Path to poor coherence in the periodic Anderson model from Mott physics and hybridization

We investigate the anomalous metal arising from hole-doping the Mott insulating state in the periodic Anderson model. Using dynamical mean-field theory we show that, as opposed to the electron-doped case, in the hole-doped regime the hybridization between localized and delocalized orbitals leads to the formation of composite quasiparticles reminiscent of the Zhang-Rice singlets. We compute the coherence temperature of this state, showing its extremely small value at low doping. As a consequence the weakly doped Mott state deviates from the predictions of Fermi-liquid theory already at small temperatures. The onset of the Zhang-Rice state and of the consequent poor coherence is due to the electronic structure in which both localized and itinerant carriers have to be involved in the formation of the conduction states and to the proximity to the Mott state. By investigating the magnetic properties of this state, we discuss the relation between the anomalous metallic properties and the behavior of the magnetic degrees of freedom.

Figure 1

Schematic representation of the doped Kondo (a) and doped Mott (b) insulators, inspired by Ref. 33. A schematic picture of the band structure is reported on the left side of each figure. The hybridized bands are indicated with thick (blue online) lines; dashed lines are used for the bare bands ($V_{fp}=U=0$). On the right sides we sketched the corresponding density of states. A lighter color indicates the more correlated character of the hybridized bands.

Figure 2

Evolution of the $f$- (solid line) and $p$-orbital (dashed line) projections of the DOS. Data from QMC calculations at $T=0.0125$, $V_{fp}=0.9$, $n_{\mathrm{tot}}=3$, analytically continued on the real axis using maximum entropy method (Ref. 41). The figure qualitatively illustrates the Mott metal-insulator transition driven by correlation in the PAM.

Figure 3

Left panel: Renormalization constant $Z$ as a function of the doping $\delta =|3-n_{\mathrm{tot}}|$. Data are from Lanczos ED at $T=0$, $U=2$, $V_{fp}=0.9$ and increasing size of the effective bath $N_s=8$ (diamonds, circles) and 10 (triangles, squares). Right panel: Moment-moment correlation $-\langle m_{zp}{m}_{zf}\rangle$ as a function of the doping $\delta$ in the hole-doped regime. Data are from full ED calculations (see Appendix 7) for $T=0.008$ and for the same model parameters.

Figure 4

Evolution of the imaginary part of the conduction electron self-energy $\mathrm{Im}{\Sigma }_p\left(i{\omega }_n\right)$ for increasing temperature. Data are from finite-temperature Lanczos ED with doping $\delta =0.1$.

Figure 5

Main panel: Imaginary part of the conduction electron self-energy $\mathrm{Im}{\Sigma }_p\left(i{\omega }_n\right)$ for increasing value of the hole doping and $T=0.001$. Data are from Lanczos ED calculations. Inset: Comparison of the $\mathrm{Im}{\Sigma }_p\left(i{\omega }_n\right)$ behavior from different numerical methods for $\delta =0.05$. The other model parameters are the same as in the main panel. The QMC and full ED calculations are performed at $T=0.008$. DMRG is a $T=0$ calculation performed with a cluster of $N_{\mathrm{s}}=30$ sites and plotted down to the position of the lowest energy pole.

Figure 6

$\sigma =\mathrm{Im}{\Sigma }_p(i{\omega }_n\to 0)$ as a function of the temperature for different values of the doping. The data shown are from full ED calculations.

Figure 7

Scaling of the inverse lifetime ${\tau }^{-1}$ as a function of $T^2$ in the low-temperature limit. Data are from Lanczos ED calculations. Lines are guides to the eye.

Figure 8

Local spin susceptibility ${\chi }_{\mathrm{loc}}$ as a function of the temperature and increasing value of the hole doping. Data are from Lanczos ED (open symbols) and full ED (pluses, crosses, and stars) calculations.

Figure 9

Coherence temperature scale $T_{\mathrm{coh}}$ as extrapolated from the inverse local spin susceptibility ${\chi }_{\mathrm{loc}}^{-1}\left(T\right)$. The extrapolations from different numerical methods are found to be in satisfactory agreement.

Figure 10

Phase diagram of the PAM near the Mott insulating state as a function of temperature and hole doping. The diagram is obtained from $\mathrm{Im}{\Sigma }_p(i{\omega }_n\to 0)$. The dotted line indicates the crossover temperature scale $T_{\mathrm{coh}}$.

Figure 11

Imaginary part of the majority-spin $p$-electron self-energy for increasing external magnetic field $\mathbf{B}$. The data are from QMC solution at $T=0.016$ and $\delta =0.05$.

Figure 12

Imaginary part of conduction band electron Green's function $\mathrm{Im}{G}_{p\sigma }\left(i{\omega }_n\right)$ for $T=0.016$, $\delta =0.05$ and increasing strength of external magnetic field. Data from QMC calculations.

Figure 13

Main panel: Staggered magnetization $m_{AF}$ as a function of temperature and increasing value of hole doping. The data are from full ED calculations.

Figure 14

Conduction electron self-energy $\mathrm{Im}{\Sigma }_{p\sigma }\left(i{\omega }_n\right)$ (left panel) and Green's function $\mathrm{Im}{G}_p\left(i{\omega }_n\right)$ (right panel). Data from full ED calculations for $\delta =0.01$ and $T=0.005$.

Figure 15

Intensity plot of $\mathrm{Im}{\Sigma }_p(\omega \to 0)$ as a function of external magnetic field $\mathbf{B}$ and $T$ at fixed doping $\delta =0.01$. For visualization, the data have been normalized to $\max \left\{\mathrm{Im}{\Sigma }_p\left({\omega }_n\right)\right\}$ at each ($\mathbf{B}$, $T$). Dashed lines are drawn to better visualize the crossover regions in the phase diagram.