Combined density functional and dynamical cluster quantum Monte Carlo calculations of the three-band Hubbard model for hole-doped cuprate superconductors

Using a combined local density functional theory (DFT-LDA) and quantum Monte Carlo (QMC) dynamic cluster approximation approach, the parameter dependence of the superconducting transition temperature $T_c$ of several single-layer hole-doped cuprate superconductors with experimentally very different $T_{c\text{max}}$ is investigated. The parameters of two different three-band Hubbard models are obtained using the LDA and the downfolding $N$th-order muffin-tin orbital technique with $N=0$ and 1, respectively. QMC calculations on four-site clusters show that the $d$-wave transition temperature $T_c$ depends sensitively on the parameters. While the $N=1\text{MTO}$ basis set which reproduces all three $pd\sigma$ bands leads to a $d$-wave transition, the $N=0$ set which merely reproduces the LDA Fermi surface and velocities does not.

Figure 1

Comparison of the downfolded $N=0$ MTO three-band (bold) and complete LDA band structures (dashed) of four undoped single-layer HTSC materials. The zero of energy is the Fermi level.

Figure 2

(Color online) Calculated in-layer hoppings for five single-layer cuprates for $N=0$. The materials are ordered by $T_{c\text{max}}$.

Figure 3

Comparison of the downfolded $N=1$ three-band (bold) and complete LDA band structures (dashed) of the single-layer HTSC materials ${\text{HgBa}}_2{\text{CuO}}_4$ and ${\text{La}}_2{\text{CuO}}_4$. The zero of energy is the Fermi level.

Figure 4

(Color online) Comparison of calculated in-layer hoppings for two single-layer cuprates for $N=0$ and $N=1$ (see text).

Figure 5

(Color online) Calculated transition temperatures $T_c$ for the three-band $t_{pd}-t_{pp}$ model (see text). The temperature variation is shown for variations in $t_{pp}$ with $t_{pd}$, held fixed (blue crosses), and vise versa (red plusses). The guide lines are a linear fit.

Figure 6

(Color online) Inverse $d$-wave pair-field susceptibility $\left(P_d^{-1}\right)$ as a function of temperature for different hopping-parameter sets calculated from ${\text{HgBa}}_2{\text{CuO}}_4$ with $N=0$ (see text). The lines are power-law fits to the lowest five points in each series.

Figure 7

(Color online) Inverse $d$-wave pair-field susceptibility $\left(P_d^{-1}\right)$ as a function of temperature for different hopping-parameter sets calculated from ${\text{HgBa}}_2{\text{CuO}}_4$ and for ${\text{La}}_2{\text{CuO}}_4$ with $N=1$ (see text). The lines are power-law fits to the lowest five points in each series.