First-Principles Study of the Fermi Surface Topology of CeCu$_{2}$Si$_{2}$

TL;DR

The paper tackles the Fermi surface topology of CeCu$_{2}$Si$_{2}$ under strong electronic correlations and crystal-field effects relevant to heavy-fermion superconductivity. It combines density functional theory with the Gutzwiller Wavefunction Approximation (GWA) and spin-orbit coupling to compute renormalized band structures, orbital weights, and Fermi-surface sheets, validated by de Haas–van Alphen simulations. A key finding is that including crystal-field splitting within the GWA yields two Fermi-surface sheets with heavy and light quasiparticle masses $m^* approx 488\,m_{e}$ and $m^* approx 4.35\,m_{e}$ at $U rightarrow 5.1$ eV, consistent with experiment and renormalized-band theory. The results emphasize the essential role of crystal-field effects in concert with correlations for accurately describing heavy-fermion superconductivity, and they establish a computationally efficient framework for complex correlated materials. Future work may extend to temperature dependence and possible electron-phonon contributions to Cooper pairing.

Abstract

Since the discovery of heavy-fermion superconductivity in CeCu$_{2}$Si$_{2}$, the material has attracted great interest particularly with regard to the nature of the superconducting pairing and its mechanism. Consequently, it is essential to better understand the electronic Fermi surface topology and its role in strong antiferromagnetic fluctuations. The standard density functional theory method is insufficient to model the interplay of strong onsite Coulomb repulsion in localized 4{\it f}-electrons and their hybridization with itinerant ligand-orbital electrons. We have performed electronic ground state calculations on CeCu$_{2}$Si$_{2}$ using the Gutzwiller wavefunction approximation. The Gutzwiller approximation captures the quasiparticle band renormalization from the strong onsite Coulomb repulsion. We have performed an analysis of this effect on the electronic structure and the Fermi surface topology by varying the interaction strength and taking into account the crystal-field splitting. Using the de Haas van Alphen effect, the extremal Fermi surface cross-sectional areas were calculated to quantify the effects of quasiparticle mass renormalization on the Fermi surface. Our results confirm two Fermi surface sheets corresponding to the heavy (488m$_{e}$) and light (4.35m$_{e}$) quasiparticles, which is in close agreement with experimental measurements as well as the renormalized band method.

Figures (3)

• Figure 1: Crystal Structure of CeCu$_{2}$Si$_{2}$ where (a) shows the ideal crystal configuration with the yellow atoms representing Ce, the dark blue representing Cu, and the light blue representing Si. The mechanism of the crystal field splitting is shown in (b). Here the red atoms represent Si and the green represent Ce. The diagram shows the compression of the z-axis which results in the body centered tetragonal (BCT) configuration of the Si and Ce atoms centered in the real crystal structure shown in (a). This results in the fine structure splitting depicted in (c) with the energetic separation of $\Gamma_{7}^{(1)}$ and $\Gamma_{7}^{(2)}$.
• Figure 2: The electronic ground state calculations for CeCu$_{2}$Si$_{2}$ calculated using the GWA in the generalized gradient approximation (GGA) with spin orbit coupling. (a) and (d) give the electronic band structure and DOS respectively for the $U=0.0$ case, (b) and (e) show the $U=5.1$ eV calculation with CFS accounted for in the GWA band renormalization, and (c) and (f) show the results for $U=6.0$ eV with CFS. The black lines in the band structures show the eigenenergy bands, and red lines indicate the f-electron contribution. Similarly, in the DOS, the black line is the total DOS and the red line is the projected f-electron DOS. The high symmetry path through the BZ is shown in FIG.S2 of the Supplementary MaterialsSupMat.
• Figure 3: The Fermi surface topology for CeCu$_{2}$Si$_{2}$ calculated using the GWA both without (a) and with (b) CFS. The Fermi sheets are are shown by descending band number and energy. Each sheet is doubly degenerate. Calculation for $U=0.0$, $U=5.1$ eV, and $U=6.0$ eV are shown. The complete results for $U=0$ though 6 eV are discussed in the Supplementary MaterialsSupMat.