Probing band structures and Fermi surfaces of CeCoSi by ARPES

Strongly correlated electron systems exhibit various physical properties closely related to charge, spin, and orbital degrees of freedom; in $f$-electron systems, multipoles, which are combinations of spin and orbital degrees of freedom, play a major role. The centrosymmetric CeCoSi, which belongs to the non-symmorphic space group (P4/nmm), has attracted much attention from the viewpoint of the odd-parity multipoles below the phase transition temperature $T_0$. Recently, a Ce $4f$-driven antiferroquadrupolar order below $T_0$ was proposed by a detailed study using single crystal samples, followed by a complete phase diagram and further clarification of the finite $T_0$ ~12 K even at ambient pressure [1,2]. Subsequently, $^{59}$Co NMR revealed anomalies suggestive of quadrupolar order [3], and odd-parity multipole order was theoretically proposed [4]. However, a fundamental question has remained unsolved as to why the localized Ce $4f$ state is so sensitive to external pressure and why the $T_0$ increases substantially. We used angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation to address such issues including the microscopic origin of the phase transition and its pressure effect in CeCoSi. The out-of-plane momentum resolved measurements revealed the coexistence of two- (2D) and three-dimensional (3D) Fermi surfaces (FSs). The observed FSs and band dispersions of CeCoSi resemble those of LaCoSi and are reproduced by first-principles calculations of LaCoSi. Comparing the observed and calculated FSs, it is found that the Co $3d_{x^2-y^2}$ orbital component contributes significantly to the 2D FS and the 3D FS is mainly driven by $3d_{z^2}$ and $3d_{yz/zx}$ orbitals. Ce $3d-4f$ resonant photoemission spectroscopy and high-resolution ARPES measurements show that the Ce $4f$ states do not cross the Fermi level ($E_{\rm F}$) but is located at 10 meV below $E_{\rm F}$. This proximity of the Ce $4f$ states to the $E_{\rm F}$ may explain the puzzle described above. Our findings pave the way to understanding the electrical properties and multipole order of CeCoSi.