition to charge density wave (CDW) order, there are PDW ground states that induce spin density wave (SDW) order when there is no applied magnetic field. Furthermore, we show that PDW phases support topological defects that combine dislocations in the induced CDW/SDW order with a fractional vortex in the usual superconducting order. These defects provide a mechanism for fluctuation driven non-superconducting CDW/SDW phases and conventional vortices with CDW/SDW order in the core.