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

TL;DR

The study tackles whether quantum criticality underlies the strange-metal behavior in superconducting infinite-layer nickelates by using the Seebeck coefficient as a low-temperature proxy for entropy per carrier. It demonstrates a $S/T$ divergence, $S/T \propto \log T$, at the onset of $T$-linear resistivity for $La_{1-x}Sr_xNiO_2$ with $x=0.20$, and shows that ARPES-informed Boltzmann transport reproduces the high-temperature Seebeck magnitude while revealing a threefold mass renormalization at the Fermi level. Hall analyses with a minimal two-band model (Ni-$d_{x^2-y^2}$ and Nd-$s$ pockets) indicate Planckian $T$-linear scattering in the correlated Ni band and a $T^2$ Nd band, from which the Ni-$d$ carrier density collapses from $n_d=1+p$ to $p$ across the critical doping in the absence of long-range magnetic order. These results establish a quantum critical point at the end of a pseudogap-like phase in infinite-layer nickelates and generalize the link between strange-metal behavior and quantum criticality across correlated superconductors, including cuprates.

Abstract

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.

Figures (3)

• Figure 1: (a,b) Temperature vs hole doping phase diagram of (a) the infinite-layer nickelate Nd$_{\rm 1-x}$Sr$_{\rm x}$NiO$_2$ (NSNO), the data is reproduced from Lee et al.lee_linear_character_2023 and (b) the hole-doped cuprate La$_{\rm 2-x}$Sr$_{\rm x}$CuO$_4$ (LSCO). Lines are a guide to the eye. The red and blue arrow represents the doping displayed in the figure; c,d underneath. (c,d) In-plane resistivity $\rho$ vs $T$ measured at zero field of NSNO (data reproduced from Lee et al.lee_linear_character_2023) for hole doping in Sr $x=0.05$ and $x=0.15$ (with $T$-linear resistivity) and La$_{\rm 1.6-x}$Nd$_{0.4}$Sr$_{\rm x}$CuO$_4$ (Nd-LSCO) cuprate collignon_2017 for hole doping in Sr $x=0.22$ and $x=0.24$. Compounds plotted in red full line belong to the strange metal phase. Compounds plotted in blue belong to the lower doping phase -- for cuprates, the pseudogap phase. (e) Seebeck coefficient plotted $S/T$ vs $T$ on a logarithmic scale for Nd-LSCO $p=0.24$ just above $p^\star=0.23$ (data reproduced from Gourgout et al.Gourgout2022Seebeck). Dashed line is a guide for the eye. (f) Electronic specific heat of the cuprate La$_{\rm 1.8-x}$Eu$_{0.2}$Sr$_{\rm x}$CuO$_4$ (Eu-LSCO) $p=0.24$ just above $p^\star=0.23$ plotted as $C_{\rm el}/T$ vs $T$ (data reproduced from Michon et al.Michon2019Thermodynamic). Dashed line is a guide for the eye.
• Figure 2: (a) Seebeck coefficient plotted as $S/T$ vs $T$ of La$_{\rm 1-x}$Sr$_{\rm x}$NiO$_2$ (LSNO) $x=0.20$. Seebeck data (red line) at $B=14$ T is plotted alongside Boltzmann transport calculation (light red). The Boltzmann calculation was performed using Sun et al.’s tightbinding model Sun2025Electronic and by considering the effective mass three times larger than what was reported by ARPES; (b) Seebeck coefficient plotted as $S/T$ vs $T$ in logarithmic scale. The dashed line is a guide to the eye that shows the linearity $S/T$. (c) Seebeck coefficient of LSNO plotted as $S/T$ vs $T$ at different magnetic field $B=0,7,14$ T. The grey rectangle represents the region of sharp change in the Seebeck coefficient around 60 K; (d) In-plane resistivity $\rho$ vs $T$ for $B=0,14$ T. The grey rectangle reveals the absence of signature in $\rho$ around 60 K.
• Figure 3: (a) Hall coefficient $R_{\rm H}$ vs $T$ of NSNO $x=0.2125$ (data on NSNO are reproduced from Lee et al.lee_linear_character_2023): data (red points) and two-band model calculations (red line); (b) $R_{\rm H}$ vs hole doping in Sr, $x$, in the $T\rightarrow 0$ limit (see Fig. S1). Solid is a guide to the eye; (c) Carrier concentration of the Ni-$d_{\rm x^2-y^2}$ band as a function $x$ extracted from the two-band model. The top (bottom) dashedline that represent $1+x$ ($x$) are guide to the eye.