Spin-orbit coupling has proven indispensable in realizing topological materials and more recently Ising pairing in two-dimensional superconductors. This pairing mechanism relies on inversion symmetry breaking and sustains anomalously large in-plane polarizing magnetic fields whose upper limit is expected to diverge at low temperatures, although experimental demonstration of this has remained elusive due to the required fields. In this work, the recently discovered superconductor few-layer stanene, i.e. epitaxially strained -Sn, is shown to exhibit a new type of Ising pairing between carriers residing in bands with different orbital indices near the Γ-point. The bands are split as a result of spin-orbit locking without the participation of inversion symmetry breaking. The in-plane upper critical field is strongly enhanced at ultra-low temperature and reveals the sought for upturn.

No abstract

Although multilayer systems possess global inversion symmetry, some of the layers lack local inversion symmetry because no global inversion centers are present on such layers. Such locally non-centrosymmetric systems exhibit spatially modulated Rashba spin-orbit coupling. In this study, the superconductivity in multilayer models exhibiting inhomogeneous Rashba spin-orbit coupling is investigated. We study the electronic structure, superconducting gap, and spin susceptibility in the superconducting state with mixed parity order parameters. We show the enhancement of the spin susceptibility by Rashba spin-orbit coupling and interpret it on the basis of the crossover from a centrosymmetric superconductor to a non-centrosymmetric superconductor. It is also shown that the spin susceptibility is determined by the phase difference of the order parameter between layers and is nearly independent of the parity mixing of order parameters. An intuitive understanding is given on the basis of the analytic expression of superconducting order parameters in the band basis. The results indicate that not only a broken global inversion symmetry but also a broken local inversion symmetry leads to unique properties of superconductivity. We discuss the superconductivity in artificial superlattices involving CeCoIn5 and multilayer high-Tc cuprates.

Stimulated by recent studies of quantum phases with broken local inversion symmetry, we study the magnetoelectric effect in locally noncentrosymmetric metals. We consider threedimensional (3D) coupled zigzag chains and demonstrate that the antiferromagnetic moment is induced by the electric current through a staggered antisymmetric spin-orbit coupling. This current-induced magnetism is much larger than that in globally noncentrosymmetric metals. We provide an intuitive understanding of the current-induced antiferromagnetic moment by showing the inverse magnetoelectric effect, that is, the ferroic p-wave charge nematic order accompanied by the asymmetric band structure in the antiferromagnetic state. We also examine conduction electrons coupled to localized spins via Kondo exchange coupling and demonstrate a significant enhancement of the magnetoelectric effect. A possible experimental observation of the magnetoelectric effect in metals is discussed, with focus on LnM2Al10 compounds, such as NdRu2Al10 and TbRu2Al10.

Spin singlet superconductors with quasi-two dimensional multilayer structure are studied in high magnetic fields. Specifically we concentrate on bi-and tri-layer systems whose layers by symmetry are subject Rashba-type spin-orbit coupling. The combination of magnetic field and spin-orbit coupling leads to a first order phase transition between different states of layer-dependent superconducting order parameters upon rising the magnetic field. In this context we distinguish the low-field Bardeen-Cooper-Schrieffer state where all layers have order parameters of the same sign and the high-field pair-density wave state where the layer-dependent order parameters change the sign at the center layer. We also show that progressive paramagnetic limiting effects yield additional features in the H-T phase diagram. As possible realizations of such unusual superconducting phases we consider artificial superlattices of CeCoIn5, as well as some multilayer high-Tc cuprates.

