Quantum critical origin of strange-metals at the end of a pseudogap phase in infinite-layer nickelates

The quantum-critical origin of strange metals remains debated, particularly in cuprates where $T$-linear resistivity emerges at the end of the pseudogap phase, a regime without long-range order whose nature remains one of the largest mysteries of quantum materials~\cite{Michon2019Thermodynamic, zhong_2022}. Superconducting infinite-layer nickelates provide a new platform to revisit this issue, given their close similarities to cuprates. Here too, $T$-linear resistivity onsets at a critical doping $x^\star$ near the middle of the superconducting dome. Establishing whether $x^\star$ is a quantum critical point (QCP) -- a zero-temperature phase transition -- typically relies on the electronic specific heat $C_{\rm el}$, which follows $C_{\rm el}/T \propto \log(T)$ at a QCP, rather than the constant behaviour of a conventional metal. However, the thin-film form of infinite-layer nickelates precludes calorimetry. We therefore use the Seebeck coefficient as a low-temperature proxy for specific heat per carrier. In La$_{\rm 1-x}$Sr$_{\rm x}$NiO$_2$ at $x^\star$, the high-temperature Seebeck response is quantitatively captured by the ARPES-measured band structure, indicating well-defined quasiparticles. Below 60 kelvin, however, $S/T$ develops a logarithmic divergence, $S/T \propto \log(T)$, persisting to the lowest temperature once superconductivity is suppressed by $B=41.5$~T. This identifies $x^\star$ as a QCP terminating the underdoped phase. Finally, we find that the carrier density $n_{\rm d}$ of the Ni-$d_{\rm x^2-y^2}$ pocket drops from $1+x$ above $x^\star$ to $x$ below, mirroring the hallmark of the pseudogap phase in cuprates and iridates. These results point to a pseudogap-like underdoped regime ending at $x^\star$, from which strange-metal behaviour emerges.