Abstract
We discuss a few possibilities of high- T c superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of x 2 − y 2 symmetry doped by holes. Next, several routes towards involving both e g orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO 2 monolayer on Bi2212 superconductors, Sr 2 CuO 4 − δ , Ba 2 CuO 4 − δ , while (ii) others as nickelate heterostructures or Eu 2 − x Sr x NiO 4 , could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of t 2 g symmetry contribute in Sr 2 RuO 4 . Finally, electrons with both t 2 g and e g orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.
Highlights
Towards Superconductivity with Orbital Degrees of FreedomSignificance of the discovery of high-Tc superconductivity by Bednorz and Muller [1] for recent progress in the quantum many-body theory cannot be overestimated—it triggered a huge amount of innovative research on quantum materials and unconventional superconductors, both in the experiment and in the theory
Some are related to cuprates, as the astonishing complexity of the phase diagram and the physical origin of the temperature T∗ observed well above Tc itself [2,3,4,5,6]; others are more general and include questions about the origin of pairing [7,8,9,10,11], optimal conditions for the onset of the SC state [12,13,14,15], variation under pressure [16], and the actual orbital symmetry at the Fermi surface [17]
Typically in cuprates degeneracy is quite lifted and relevance of Jahn-Teller effect is controversial. It is under discussion whether the effective model for cuprates has nondegenerate orbitals and may be represented by extended Hubbard model with on-site Coulomb and further neighbor hopping [21]. It is derived for the case of large splitting of eg orbitals, while orbital degrees of freedom might play an important role in the SC instability and the multiorbital Hubbard model is a standard model for all high-Tc superconductors in general, where the dome of Tc occurs by driving the chemical potential in the proximity of a Lifshitz transition [22]
Summary
Significance of the discovery of high-Tc superconductivity by Bednorz and Muller [1] for recent progress in the quantum many-body theory cannot be overestimated—it triggered a huge amount of innovative research on quantum materials and unconventional superconductors, both in the experiment and in the theory. Certainly an interesting question is whether allowing for the presence of holes in both eg orbitals would not lead to enhanced SC instabilities This idea has its roots in the Jahn-Teller physics in cuprates [25,26], as well as in the observation that the propagation of a hole in a Mott (or charge-transfer) insulator is much richer when both eg orbitals can participate [27]. We emphasize that two-dimensional (2D) systems are special, and possible SC instability was predicted for a layered geometry of NiO2 planes in LaNiO3/LaMO3 superlattices [36] We follow this idea and discuss briefly remarkable similarity between overdoped cuprates and nickelates in Sections 3.1 and 3.2. Superconductivity occurs in metallic systems with t2g degrees of freedom, i.e., in planar ruthenate Sr2RuO4 (Section 3.3) and in Fe-based superconductors (Section 3.4) In the latter systems orbital fluctuations are expected to contribute [8,37].
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