Single-orbital realization of high-temperature $s^{\pm }$ superconductivity in the square-octagon lattice

We propose possible high-temperature superconductivity (SC) with singlet $s^{\pm }$-wave pairing symmetry in the single-orbital Hubbard model on the square-octagon lattice with only nearest-neighbor hopping terms. Three different approaches are engaged to treat with the interacting model for different coupling strengths, which yield consistent results for the $s^{\pm }$ pairing symmetry. We propose octagraphene, i.e., a monolayer of carbon atoms arranged into this lattice, as a possible material realization of this model. Our variational Monte Carlo study for the material with realistic coupling strength yields a pairing strength comparable with the cuprates, implying a similar superconducting critical temperature between the two families. This study also applies to other materials with similar lattice structure.

Figure 1

(a) Sketch of the square-octagon lattice and illustration of the intrasquare nearest-neighbor hopping $t_1$ and the intersquare nearest-neighbor hopping $t_2$. The dotted square denotes the unit cell. (b) Band structure of the TB model (1) along the high symmetric lines in the first Brillouin zone. Panels (c) and (d) show the FSs of the undoped and $10\%$ electron-doped cases, respectively. The site contributions on the FS sheets are shown by color: the red (green) represents that the weights contributed by the sublattices 1 and 3 (2 and 4) are dominant. The TB parameters are $t_1=1$, $t_2=1.2$ throughout the work.

Figure 2

Panels (a) and (b) show the $\mathbf{q}$ dependence of the eigensusceptibilities $\chi \left(\mathbf{q}\right)$ in the first Brillouin zone, corresponding to the undoped and $10\%$ electron-doped compounds, respectively. The temperature is set as $T=0.001$. (c) The incommensurability $\delta$ as a function of doping $x$. (d) The AFM-ordered spin pattern in the octagraphene.

Figure 3

(a) $U_c/t_1$ as a function of the electron doping density $x$. The largest pairing eigenvalues $\lambda$ in four different pairing symmetry channels as a function of (b) $U/t_1$ and (c) $x$. (d) The $\mathbf{k}$-dependent superconducting order parameter ${\mathrm{\Delta }}_{\alpha }\left(\mathbf{k}\right)$ projected onto the FS for the leading $s^{\pm }$-wave pairing. The doping density for panels (b) and (d) is $x=10\%$. The interaction parameter adopted is $U=1.8t_1$.

Figure 4

The SBMF results. (a) Doping dependence of the energy (per unit cell) difference between the $s$-wave pairing and the $d$-wave one, $\mathrm{\Delta }E\equiv E_s-E_d$, in units of $t_1$. (b) Doping dependence of the four SBMF order parameters for the $s$-wave solution. (c) The $s$-wave gap function projected on the FS. (d) Doping dependence of the superconducting order parameter.

Figure 5

(a) The VMC results for the energy per unit cell as function of $\mathrm{\Delta }$ for the four different gap form factors $s^{\pm }$, $s^{++}$, $d_{x^2-y^2}$, and $d_{xy}$ with $g$ and ${\mu }_c$ optimized for each $\mathrm{\Delta }$. (b) The $\mathit{k}$-dependent superconducting order parameter $\mathrm{\Delta }\left(\mathit{k}\right)$ projected on the FS for the 10% electron-doped compound. The interaction parameter is $U=4t_1=10$ eV.