Local Nodal Cooper Pairs in Multiorbital Systems

Abstract

We show the occurrence of a new class of superconductivity in multiorbital systems, focusing on nonKramers f 2 states. The Cooper pairs in this class of superconductivity are mainly local pairs with the same symmetry as the local f 2 ground states. When the local ground state is an anisotropic representation, the superconducting gap has nodes on the Fermi surface. This nodal superconductivity is mediated by the strong on-site interorbital attractions arising from the negative-U physics, generalized in multiorbital systems. We show that this is realized in a simple two-orbital model with antiferro Hund's coupling and enhanced inter-orbital interactions derived via a systematic local down folding. Finally, we briefly discuss superconductivity in Pr-1-2-20 compounds, UBe13, and PrOs4Sb12, in view of the present mechanism.Unconventional superconductivity (SC) shows various interesting phenomena and has attracted great attention in the field of condensed matter physics. The existence of nodes in their superconducting gap functions is required for these phenomena to occur in unconventional superconductors, such as cuprates, 1) ruthenates, 2) iron-based pnictides, 3) and heavy-fermion superconductors. 4) Apart from cuprates and some others, the gap functions in many unconventional superconductors are not fully understood and continue to be under debate, despite the intensive experimental and theoretical studies conducted on them since their discovery. Thus, explaining their mechanism is a challenging problem in condensed matter theory.A promising mechanism for unconventional SC in single band (orbital) systems, fluctuation-mediated SC, has been established by the 80th, 5) and is analogous to the theory of 3 He superfluids. 6) In particular, intersite fluctuations in the presence of strong local repulsions, such as ferro-or antiferro-magnetic fluctuations, lead to nodal SC. Many unconventional superconductors have been observed in close vicinity to ordered phases.In recent years, much attention has been paid to multiorbital superconductors, such as iron-based pnictides. 3) Some heavy-fermion superconductors have attracted renewed interest, since for example, the discovery of fullgap behavior in the low-temperature specific heat of CeCu 2 Si 2 . 7) Thus, it is important to clarify the impact of the orbital degrees of freedom on SC. Recently, to clarify the multiorbital character of such SC, we classified multipole SC 8) and discussed that nodal SC can occur through the formation of local Cooper pairs in multiorbital systems. The pairs are local but have orbital degrees of freedom, which form the nodal gap structure.In this letter, we show that such nodal and local SC can emerge in multiorbital systems and that it is related to two-electron ground state configurations, when the electron filling is nealy two per site. We start first by demonstrating that low-energy effective interactions in such * E-mail: hattori@tmu.ac.jp multiorbital models with the spin-orbit interaction (SOI) are completely different from the conventio...

Classification of atomic-scale multipoles under crystallographic point groups and application to linear response tensors

“…For example, the magneto-electric effects in Cr 2 O 3 [83][84][85] and Co 4 Nb 2 O 9 [86][87][88][89][90] are understood by the M quadrupole, magneto-current effect in metallic UNi 4 B by the MT dipole [91][92][93] , valley splitting in the electronic band structure by the MT octupole 94 , nonreciprocal magnon excitations in BiTeBr 95 and α-Cu 2 V 2 O 7 [96][97][98][99][100] by the E and MT dipoles, orbital Edelstein effect in Te by the ET monopole and quadrupole 101,102 , and large anomalous Hall effect, Nernst effect, and Kerr rotation in Mn 3 Sn by the M octupole 38,[103][104][105][106] . Moreover, unconventional superconductivities are also discussed in the language of multipoles [107][108][109][110] .…”

Microscopic Theory of Γ3 Quadrupole Ordering in Pr Compounds on the Basis of a j–j Coupling Scheme

“…To calculate the multipole susceptibility, in this paper, we resort to the RPA on the basis of the perturbation expansion in terms of the Coulomb interactions. In the RPA, the susceptibility is expressed in a compact matrix form as 28)…”

“…When we consider the local f -electron states on the basis of the j-j coupling scheme, 24) we notice that the Γ 3 ground states are mainly composed of two singlets among Γ 7 and Γ 8 electrons. [25][26][27][28][29][30] Note that the double degeneracy originates from the orbital degrees of freedom in Γ 8 electrons. This is consistent with the fact that Γ 3 is included in the direct products of Γ 7 and Γ 8 .…”

Anisotropic Superconductivity Emerging from the Orbital Degrees of Freedom in a Γ3 Non-Kramers Doublet System

“…In two-orbital models, there is an interesting possibility to realize anisotropic superconductivity originating from the orbital anisotropy. 25,26) For example, we obtained d-wave spintriplet superconductivity in a model for e g orbitals on a square lattice. 25) However, it was shown that a two-orbital model is inadequate for describing the multipole degrees of freedom in the Γ 3 CEF state.…”

“…Notably, this superconducting phase extends far from the SDW phase and does not require particular fluctuations. Even in an unrealistic two-orbital model for the Γ 3 CEF state, E g superconductivity was obtained, 26) indicating that E g superconductivity is relatively stable in Γ 3 systems.…”