We report a highly unusual angular variation of the upper critical field (Hc2) in epitaxial superlattices CeCoIn5(n)/YbCoIn5(5), formed by alternating layers of n and a 5 unit-cell thick heavy-fermion superconductor CeCoIn5 with a strong Pauli effect and normal metal YbCoIn5, respectively. For the n = 3 superlattice, Hc2(θ) changes smoothly as a function of the field angle θ. However, close to the superconducting transition temperature, Hc2(θ) exhibits a cusp near the parallel field (θ = 0 • ). This cusp behavior disappears for n = 4 and 5 superlattices. This sudden disappearance suggests the relative dominance of the orbital depairing effect in the n = 3 superlattice, which may be due to the suppression of the Pauli effect in a system with local inversion symmetry breaking. Taking into account the temperature dependence of Hc2(θ) as well, our results suggest that some exotic superconducting states, including a helical superconducting state, might be realized at high magnetic fields.PACS numbers: 74.25. Op, 81.15.Hi In the absence of time reversal symmetry or space inversion symmetry, the Fermi surface (FS) can often be split into portions with different spin structures. To stabilize superconductivity under such conditions where spin degeneracy is lifted, unconventional pairing of quasiparticles is needed, leading to exotic superconducting states very different from the conventional BCS pairing state of (k ↑, -k ↓). Considering the situation of the broken time reversal symmetry alone, Fulde and Ferrell [1], and Larkin and Ovchinnikov [2] proposed the pairing state of (k ↑, -k+q ↓) on a Zeeman-split FS. This so-called FFLO pairing state leads to the modulation of the superconducting order parameter in real space with the modulation wavelength of the order of 1/|q|. On the other hand, in the lack of space inversion symmetry, a Rashba-type spin-orbit coupling splits the FS into branches with spins of opposite rotation sense [3]. When the magnetic field is applied to such a system, a pairing state with a finite center-of-mass momentum can also be realized, resulting in a helical superconducting state analogous to the FFLO phase.However, such exotic superconducting states have been poorly explored because of the lack of suitable materials. Recent advancement in heavy fermion thin film fabrication technology [4,5] has enabled the preparation of superlattices formed by alternate stacking of c-axis oriented CeCoIn 5 and YbCoIn 5 with atomic layer thicknesses. The large Fermi velocity mismatch across the interface between CeCoIn 5 and YbCoIn 5 significantly reduces the transmission probability of quasiparticles, thereby ensuring quasi-two-dimensional superconductivity confined within CeCoIn 5 layers [6,7]. This provides a unique opportunity to explore the physics discussed above. This is because bulk CeCoIn 5 with strong Pauli effect has been reported to host the FFLO phase at low temperatures and high magnetic field [8][9][10][11]. In the superlattice, the electronic structure becomes two-dimensional, which is expec...

Triplet superconductivity in Sr 2 RuO 4 is investigated with main interest on its internal degree of freedom. We perform a microscopic calculation to investigate how the chiral stated dðkÞ ¼ ðk x AE ik y Þẑ z is realized among the underlying six degenerate states. Starting from the three band Hubbard model with spin-orbit interaction, we use a perturbation theory in order to calculate the pairing interaction. The pwave superconductivity with T c $ 1:5 K is obtained in the moderately weak coupling region. It is shown that the orbital dependent superconductivity (ODS) robustly appears in Sr 2 RuO 4 . We determine the stabilized state by solving the Eliashberg equations. We find that the Hund coupling term as well as the spin-orbit interaction is necessary for the ''symmetry breaking interaction''. The main result is that the chiral state is stabilized in case of the p-wave symmetry with the main -band, which is obtained in the perturbation theory. When we assume the other pairing symmetry including the f -wave state, the symmetry breaking interaction gives the other d-vector. The electronic structure constructed from the t 2g -orbitals is essential for this result.

We study an odd-parity magnetic multipole order in Ba1−xKxMn2As2 and related materials. Although BaMn2As2 is a seemingly conventional Mott insulator with G-type antiferromagnetic order, we identify the ground state as a magnetic hexadecapole ordered state accompanied by simultaneous time-reversal and space-inversion symmetry breaking. A symmetry argument and microscopic calculations reveal the ferroic ordering of leading magnetic hexadecapole moment and admixed magnetic quadrupole moment. Furthermore, we clarify electromagnetic responses characterizing the magnetic hexadecapole state of semiconducting BaMn2As2 and doped metallic systems. A magnetoelectric effect and antiferromagnetic Edelstein effect are shown. Interestingly, a counter-intuitive currentinduced nematic order occurs in the metallic state. The electric current along the z -axis induces the xy-plane nematicity in sharp contrast to the spontaneous nematic order in superconducting Fe-based 122-compounds. Thus, the magnetic hexadecapole state of doped BaMn2As2 is regarded as a magnetopiezoelectric metal. Other candidate materials for magnetic hexadecapole order are proposed.