Theoretical Prediction and Spectroscopic Fingerprints of an Orbital Transition in ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$

We show that the heavy-fermion compound ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ undergoes a transition between two regimes dominated by different crystal-field states. At low pressure $P$ and low temperature $T$ the Ce $4f$ electron resides in the atomic crystal-field ground state, while at high $P$ or $T$, the electron occupancy and spectral weight is transferred to an excited crystal-field level that hybridizes more strongly with itinerant states. These findings result from first-principles dynamical-mean-field-theory calculations. We predict experimental signatures of this orbital transition in x-ray spectroscopy. The corresponding fluctuations may be responsible for the second high-pressure superconducting dome observed in this and similar materials.

Figure 1

(a),(b) The ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ crystal structure. The pink (large), white (medium), and yellow (small) spheres are Ce, Cu, and Si sites, respectively. (b) At the central Ce site, wave functions of the two CF levels are shown [$|0⟩$ in (a) and $|2⟩$ in (b)]. (c) Imaginary part of the DMFT hybridization functions $\mathrm{\Delta }$ of states $|0⟩$ (red solid line) and $|2⟩$ (blue dashed line) on the real energy axis at $P=0\mathrm{GPa}$.

Figure 2

Occupancies $n_0$ (red circles) and $n_2$ (blue squares) of the CF states $|0⟩$ and $|2⟩$, as a function of pressure and temperature. The large, medium, and small symbols denote the occupancies at 58, 14, and 7 K, respectively. The curves are linear interpolations between the corresponding points. Inset: the ($T$, $P$) map of the $n_0/n_2$ ratio. The dots indicate the values of $T$ and $P$ for which the $\mathrm{LDA}+\mathrm{DMFT}$ calculations were performed. The dashed line is the $n_0=n_2$ boundary between the two regions, see text.

Figure 3

(a),(b) The $\mathrm{LDA}+\mathrm{DMFT}$ partial densities of states of $|0⟩$, $|1⟩$, and $|2⟩$ states in the vicinity of the Fermi level at $P=0$ (a) and 4 GPa (b) at $T=7\mathrm{K}$. The orbital character of the main Kondo peak changes as $P$ increases. (c),(d) The corresponding Fermi surfaces (FS) at the same temperature. One may notice that the large colored in green (or light gray) FS sheet present at zero pressure disappears at 4 GPa. (e) The mass enhancements $m_{\text{GS}}^{*}$, $m_0$, and $m_2$ for the most-occupied, $|0⟩$, and $|2⟩$ states, respectively, as well as the average one $m_{\text{av}}^{*}$ as a function of $P$ at $T=7\mathrm{K}$.

Figure 4

Simulation of NIXS cross sections. In the top panel we show the spectral functions of the momentum-transfer-dependent spectra (solid and dashed thin black line) and the difference sprectrum (thick red line). In the middle and bottom panels we display the NIXS difference spectrum upon increasing pressure at constant $T=7\mathrm{K}$ and increasing temperature at ambient pressure, respectively. One may notice that the NIXS difference sprectrum undergoes structural changes due to the predicted orbital transition.