Quantum criticality at the end of a pseudogap phase in superconducting infinite-layer nickelates

In many unconventional superconductors, the strange-metal regime is thought to emerge from quantum criticality, yet in cuprates this link is obscured by the enigmatic pseudogap. Superconducting infinite-layer nickelates provide a new arena to test this paradigm but are constrained to thin films, precluding calorimetry. We use the Seebeck coefficient as a low-temperature proxy for entropy per carrier and uncover a clear quantum-critical thermodynamic signature: in La$_{1-x}$Sr$_x$NiO$_2$ at the onset of $T$-linear resistivity ($x=0.20$), $S/T$ diverges logarithmically upon cooling, $S/T \propto \log T$. Boltzmann transport based on ARPES-derived band structure reproduces the high-temperature magnitude and sign of $S/T$ and reveals a threefold mass renormalization at the Fermi level. To identify the terminating phase, we analyze Hall data across Nd$_{1-x}$Sr$_x$NiO$_2$ and show that its temperature evolution is quantitatively captured by a minimal two-band model in which a strongly correlated Ni-$d_{x^2-y^2}$ Fermi surface exhibits Planckian $T$-linear scattering while the rare-earth Nd-$s$ pocket remains Fermi-liquid-like. Inverting the zero-temperature Hall response reveals a collapse of the Ni-$d_{x^2-y^2}$ band carrier density from $1+p$ to $p$ holes across the critical doping, without long-range magnetic order -- mirroring the cuprate pseudogap transition in cuprates. These results establish a quantum critical point at the end of a pseudogap-like phase in infinite-layer nickelates and unify the broader paradigm among correlated superconductors that strange metal behaviour is intimately linked to quantum criticality.