Coexistence of pairing tendencies and ferromagnetism in a doped two-orbital Hubbard model on two-leg ladders

Using the Density Matrix Renormalization Group and two-leg ladders, we investigate an electronic two-orbital Hubbard model including plaquette-diagonal hopping amplitudes. Our goal is to search for regimes where charges added to the undoped state form pairs, presumably a precursor of a superconducting state. For the electronic density $\rho =2$, i.e., the undoped limit, our investigations show a robust $\left(\pi ,0\right)$ antiferromagnetic ground state, as in previous investigations. Doping away from $\rho =2$ and for large values of the Hund coupling $J$, a ferromagnetic region is found to be stable. Moreover, when the interorbital on-site Hubbard repulsion is smaller than the Hund coupling, i.e., for $U^{\prime }<J$ in the standard notation of multiorbital Hubbard models, our results indicate the coexistence of pairing tendencies and ferromagnetism close to $\rho =2$. These results are compatible with previous investigations using one-dimensional systems. Although further research is needed to clarify if the range of couplings used here is of relevance for real materials, such as superconducting heavy fermions or pnictides, our theoretical results address a possible mechanism for pairing that may be active in the presence of short-range ferromagnetic fluctuations.

Figure 1

(Color online) (a) Spin-structure factor $S\left(q_x\right)$ vs $q_x$ for the two-leg ladder system with sizes $L=12$, 16, and 24, and for density $\rho =2$, $J=1.5$, and $U_{\text{eff}}=-0.5$. (b) $S\left(\pi ,0\right)$ as a function of $J$ for ladders with linear sizes $L=8$ and $U_{\text{eff}}=-0.5$. The inset shows the magnitude of this peak as a function of $U_{\text{eff}}$, for the coupling $J=1.5$. (c) Spin-spin correlation $C_{\text{spin}}\left(j\right)$ vs $j$ along the long ladder direction, for a system with size $L=24$, and for the couplings $U_{\text{eff}}=-0.5$ and $J=1.5$. The dashed curve is a fit given by Eq. (5).

Figure 2

(Color online) (a)–(b) Phase diagram ($J$ vs $-U_{\text{eff}}=3J-U$) for the $2\times 3$ cluster showing the region where the binding energies of electrons (a) and holes (b) is smaller than ${\Delta }_b<-0.1$, indicative of pairing. Above the red line, the total spin saturates to its maximum value. Below this line, the total spin changes continuously from the maximum value to zero at $J=0$. The blue lines show the region of $J$ where ${\Delta }_b<-0.1$ for $U_{\text{eff}}=-0.5$. These lines are the same as presented in Fig. 3. (c) ${\Delta }_b$ vs $1/L$ for some couplings (see legend).

Figure 3

(Color online) (a) Phase diagram of the two-leg ladder model Hamiltonian defined in Eq. (1). The region above the symbols is a fully saturated ferromagnetic phase (see text). The blue lines correspond to regions where ${\Delta }_b<-0.1$ for the cluster $2\times 3$ with two doped electrons/holes, as presented in Figs. 2a, 2b.

Figure 4

(Color online) Spin-structure factor $S\left(q_x\right)$ vs $q_x$ for the two-leg ladder system with size $L=16$, $J=1.5$, and $U_{\text{eff}}=-0.5$. (a) $S\left(q_x\right)$ for the densities $\rho =15/8$, $\rho =33/16$, and $\rho =17/8$ (see legend). (b) $S\left(q_x\right)$ for the densities $\rho =7/4$ and $\rho =9/4$.