† Corresponding author. E-mail:
In this work we have used density-functional theory methods such as full-potential local orbital minimum basis (FPLO) and ELK-flapw to study the electronic structure of newly discovered Laves phase superconductor CaIr2. The calculation of density of states (DOS) indicates that the bands near Fermi level are mostly occupied by the d-electrons of iridium. The simulation of de Haas–van Alphen (dHvA) effect has been performed by using Elk code to check the Fermi surface topology. The results show that there exist four Fermi surfaces in CaIr
For the past few years, it has been reported that spin–orbit interaction plays an important role in determining the electronic properties of metallic compounds, especially those that contain f-electrons, which sometimes causes the time-reversal-invariant topological insulators or superconductors.[1–9] Iridium oxides with the pyrochlore lattice have been predicted to have extraordinary electronic properties and behaviors like metal-insulator transition.[10,11] In addition to this work, Neel Haldolaarachchige et al.[12] found that the Laves phase[12–14] compound CaIr2 is a superconductor of
Frankly the band-structure calculation in Ref. [12] could not be viewed as a complete one. We have evaluated the electronic structure by different codes and found that the topology of Fermi surfaces in Ref. [12] is actually problematic. In order to get more detailed insights for this material, we present our first-principle calculation on CaIr2 by density-functional based on FPLO code[22] and Elk code.[23] As for the topology of Fermi surfaces, this study really yields somewhat different pictures. Furthermore we perform an optical calculation based on the density-functional theory which might provide theoretical reflection spectrum and optical conductivity spectrum. The authors believe that these data may be used as references for experiments.
This paper is organized as follows: In Section
The space group of Laves phase CaIr2 is Fd-3m (No. 227) and the corresponding experimental lattice parameters, i.e., a = 7.545 Å have been reported in an earlier paper.[24] This lattice parameter will be used throughout this work. The Ca atoms are located at 8b (3/8, 3/8, 3/8) site and Ir are located at 16c (0, 0, 0). Each face of the cubic cell contains 5 Ir atoms along the diagonal and the remaining six ones form a hexagon inside the body. They make a centrosymmetric structure with respect to Ca in the unit cell. The calculations of electronic structures are performed by using Perdew–Zunger LSDA exchange[25] and the correlation potential implemented in Elk-flapw and FPLO codes. We also calculated de Haas-van Alphen frequencies.[26] It has been used to detect the Fermi surfaces on experimental work since it appeared.[27–32] However, it can also be considered as an effective simulation method on checking Fermi surface geometry depending on the results of band energiesby using the Supercell k-space Extremal Area Finder (SKEAF) code which can be downloaded from Ref. [23], also belonging to Elk code. The optics properties are studied and tested by Wien2k and FPLO, based on Kramer–Kronig relation as many other simulation works did.[33–36]
Figure
![]() | Fig. 2. (color online) The DOS of CaIr2 and a comparison of d electron states without SOI. The compositions of states near the Fermi level are pointed out. |
Figure
![]() | Fig. 4. (color online) The four Fermi surfaces calculated by Elk and drawn by XCrySDen.[16] Panels (a)–(d) correspond to the bands which are ordered from the highest energy to the lowest energy. |
It is clear in Fig.
Figure
The electron energy loss spectra (EELS) in Fig.
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![](cpb_26_4_047401/cpb_26_4_047401_eqn024.gif)
![](cpb_26_4_047401/cpb_26_4_047401_eqn025.gif)
The energy loss spectrum physically shows how the energy is absorbed when electron moves across the solid, so the expression of EELS can fit the reflection spectrum well on each peak and valley.[42,43] That is why we did not display the reflection spectrum. The flat part from 10 eV to 20 eV which seems to contain lots of peaks can be viewed as the combination of excitation loss peaks of valence electrons and plasma elementary loss peaks. The peaks at 25.5 eV and 29.3 eV and the valleys between them correspond to the opposite shapes in conductivity spectrum at the same energy. They shows the plasma oscillation near the plasma edge.[36] Since the SOC affected the electric structures, the optical properties should also be recalculated. However, the psudopotential under the circumstance of SOC has not been worked out yet, which might give an inaccuracy result of optical properties. That is why we did not perform the results under SOC.
All the results carried out by Wien2k are same as those carried out by FPLO.
In summary we have demonstrated the electronic structure and related optical properties of CaIr2 in this work. Specifically the Fermi surfaces and dHvA data have been drawn by using ELK-flapw code in this work firstly. The states near the Fermi surface are mostly 5d-electrons of Ir. Furthermore the σ (ω) and EELS indicates that the main absorption is intra-band type before 0.8 eV and turns to be inter-band type near 1.45 eV. The results calculated by using different methods (FPLO & Wien2k) are the same. A further study on its electron–phonon interaction may reveal more properties and provides insight regarding the origins of superconductivity of this compound. Since now there are few experimental results on CaIr2, we hope that this simulation work can push on some extra-works on it, especially electronic structure scanning and optical properties exploring.
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