Orbital-selective Mott transitions in a doped two-band Hubbard model

We extend previous studies on orbital-selective Mott transitions in the paramagnetic state of the half-filled degenerate two-band Hubbard model to the general doped case, using a high-precision quantum Monte Carlo dynamical mean-field theory solver. For sufficiently strong interactions, orbital-selective Mott transitions as a function of total band filling are clearly visible in the band-specific fillings, quasiparticle weights, double occupancies, and spectra. The results are contrasted with those of single-band models for similar correlation strengths.

Figure 1

(Color online) Band-specific fillings for the two-band model versus total filling for a range of interactions $U$. Open and solid symbols represent the narrow and the wide band, respectively.

Figure 2

(Color online) Intraorbital double occupancy for various $U$-values as a function of doping for the two-band model. Panel $\left(a\right)$ shows for dopings near half filling and panel $\left(b\right)$ in the entire doping range $2\le n\le 4$ that the intraorbital double occupancy for the wide band becomes nearly independent of the interaction for intermediate $U$ and all fillings $n\gtrsim 2.2$. In $\left(b\right)$, results for the noninteracting case ($U=0$, black line) and within Hartree-Fock approximation (for $U=2.4$, long-dashed line) are included for comparison.

Figure 3

(Color online) $\left(a\right)$ DOS of a rigid-band model with a semielliptic DOS and bandwidths $W_{\text{n}}=2$ and $W_{\text{w}}=4$, representative of interactions $U\simeq 2.4$. $\left(b\right)$ Band-specific fillings within this model, compared to QMC results for $U=2.4$ and $T=1/40$.

Figure 4

(Color online) Intraorbital double occupancy versus $U$ for density $n=3$ (squares). In the interaction range $2.5\lesssim U\lesssim 5$, the intraorbital double occupancy is only very weakly dependent on $U$. Density-dependent upper and lower bounds on the double occupancies are obtained in the limits of weak (dashed/solid lines) and strong (dotted lines) correlation, respectively. Inset: quasiparticle weight $Z$ (cf. Sec. 3C).

Figure 5

(Color online) The $\uparrow \downarrow$-density-density correlation function for total fillings $n\gtrsim 2.2$, corresponding to quantum fluctuations in the intraorbital double occupancy around the uncorrelated limit. The correlations are generally negative since an enhanced $\uparrow$-density on a site implies a decreased $\downarrow$ density. At fixed interaction $U$, the amplitude of the correlation function decreases monotonically with filling, since the available phase space for density fluctuations decreases with increasing $n>2$.

Figure 6

(Color online) Orbital-selective Mott phase diagram of the two-band model for particle densities $1.85\le n\le 2.15$. For interaction $U<U_{\text{c}1}$, both bands are metallic at all densities. The insulating phase at half filling (thick black line) only exists for $U>U_{\text{c}2}$.

Figure 7

(Color online) Phase diagram of the two-band model for densities $2\le n\le 2.6$. Within the range of parameter values, for which both bands are metallic, the solid green (or patterned red) area indicates that the wide (or narrow) band contributes stronger to the doping, implying $n_{\text{w}}>n_{\text{n}}$ (or $n_{\text{n}}>n_{\text{w}}$). At the boundary (dashed line), both bands are equally filled.

Figure 8

(Color online) DOS calculated for various particle densities near half filling as a function of frequency $\left(a\right)$ for the wide band in the two-band model with interaction $U=2.4$, and $\left(b\right)$ for a single-band calculation with identical parameters (bandwidth $W=4$, interaction $U=2.4$, and temperature $T=1/40$).

Figure 9

(Color online) DOS calculated for various particle densities near half filling as a function of frequency, both for the narrow band in the two-band model (left column) and for a single-band calculation (right column). Panels within one row have approximately matching scaled interactions $\tilde{U}$. In the two-band case (left column), the total filling is varied in the range $2\le n\le 2.2$ in uniform steps of 0.01, with a corresponding offset. In the single-band case (right column), the filling is varied nonuniformly: here, the offset is chosen so that adjacent spectra with the same offset have (roughly) the same partial filling (i.e., $n_{\text{n}}$ in the two-band model equals $n$ of the single-band model).

Figure 10

(Color online) Spectral weight at the Fermi level for the two-band model. The thin dashed curves represent the spectral weights at the Fermi level according to Luttinger’s theorem. All other curves are guides to the eyes only.

Figure 11

(Color online) $\left(a\right)$ Quasiparticle weight $Z_{\text{n}}$ as defined in Eq. (2) for the narrow band in the two-band model. $Z_{\text{n}}$ develops a local maximum as a function of filling in the weakly doped regime $2.05\lesssim n\lesssim 2.15$ with increasing interaction $U$. There are no further anomalies at stronger doping (see inset). $\left(b\right)$ Real part of the self-energy calculated for $U=2.4$ at discrete Matsubara frequencies for the two-band model. The self-energy exhibits an anomaly (i.e., a strong enhancement at small frequencies) in the intermediate doping range $\left(2.05\lesssim n\lesssim 2.2\right)$. The lines are guides to the eyes only.

Figure 12

(Color online) $\left(a\right)$ Imaginary part of the self-energy $\text{Im}\Sigma \left(i{\omega }_n\right)$ for various total fillings $n$ at $U=2.4$ and $T=1/40$; intermediate minima are seen at low frequencies only for $n\ge 2.15$. $\left(b\right)$ Results for $\text{Im}\Sigma$ computed at different temperatures for selected densities (at $U=2.4$). The curves are hardly distinguishable for $n=2.1$; for $n=2.2$, the low-frequency minimum becomes more pronounced with decreasing $T$.