Quasiparticle to local moment crossover in bad metals

TL;DR

The study addresses non-Fermi-liquid transport near a Mott metal-insulator transition in a family of organic salts, showing that bad-metal behavior arises from gradual destruction of coherent quasiparticles with increasing temperature rather than extreme scattering. By combining transport and NMR on the same crystals with DMFT calculations, the authors identify four transport regimes: a low-T Fermi-liquid with resistivity rho(T)=rho0+AT^2, a quasiparticle-dominated bad-metal with faster-than-quadratic growth of resistivity, a regime with resistivity above the MIR limit, and a high-T insulating state with a thermally filled pseudogap. DMFT reproduces the resistivity data and reveals the gradual collapse of the quasiparticle peak in the spectral function as temperature increases, consistent with the NMR peak in relaxation rate signaling local moments. The analysis shows that the Einstein relation and a Drude-like decomposition highlight the dominant roles of electronic compressibility and kinetic energy in transport across the MIT, offering a unified framework applicable to moiré materials.

Abstract

Non-Fermi-liquid charge transport in the vicinity of electronic instabilities has been intensely studied for decades. Deviations from $ρ_{\rm FL}=ρ_0+AT^2$ in bad and strange metals are commonly ascribed to a breakdown of Landau's quasiparticle (QP) concept. Yet, it remains unclear what mechanism drives the temperature dependence of $ρ(T)$ beyond $ρ_{\rm FL}$. Here, we examine the bad metal upon approaching the Mott metal-insulator transition via chemical pressure in $κ$-[(BEDT-STF)$_x$(BEDT-TTF)$_{1-x}$]$\rm _2 Cu_2 (CN)_3$. Through nuclear magnetic resonance (NMR) and transport experiments on the same single crystals, we directly link the onset of deviations from Korringa law $(T_1T)^{-1} = \mathrm{const.}$ with the rise of $ρ(T)$ beyond $ρ_{\rm FL}$. From the NMR relaxation rate, we can identify the gradual crossover between the QP-dominated regime at low $T$ to predominant local moments at higher $T$. By comparing our experimental findings with dynamical mean-field theory calculations, which accurately reproduce the transport data, we reveal how this crossover is reflected in $T$-dependent changes of the QP spectrum. Near the Mott insulator, where $dρ/dT<0$ at high $T$, an Einstein-relation analysis shows that bad-metal behavior with $dρ/dT>0$ is driven by the temperature dependence of the electronic compressibility rather than the diffusion constant.

Figures (8)

• Figure 1: Phase diagrams of (a) a strange metal above a QCP and (b) a bad metal nearby a Mott MIT. (c) While $\rho(T) \propto T$ in (a) yields a slower rise than $\rho_{\mathrm{FL}}(T)$, in (b) $\rho(T)$ rises faster than $T^2$Kurosaki2005Shimizu2011Shimizu2016Furukawa2018Pustogow2021-LandauPustogow2021-percolationPustogow2023Lin2015. (d) The transition from bad metal to Mott insulator yields a resistivity maximum with $\rho \gg \rho_{\rm MIR}$Kurosaki2005Shimizu2011Shimizu2016Furukawa2018Pustogow2021-LandauPustogow2021-percolationPustogow2023.
• Figure 2: (a) The Mott transition in $\kappa$-STF$_x$ yields a bifurcation of insulating and metallic NMR relaxation. (b) The pronounced $T$-dependence and generally faster $(T_1T)^{-1}$ for $x\leq 0.16$ are consistent with the response of local moments. In the low-$T$ Fermi-liquid state ($x\geq 0.19$) Korringa-type behavior with $T$-independent $(T_1T)^{-1}$ is established. (c) By comparing our $^1$H NMR results to optical and specific heat data Pustogow2021-LandauYesil2023, we find that $(T_1T)^{-1}$ scales with the effective mass enhancement $\left( m^{\star}/m \right)^2$.
• Figure 3: Combined assessment of FL and bad-metal behavior in resistivity and NMR relaxation. The plots versus $T^2$ (a-e) and on double-logarithmic scales (f-j) reveal $\rho(T)=\rho_0+AT^2$ at $T<$$T_{\rm FL}$. Above that, the increase is steeper than quadratic (orange shaded) until $\rho$ reaches a maximum at $T_{\rm max}$Pustogow2021-LandauPustogow2021-percolation. Sample geometry precluded precise determination of absolute resistivity, see End Matter. (k-o) $(T_1T)^{-1}$ probed by $^1$H NMR (in panel (o) appropriately scaled $^{13}$C data were added) is (1) $T$-independent at $T\leq$$T_{\rm FL}$ and (2) increases at higher $T$ where $\rho(T)$ rising faster than $T^2$. (3) As $(T_1T)^{-1}$ reaches the values of the 'insulating master curve' (gray shaded; see Fig. \ref{['T1T-MIT']}a,b), it forms a maximum that is most pronounced close to the Mott MIT ($x\rightarrow 0.16$Pustogow2021-LandauPustogow2021-percolation). This peak in $(T_1T)^{-1}$ is well below $T_{\rm max}$, above which (4) $\rho(T)$ acquires a non-metallic slope.
• Figure 4: The (a) experimental resistivity is accurately reproduced by (b) DMFT. (c) The FL regime with $\rho\propto T^2$ has a pronounced, almost $T$-independent QP peak in the DMFT spectral function $A(\omega,T)$. (d) The increase of $\rho$ with $T$ well above $\rho_{\rm FL}$ and beyond $\rho_{\mathrm{MIR}}$ in the bad-metal regime is concomitant with a rapid reduction of the QP peak. The $T$-dependent height of the QP peak $A(0,T)$ is displayed on top of panel (b). (e) Semiconducting behavior above $T_{\rm max}$ is found when coherent QP have vanished completely. (f) The contour plot of $\rho(T)/\rho_{\rm FL}(T)$ measured on $\kappa$-STF$_x$ illustrates the rise of $\rho$ faster than $T^2$ in the bad metal (orange). $\rho_{\rm FL}(T)$ corresponds to $T^2$ fits (black dashed lines) in Fig. \ref{['transport-NMR']}(f-j); $x=0.78$ and 1.00 data from Ref. Pustogow2021-Landau.
• Figure 5: Decompositions of the DMFT conductivity $\sigma$ (inverse of $\rho$ from Fig. \ref{['DMFT']}b). (a) The Einstein relation $\sigma = D \kappa$, or $\sigma/\sigma_{\rm MIR} = \tilde{D} \kappa$, yields the diffusion constant $D$ from $\sigma$ and the compressibility $\kappa = \partial n / \partial \mu$. (b) The Drude-like relation $\sigma/\sigma_{\rm MIR} = \tau_{\rm tr} E_{\rm kin}$ yields the transport scattering time $\tau_{\rm tr}$ from $\sigma$ and the kinetic energy $E_{\rm kin}$. In the FL regime, $\tau_{\rm tr}$ is comparable to the QP scattering time $\langle {\tau_\omega} \rangle/Z$ (see End Matter).