Non-centrosymmetric superconductors

external pageOrbitally limited pair-​density-wave phase of multilayer superconductorscall_made

David Möckli, Youichi Yanase and Manfred Sigrist

We investigate the magnetic field dependence of an ideal superconducting vortex lattice in the parity-mixed pair-density-wave phase of multilayer superconductors within a circular cell Ginzburg-Landau approach. In multilayer systems, due to local inversion symmetry breaking, a Rashba spin-orbit coupling is induced at the outer layers. This combined with a perpendicular paramagnetic (Pauli) limiting magnetic field stabilizes a staggered layer dependent pair-density-wave phase in the superconducting singlet channel. The high-field pair-density-wave phase is separated from the low-field BCS phase by a first-order phase transition. The motivating guiding question in this paper is: What is the minimal necessary Maki parameter α_M for the appearance of the pair-density-wave phase of a superconducting trilayer system? To address this problem we generalize the circular cell method for the regular flux-line lattice of a type-II superconductor to include paramagnetic depairing effects. Then, we apply the model to the trilayer system, where each of the layers are characterized by Ginzburg-Landau parameter κ₀ and a Maki parameter α_M. We find that when the spin-orbit Rashba interaction compares to the superconducting condensation energy, the orbitally limited pair-density-wave phase stabilizes for Maki parameters α_M>10.

external pageSuperconductors with Staggered Non-​centrosymmetricitycall_made

Manfred Sigrist, Daniel F. Agterberg, Mark H. Fischer, Jun Goryo, Florian Loder, Sung-​Hyon Rhim, Daisuke Maruyama, Youichi Yanase, Tomohiro Yoshida and Suk-​Joo Youn

Non-centrosymmetric superconductors have attracted much interest in the context of heavy Fermion and interface superconductivity. Here we show that a sublattice structure of staggered subunits without inversion center can have important implications for superconductivity even in a globally centrosymmetric system. After discussing general aspects of systems with alternating non-centrosymmetric layers, two concrete examples are studied: (1) the artificially grown superlattices of CeCoIn₅/YbCoIn₅ and (2) the pnictide superconductor SrPtAs. For example (1) implications on the upper critical field are analysed and novel phases in a magnetic field are explored. Example (2) realizes likely a chiral d-wave phase for which a few implications of staggered non-centrosymmetricity are discussed.

external pageSignatures of the helical phase in the critical fields at twin boundaries of noncentrosymmetric superconductorscall_made

Kazushi Aoyama, Lucile Savary and Manfred Sigrist

Domains in noncentrosymmetric materials represent regions of different crystal structure and spin-orbit coupling. Twin boundaries separating such domains display unusual properties in noncentrosymmetric superconductors (NCSs), where magnetoelectric effects influence the local lower and upper critical magnetic fields. As a model system, we investigate NCSs with tetragonal crystal structure and Rashba spin-orbit coupling (RSOC), and with twin boundaries parallel to their basal planes. There, we report that there are two types of such twin boundaries which separate domains of opposite RSOC. In a magnetic field parallel to the basal plane, magnetoelectric coupling between the spin polarization and supercurrents induces an effective magnetic field at these twin boundaries. We show that this leads to unusual effects in such superconductors, and in particular to the modification of the upper and lower critical fields, in ways that depend on the type of twin boundary, as analyzed in detail, both analytically and numerically. Experimental implications of these effects are discussed.

external pageJosephson effect and triplet-​singlet ratio of noncentrosymmetric superconductorscall_made

Ludwig Klam, Anthony Epp, Wei Chen, Manfred Sigrist and Dirk Manske

State and measurement tomography make assumptions about the experimental states or measurements. These assumptions are often not justified because state preparation and measurement errors are unavoidable in practice. Here we describe how the Gram matrix associated with the states and measurement operators can be estimated via semidefinite programming if the states and the measurements are so-called globally completable. This is, for instance, the case if the unknown measurements are known to be projective and nondegenerate. The computed Gram matrix determines the states, and the measurement operators uniquely up to simultaneous rotations in the space of Hermitian matrices. We prove the reliability of the proposed method in the limit of a large number of independent measurement repetitions.

external pageGinzburg–Landau Description of Twin Boundaries in Noncentrosymmetric Superconductorscall_made

