Revealing the Heavy Quasiparticles in the Heavy-Fermion Superconductor ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$

The superconducting order parameter of the first heavy-fermion superconductor ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$ is currently under debate. A key ingredient to understand its superconductivity and physical properties is the quasiparticle dispersion and Fermi surface, which remains elusive experimentally. Here, we present measurements from angle-resolved photoemission spectroscopy. Our results emphasize the key role played by the Ce $4f$ electrons for the low-temperature Fermi surface, highlighting a band-dependent conduction-$f$ electron hybridization. In particular, we find a very heavy quasi-two-dimensional electron band near the bulk $X$ point and moderately heavy three-dimensional hole pockets near the $Z$ point. Comparison with theoretical calculations reveals the strong local correlation in this compound, calling for further theoretical studies. Our results provide the electronic basis to understand the heavy-fermion behavior and superconductivity; implications for the enigmatic superconductivity of this compound are also discussed.

Figure 1

Overview of electronic structure of ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$. (a) Crystal structure. (b) 3D bulk BZ (black) and projected surface BZ (red). (c) 3D view of electronic structure taken with 150 eV photons from second surface BZ. (d) ARPES data taken along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ under some representative photon energies in comparison with results of localized $4f$ calculations. Only calculation results in second BZ are shown for clarity.

Figure 2

Heavy electron band near $\overline{M}$ at 10 K. (a) Band dispersion along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ recorded with 132 eV photons. (b) Spectrum in Fig. 2 divided by RC-FDD near $E_F$. (c) Energy distribution curves (EDCs) of Fig. 2. Extracted peak positions highlighted as black dots, which are fitted by a parabola shown as a white dashed curve in Fig. 2. Band dispersions from (d) $\mathrm{DFT}+U$ (d) and (e) localized $4f$ calculations, for comparison with Fig. 2. Orbital contributions are indicated. (f) Photon-energy dependence of heavy electron band along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$.

Figure 3

(a) Experimental $k_x\text{−}{k}_y$ FS at 10 K, taken with 135 eV photons. Energy integration window of 50 meV are used for better statistics. (b) Calculated two-dimensional (2D) FS contour from $\mathrm{DFT}+U$ for comparison with Fig. 3. In Fig. 3, black lines mark bulk BZ boundaries and band color indicates group velocity $v_F$ at $E_F$ (blue indicates heavy band).

Figure 4

$4f$ contribution to pockets near bulk $Z$ point. (a) FS near $Z$ point (from second surface BZ using 150 eV photons). (b) Calculated 2D FS from $\mathrm{DFT}+U$, in comparison with Fig. 4. Color indicates $v_F$, similar to Fig. 3. ARPES spectra along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$: (c) off-resonant (115 eV) and (d) on-resonant (122 eV); and (e) corresponding EDCs at marked momentum point. (f) Zoomed-in view of quasiparticle dispersion near $E_F$. (g) Simulation of quasiparticle band dispersion using simplified hybridized band approach within PAM for comparison with Fig. 4.