Possible spin excitation structure in monolayer FeSe grown on ${\mathrm{SrTiO}}_3$

Based on recent high-resolution angle-resolved photoemission spectroscopy measurement in monolayer FeSe grown on ${\mathrm{SrTiO}}_3$, we constructed a tight-binding model and proposed a superconducting (SC) pairing function which can well fit the observed band structure and SC gap anisotropy. Then we investigated the spin excitation spectra in order to determine the possible sign structure of the SC order parameter. We found that a resonancelike spin excitation may occur if the SC order parameter changes sign along the Fermi surfaces. However, this resonance is located at different locations in momentum space compared to other FeSe-based superconductors, suggesting that the Fermi surface shape and pairing symmetry in monolayer FeSe grown on ${\mathrm{SrTiO}}_3$ may be different from other FeSe-based superconductors.

Figure 1

(a) Calculated band structure along the high-symmetry directions in the 2Fe/cell BZ. The energy is defined with respect to the Fermi level (the black dotted line). (b) The Fermi surfaces in the first quadrant of the 2Fe/cell BZ (black and red), while the blue dotted lines show schematically the Fermi surfaces adopted in Refs. [24, 27, 31].

Figure 2

(a) The maximal eigenvalue of ${\widehat{U}}_s\text{Re}{\widehat{\chi }}^0(\mathbf{q},0+i\eta )$ in the normal state $[D_{\mathbf{k}}=0$ in Eq. (1)], by setting $U=6.8$. (b) The magnitude of the SC gap $\left|\mathrm{\Delta }\right|$ along ${\delta }_1$ (red) and ${\delta }_2$ (black), defined as the minimal positive eigenvalue of $A_{\mathbf{k}}$ in Eq. (1) along the Fermi surfaces. $\theta$ is defined in Fig. 1. The inset in (b) shows the DOS.

Figure 3

The pairing function in the band basis. (a) ${\mathrm{\Delta }}_{\mathbf{k}}^1$. (b) ${\mathrm{\Delta }}_{\mathbf{k}}^3$. ${\mathrm{\Delta }}_{\mathbf{k}}^2$ (${\mathrm{\Delta }}_{\mathbf{k}}^4$) is qualitatively the same as ${\mathrm{\Delta }}_{\mathbf{k}}^1$ (${\mathrm{\Delta }}_{\mathbf{k}}^3$), but with some minor quantitative difference.

Figure 4

The sign of the SC order parameter on the Fermi surface. (a) For cases I and II, while (b) is for case III. The black/red color denotes that the sign of the SC order parameter is negative/positive. In the inset of (a), the solid and dotted lines denote the 2Fe/cell BZ and 1Fe/cell BZ, respectively. In (b), the gray dotted arrow represents $\mathbf{q}={\mathbf{Q}}_{\mathbf{1}}$ that connects the region of ${\delta }_1$ and ${\delta }_2$, where the SC order parameters have opposite signs.

Figure 5

Difference of $\text{Im}\chi (\mathbf{q},\omega +i\eta )$ between the SC and normal states, calculated along the red arrow in the inset of Fig. 4. The gray dotted lines denote $2{\mathrm{\Delta }}_1=0.28$. (a) For cases I and II, while (b) is for case III.

Figure 6

Spin susceptibility as a function of $\omega$, at $\mathbf{q}={\mathbf{Q}}_1$. The gray dotted lines denote $\omega =2{\mathrm{\Delta }}_1$.

Figure 7

Spin susceptibility as a function of $\omega$, at $\mathbf{q}=\mathbf{Q}$. The inset shows schematically the scattering process connected by $\mathbf{Q}$ (gray dotted arrow). Here the red pocket around $\mathrm{\Gamma }$ is incipient, which sinks below the Fermi level.