The heavy-fermion compound CeRh2As2 exhibits a complex phase diagram with rather unusual states at low temperatures. A prominent example is multi-phase superconductivity [1] which seems to develop inside a normal state characterized by itinerant multi-polar order. The present talk focusses on the instabilities of the strongly renormalized Fermi liquid state in the heavy-fermion compound CeRh2As2. The central focus is the role played by the non-symmorphic lattice structure and the consequences of the Crystalline Electric Field (CEF) which partially removes the orbital degeneracy of the Ce 4f states. The narrow quasiparticle bands which arise from the Ce-4f degrees of freedom via the Kondo effect are calculated by means of the Renormalized Band (RB) method.  We conjecture that the quasi-quartet CEF ground state in combination with pronounced nesting features of the Fermi surface may give rise to ordered states involving multipolar degrees of freedom [2].

[1] S. Khim et al., Science 373, 1012 (2021).

[2] D. Hafner et al., Phys. RevX 12, 011023 (2022)