Separation of transport lifetimes in $\mathrm{SrTi}{\mathrm{O}}_3$-based two-dimensional electron liquids

Deviations from Landau Fermi-liquid behavior are ubiquitous features of the normal state of unconventional superconductors. Despite several decades of investigation, the underlying mechanisms of these properties are still not completely understood. In this work, we show that two-dimensional electron liquids at $\mathrm{SrTi}{\mathrm{O}}_3/R\mathrm{Ti}{\mathrm{O}}_3$ $(R=\mathrm{Gd}$ or Sm) interfaces reveal strikingly similar physics. Analysis of Hall and resistivity data shows a clear separation of transport and Hall scattering rates, also known as “two-lifetime” behavior. This framework gives a remarkably simple and general description of the temperature dependence of the Hall coefficient. Distinct transport lifetimes accurately describe the transport phenomena irrespective of the nature of incipient magnetic ordering, the degree of disorder, confinement, or the emergence of non–Fermi-liquid behavior. The Hall scattering rate diverges at a critical quantum well thickness, coinciding with a quantum phase transition. Collectively, these results introduce constraints on the existing microscopic theories of lifetime separation and point to the need for unified understanding.

Figure 1

Transport data for $R\mathrm{Ti}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3/R\mathrm{Ti}{\mathrm{O}}_3$ quantum wells as a function of temperature with $R=\mathrm{Sm}$ (top row) and Gd (bottom row). (a,b) Longitudinal resistance $R_{xx}$, (c,d) inverse of the Hall coefficient, ${\left(e{R}_H\right)}^{-1}$, and (e,f) Hall angle $R_{xx}/R_H$ on a $T^2$ scale. The labels indicate the $\mathrm{SrTi}{\mathrm{O}}_3$ quantum well thickness in terms of the number of SrO layers they contain. The solid lines are fits to the data, using Eqs. (1, 2, 3) and a single set of adjustable parameters.

Figure 2

Transport parameters as a function of $\mathrm{SrTi}{\mathrm{O}}_3$ thickness for $R=\mathrm{Sm}$ (blue) and Gd (red). (a) ${\left(e{R}_H\right)}^{-1}$ in the $T=0\mathrm{K}$ limit, from fitting to Eq. (3) (full symbols) and measured ${\left(e{R}_H\right)}^{-1}$ at $T=2\mathrm{K}$. (b,c) Residuals $R_0$ and C. The insets show the same quantities multiplied by the $t_{\mathrm{QW}}$. (d) Temperature exponent $n$ in $R_{xx}$. (e,f) Transitions between FL, NFL, and insulator (top row) and magnetic ordering in the quantum well (bottom row).