Superconductivity Caused by the Pairing of Plutonium 5f Electrons in PuCoGa 5 I. Opahle and P. M. Oppeneer Leibniz-Institute of Solid State and Materials Research, P.O. Box 270016, D-01171 Dresden, Germany (Received 27 September 2002; published 15 April 2003) On the basis of electronic structure calculations we identify the superconductivity in the novel, high- temperature superconductor PuCoGa 5 to be caused by the pairing of Pu 5f electrons. Assuming delocalized Pu 5f states, we compute theoretical crystallographic constants very near to the exper- imental ones, and the calculated specific heat coefficient compares reasonably to the measured coefficient. The theoretical Fermi surface is quasi-two-dimensional and the material appears to be close to a magnetic phase instability. DOI: 10.1103/PhysRevLett.90.157001 PACS numbers: 74.70.–b, 71.28.+d A new group of fascinating heavy-fermion supercon- ductors that crystallize in the HoCoGa 5 structure was discovered a few years ago [1]. Among the superconduc- tors of this group that have drawn wide attention are CeCoIn 5 , CeRhIn 5 , and CeIrIn 5 [1–3]. CeCoIn 5 and CeIrIn 5 are superconductors at ambient pressure [2,3], with T c  2:3 and 0.4 K, respectively, whereas CeRhIn 5 becomes a superconductor (with T c  2:1K) under pres- sure [1]. At ambient pressure CeRhIn 5 orders antiferro- magnetically with an incommensurate spin spiral below the Ne ´el temperature T N  3:9K [4]. The entanglement of heavy-fermion behavior, antiferromagnetism, and superconductivity points towards an unconventional pair- ing mechanism. Experimental evidence for unconven- tional superconductivity in CeRhIn 5 and CeCoIn 5 was recently reported [5–7]. After the initial discovery of these Ce-based super- conductors, investigations of other materials in this com- position were undertaken. Recently, the discovery of superconductivity in PuCoGa 5 at an astonishing T c as high as 18.5 K was reported [8]. A T c of 18.5 K is an extremely high value for an actinide material and an unprecedented value for a Pu-based material. Single crys- tals of PuCoGa 5 have been synthesized which proved this material to crystallize in the HoCoGa 5 structure [8]. Here we report a computational investigation of the crystallographic and electronic structure of PuCoGa 5 . From full-potential, relativistic total-energy calculations we determine the equilibrium theoretical lattice param- eters of PuCoGa 5 in the tetragonal HoCoGa 5 structure (i.e., a, c=a, and the specific Ga z coordinate). For the optimized lattice parameters we investigate in detail the electronic structure of the material. This includes the total energy of the paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM) phases, the energy bands, partial density of states, and Fermi surface. We particularly investigate the character of the bands at the Fermi energy (E F ). In contrast to the Ce-based super- conductors, where the 4f electrons appear to be localized [9], we establish for PuCoGa 5 that the energy bands at E F consist dominantly of delocalized Pu 5f states. This point is of utmost relevance for determining what kind of electrons form the Cooper pairs in the superconducting state, and what the mechanism responsible for the pair formation could be. The implications of the computed electronic structure for the unexpected superconductivity are examined. Methodology.—We performed band-structure calcula- tions using the fully relativistic extension [10] of the full- potential local orbitals minimum-basis band-structure method [11]. In these calculations, the following basis sets were adopted: the 5f;6s6p6d;7s7p states of Pu were treated as valence states, while for Co and Ga we used 3d;4s4p, and 3d;4s4p4d, respectively. The high- lying 6s and 6p semicore states of Pu, which might hybridize with the 6d and 5f valence states, are thus included in the basis. For the site-centered potentials and densities we used expansions in spherical harmonics up to l max  12. The number of k points in the irreducible part of the Brillouin zone was 196, but calculations were made also with 405 and up to 2176 k points to resolve the density of states at E F . The Perdew-Wang [12] para- metrization of the exchange-correlation potential in the local spin-density approximation (LSDA) was used. As mentioned above, one important question concerns the degree of localization of the Pu 5f states. It is well known that in the actinide series around Pu a transition occurs from delocalized 5f states in the lighter actinides to localized 5f’s in the heavier actinides (see, e.g., [13]). It is currently being debated whether the  phase of elemental Pu is to be described with delocalized or lo- calized 5f states [14,15]. In the case of Pu compounds, ligand-hybridization effects may modify the localization behavior of the 5f’s. It has been found, for example, that the Pu 5f’s are rather localized in PuSb [16], whereas for PuSe the 5f’s appear to be relatively delocalized [17]. For PuCoGa 5 we adopt here, as a starting point, the assump- tion of delocalized 5f states, for which the LSDA should be appropriate. The validity of the delocalized LSDA description can be proven only from a comparison of calculated and experimental properties. Such comparison is performed here for those properties available. PHYSICAL REVIEW LETTERS week ending 18 APRIL 2003 VOLUME 90, NUMBER 15 157001-1 0031-9007= 03=90(15)=157001(4)$20.00  2003 The American Physical Society 157001-1