  CeRh2As2 has recently been reported to be a rare case of multi-phase
unconventional superconductor [S. Khim et al., arXiv:2101.09522] close to a
quantum critical point (QCP). Here, we present a comprehensive study of its
normal state properties and of the phase (I) below To ~ 0.4 K which preempts
superconductivity at Tc = 0.26 K. The 2nd-order phase transition at To presents
signatures in specific heat and thermal expansion, but none in magnetization
and ac-susceptibility, indicating a non-magnetic origin of phase I. In
addition, an upturn of the in-plane resistivity at To points to a gap opening
at the Fermi level in the basal plane. Thermal expansion indicates a strong
positive pressure dependence of To , dTo/dp = 1.5 K/GPa, in contrast to the
strong negative pressure coefficient observed for magnetic order in Ce-based
Kondo lattices close to a QCP. Similarly, an in-plane magnetic field shifts To
to higher temperatures and transforms phase I into another non-magnetic phase
(II) through a 1st-order phase transition at about 9 T. Using renormalized band
structure calculations, we found that the Kondo effect (TK ~ 30 K) leads to
substantial mixing of the excited crystalline-electric-field (CEF) states into
the ground state. This allows quadrupolar degrees of freedom in the resulting
heavy bands at the Fermi level which are prone to nesting. The huge sensitivity
of the quadrupole moment on hybridization together with nesting would cause an
unprecedented case of phase transition into a quadrupole-density-wave (QDW)
state at a temperature To << TK , which would explain the nature of phase I and
II.