Michael Achermann, Titus Neupert, Emiko Arahata and Manfred Sigrist

We study theoretically a model for twin boundaries in superconductors with Rashba spin–orbit coupling, which can be relevant to both three-dimensional noncentrosymmetric tetragonal crystals and two-dimensional gated superconductors such as the LaAlO₃/SrTiO₃ interface. In both cases, the broken inversion symmetry allows for a coexistence of singlet and triplet pairing. Within the framework of a Ginzburg–Landau theory, we identify two ℤ₂ symmetries that are broken via two consecutive second order phase transitions as the temperature is lowered. We show that a time-reversal symmetry breaking superconducting state nucleates near the twin boundary if singlet and triplet pairing amplitudes are of comparable magnitude. As a consequence, the tendency towards ferromagnetic order is locally increased along with the emergence of spontaneous supercurrents parallel to the twin boundary. Spin currents, which are present in the form of Andreev bound states, are found enhanced in the time-reversal broken phases.

 

external pageParity-​Mixed Superconductivity in Locally Non-​centrosymmetric Systemcall_made

Tomohiro Yoshida, Manfred Sigrist and Youichi Yanase

We study the parity-mixed superconductivity in locally non-centrosymmetric systems. In multilayer systems an inhomogeneous Rashba spin–orbit coupling is induced by the local violation of inversion symmetry. Our previous study revealed that a pair-density wave (PDW) phase, with a sign-modulated order parameter, is stabilized in the spin-singlet multilayer superconductors owing to the spin–orbit coupling. In this letter, we show that the uniform spin-triplet superconductivity emerges through parity mixing in the PDW phase, taking into account a weak interaction in the spin-triplet channel, which was neglected in our previous study. The spin-triplet superconducting phase is nonunitary owing to field-induced parity mixing. The critical magnetic field is markedly increased by the emergence of spin-triplet superconductivity. We calculate the density of states and analyze the signature specific to this phase.

external pageComplex-​Stripe Phases Induced by Staggered Rashba Spin-​Orbit Couplingcall_made

Tomohiro Yoshida, Manfred Sigrist and Youichi Yanase

We study superconducting phases in a quasi-two-dimensional multilayer system without local inversion symmetry. Broken local inversion symmetry induces layer-dependent Rashba-type spin–orbit couplings. We find that a complex-stripe phase, which is the intermediate phase between the Fulde–Ferrell (FF) phase and Larkin–Ovchinnikov (LO) phase, is realized in the magnetic field applied parallel to the layers. A crossover from the FF phase to the LO phase appears by tuning temperature and magnetic field. We show the local density of states that characterizes the complex-stripe phase. As a possible realization of the complex-stripe phase, we discuss the artificial superlattices of CeCoIn₅.

external pageSpin currents and spontaneous magnetization at twin boundaries of noncentrosymmetric superconductorscall_made

Emiko Arahata, Titus Neupert and Manfred Sigrist

Twin boundaries are generic crystalline defects in noncentrosymmetric crystal structures. We study theoretically twin boundaries in time-reversal-symmetric noncentrosymmetric superconductors that admit parity-mixed Cooper pairing. Twin boundaries support spin currents as a consequence of this parity mixing. If the singlet and triplet components of the superconducting order parameter are of comparable magnitude, the superconducting state breaks spontaneously the bulk time-reversal symmetry locally near the twin boundary. By self-consistently evaluating the Bogoliubov-de Gennes equations and the gap functions, we find two distinct phases: First, time-reversal-symmetry breaking enhances the spin currents but does not lead to charge current. A secondary phase transition then triggers a spin magnetization and a finite charge current near the twin boundary.

external pageSpin-​Orbit Coupling in Multilayer Superconductors with Charge Imbalancecall_made

Daisuke Maruyama, Manfred Sigrist and Youichi Yanase

In this study, we investigate the spin susceptibility in the superconducting state of a multilayer system with a layer-dependent Rashba spin–orbit coupling, representing a locally non-centrosymmetric superconductor. We show that the charge imbalance between different layers yields a strong layer dependence on the susceptibility, most significantly for a weak spin–orbit coupling, which is in contrast to a situation with an equally distributed charge. These results can be relevant for experimental test in multilayer high-𝑇_c
cuprates as well as in superconducting CeCoIn₅/YbCoIn₅ superlattices with more than two layers.