Fermi-liquid transport beyond the upper critical field in superconducting La$_2$PrNi$_2$O$_7$ thin films

Abstract

Unconventional superconductivity typically emerges out of a strongly correlated normal state, manifesting as a highly renormalized Fermi liquid or a strange metal with $T$-linear resistivity. In Ruddlesden-Popper bilayer nickelates, superconductivity with a critical temperature $T_{\rm c}$ exceeding 80 and 40~K has been respectively realised in pressurized bulk crystals and epitaxially strained thin films. These advancements call for the characterisation of fundamental normal-state and superconducting parameters in these new materials platforms of high-$T_{\rm c}$ superconductivity. Here we report detailed magnetotransport experiments on superconducting La$_2$PrNi$_2$O$_7$ (LPNO) thin films under pulsed magnetic fields up to 64~T and access the normal-state behaviour over a wide temperature range between 1.5 and 300~K. We find that the normal state of thin-film LPNO exhibits the hallmarks of Fermi-liquid transport, including $T^2$ temperature dependence of resistivity and Hall angle, and $H^2$ magnetoresistance obeying Kohler scaling. Using the empirical Kadowaki-Woods ratio, we estimate a quasiparticle effective mass $m^*/m_e \simeq 10$, thereby revealing the highly renormalized Fermi liquid state therein. Our results demonstrate that thin-film LPNO follows the same $T_{\rm c}/T_{\rm F}$ scaling observed across a myriad of strongly correlated superconductors and establish key normal-state characteristics of strained bilayer superconducting nickelates.

Figures (4)

• Figure 1: In-plane resistivity of a superconducting La$_2$PrNi$_2$O$_7$ thin film.a, Magnetoresistivity isotherms $\rho_{\rm xx}(H)$ up to 53.4 T measured at the following temperatures: 100, 80, 60, 50, 45, 40, 35, 30, 25, 20, 15, 10, 7.0, 4.1, and 1.5 K. b, Temperature-dependent resistivity $\rho_{\rm xx}(T)$ measured at 0 T (solid line) and 53 T (filled circles), and the extrapolated 0-T values (open circles). Grey dash line is a fit to the measured zero-field resistivity above between 50 and 300 K using a parallel resistor model: $1/\rho(T) = 1/(\rho_0 + A_2 T^2) + 1/\rho_{\rm max}$, which finds $\rho_0 = 102~{\rm \mu\Omega~cm}$, $\rho_{\rm max} = 780~{\rm \mu\Omega~cm}$, and $A_2=8.1~\rm{n\Omega~cm~ K^{-2}}$, respectively. Inset: $\rho_{\rm xx}$ versus $T^2$ below 60 K, showing a $\Delta\rho(T)~\propto~ T^2$ behaviour in the measured 53-T resistivity and extrapolated zero-field resistivity. For a discussion of the possible origin and impact of two-step transition below $T_{\rm c}$, refer to Supplementary Materials Sec. C.
• Figure 2: Hall resistivity, Kohler scaling, and Hall angle in La$_2$PrNi$_2$O$_7$ thin film.a, Hall resistivity isotherms $\rho_{\rm yx}(H)$ measured at indicated temperatures. Traces at different temperatures are shifted successively by 1 $\mu\Omega$ cm for clarity. Dash lines are fits made to the normal-state $\rho_{\rm yx}$ at high fields using $R_{\rm H}=\rho_{\rm yx} /(\mu_0 H)$. Inset: Hall coefficient versus temperature $R_{\rm H}(T)$. $R_{\rm H}$ approaches $-0.3$ mm$^3$/C as $T \rightarrow 0$. Vertical dashed line marks $T_{\rm c}$. b, Normalised magnetoresistance versus magnetic field scaled by zero-field resistivity i.e. $\rho_{\rm xx}/\rho_{\rm xx}(0)$ versus $\mu_0 H/\rho_{\rm xx}(0)$, known as the Kohler plot. Normal-state data measured at indicated temperatures collapses into a single curve following $\rho_{\rm xx}/\rho_{\rm xx}(0)~\propto~(\mu_0 H/\rho_{\rm xx}(0))^2$ shown by the dashed line. Note that traces of $T$ = 10, 20, 30, and 40 K deviate from the Kohler scaling function at low $\mu_0 H/\rho_{\rm xx}(0)$ until normal-state behaviour is recovered at sufficiently high fields. $\rho_{\rm xx}$ ($\rho_{\rm yx}$) traces measured below $T_{\rm c}$ are (anti-)symmetrized, whereas the 50- and 60-K data are measured using the positive-polarity trace only, which nonetheless show good agreement with measurement performed at 14 T.c, Inverse Hall angle $\cot\theta_{\rm H}=|\rho_{\rm xx}/\rho_{\rm yx}|$ versus $T^2$. Filled points correspond to measurements at 53 T and open points correspond to extrapolated 53 T values using Hall resistivity measured at 8 T (i.e. $\rho_{\rm yx}(\rm 53~T)$ = $R_{\rm H}(8~\rm{T})\times(53/8)$). Dashed line is a fit using $\cot\theta_{\rm H}=C+BT^2.$
• Figure 3: Upper critical fields of La$_2$PrNi$_2$O$_7$ thin film.$\mu_0 H_{\rm c2}$ are extracted using the criterion of $\rho_{\rm xx}(\mu_0H_{\rm c2})/\rho_{\rm xx}$(53 T) = 0.9. Filled points correspond to the configuration that the magnetic field is applied along the film surface normal (i.e. $\mathbf{H}\parallel c$) and open points the configuration that field applied parallel to the film surface (i.e. $\mathbf{H}\parallel ab$). Dash and dotted lines are fits made using the linearised Ginzburg-Landau formulae (see main text). Inset shows $\mu_0H_{c2}$ measured at 35 K with the field oriented close to the in-plane configuration (i.e. $\theta \simeq 90^{\circ}$). Solid line is a fit made using the 2D Tinkham modeltinkham1963: $\left(\frac{H_{\rm c2}\sin\theta}{H_{\rm c2, \parallel}}\right)^2 +\left|\frac{H_{\rm c2}\cos\theta}{H_{\rm c2, \perp}}\right|=1$.
• Figure 4: Superconducting critical temperature $T_{\rm c}$ versus effective Fermi temperature $T_{\rm F}$ for strongly correlated superconductors. The dotted, dotted-dash, and dashed lines indicate $T_{\rm c}/T_{\rm F}$ = 0.01, 0.05, and 0.1, respectively. For the referenced materials, $T_{\rm F}$ values are extracted assuming a quadratic energy dispersion $E_{\rm F}=\hbar^2k_{\rm F}^2/(2m^*)$ and using experimental data of effective mass and carrier density inferred from specific heat, Hall effect, and quantum oscillation measurements (refs. uemura2004cao2018matsuura2023hu2024 and references therein) or from penetration depth measurements using $E_{\rm F} = (\hbar^2/2)(3\pi^2)^{2/3}n_{\rm s}^{2/3}/m^*$ (ref. uemura1990). The series of points in gradient blue illustrates the effect of hole doping on $T_{\rm c}$ and $T_{\rm F}$ of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) with the darker colour indicating a higher doping level up to $x=0.21$ ($T_{\rm c}=27$ K). Error bars for the cuprate materials indicate the variations in $T_{\rm c}$ and $T_{\rm F}$ with carrier dopings, and for LPNO the variations in $T^*_{\rm F}$ inferred from the upper and lower limits of $\bar{m}^*$ estimates. MATBG: magic-angle twisted bilayer graphene; TMTSF: tetramethyltetraselenafulvalene; BEDT-TTF: bisethylenedithiol-tetrathiafulvalene; Ba122: BaFe$_2$(As$_{1-x}$P$_x$)$_2$; STO: SrTiO$_3$; YBCO: YBa$_2$Cu$_3$O$_{6+x}$; Tl2201: Tl$_2$Ba$_2$CuO$_{6+\delta}$; Tl2223: Tl$_2$Ba$_2$Ca$_2$Cu3O$_{10+\delta}$; Bi2223: Bi$_2$Sr$_2$Ca$_2$Cu3O$_{10+\delta}$; Hg2223: Hg$_2$Ba$_2$Ca$_2$Cu3O$_{10+\delta}$;