Phonon mechanism explanation of the superconductivity dichotomy between FeSe and FeS monolayers on ${\mathrm{SrTiO}}_3$ and other substrates

It was observed recently [Shigekawa et al., PNAS 116, 2470 (2019)] that while monolayer iron chalcigenide FeSe on a ${\text{SrTiO}}_3$ (STO) substrate has a very high critical temperature, its chemical and structural twin material FeS/STO has a very low $T_c$, if any. To explain this, the substrate interfacial phonon model of superconductivity in iron chalcogenides is further developed. The main glue is the oxygen ion ${\mathrm{\Omega }}_s=60\text{meV}$ vibrations longitudinal optical (LO) mode. The mode propagates mainly in the ${\text{TiO}}_2$ layer adjacent to the monolayer (and also generally present in similar highly polarized ionic crystals like ${\text{BaTiO}}_3,$ rutile, and anatase). It has stronger electron-phonon coupling to electron gas in FeSe than a well-known ${\mathrm{\Omega }}_h=100\text{meV}$ harder LO mode. It is shown that while (taking into account screened Coulomb repulsion effects) the critical temperature of FeSe on STO and ${\text{TiO}}_2$ is above $65\text{K}$, it becomes less than $5\text{K}$ for FeS due to two factors suppressing the electron-phonon coupling. The effective mass in the latter is twice smaller and, in addition, the distance between the electron gas in FeSe to the vibrating substrate oxygen atoms is 15% smaller than in FeS, reducing the central peak in electron-phonon interaction. The theory is extended to other ionic insulating substrates.

Figure 1

Interfacial phonon modes. Oxygen ion's vibrations in the ${\text{TiO}}_2$ substrate layer Ti, silver; O, red). The displacement in direction perpendicular ($z$ axis, blue arrow) to the one unit cell thin Fe (brown)-chalcogenide (Se, S, Te—green) layer are associated with FK modes. The two modes most relevant for the phonon-mediated pairing longitudinal optical modes are the Ti–O stretching mode (shown by black arrow) and the Ti–O–Ti bending (dark green arrow). The next layer Bi (cyan)–O (dark red) influencing the interfacial phonon frequency is also shown. Direction of propagation of the vibration wave is assumed to be along the $x$ direction.

Figure 2

Superconducting critical temperature as function of effective mass and the distance between the iron chalcogenite layer and the interface ${\text{TiO}}_2$ (where the relevant phonon modes originate). The dielectric constant ${\varepsilon }_0=3000$ is fixed to represent ${\text{SrTiO}}_3$.

Figure 3

Critical temperature of 1UC FeSe on ionic substrates as function of effective mass and the substrate dielectric constant ${\varepsilon }_0$ (in the logarithmic scale). The distance between the iron chalcogenide layer and the interface ${\text{TiO}}_2$ is fixed at $d=1.1a$. Strongly dielectric substrate material STO and moderately dielectric ${\text{TiO}}_2$ forms rutile (${\varepsilon }_0=300$) and anatase (${\varepsilon }_0=300$) are marked.

Figure 4

The Brillouin zone of the minimal one-band model. The red dashed line is the BZ containing two Fe atoms with lattice spacing $a=\sqrt{2}{a}^{\prime }$. The small electron pocket is nearly circular (with center at the $M$ point).

Figure 5

The (Matsubara) static ($n=0$) susceptibility of the electron gas with dispersion relation Eq. (A2) of the minimal model. One observes a peak near the $(\pi ,\pi )/a^{\prime }$ point, indicating a tendency toward antiferromagnetic correlations.

Figure 6

The ($n=0$ Matsubara) gap function for the $s$-wave solution of Eq. (B4). One observes that the function is concentrated in a narrow shell near the Fermi surface, see Fig. 4.

Figure 7

The anomalous average (order parameter) $F$ defined in Eq. (B1) for the $d$-wave solution at the on site repulsion $U=2t$. Note that, as for the $s$ wave, it is concentrated in the narrow shell around the Fermi surface. The correlator continuously changes signs four times.

Figure 8

The (Matsubara) gap function $\mathrm{\Delta }$ defined in Eq. (B3) for the $d$-wave solution at $U=2t$. Note that due to the on-site repulsion term, this.quantity spreads over beyond the narrow shell around the Fermi surface.

Figure 9

Comparison of energies of the $s$- and $d$-wave solutions for various values of the on-site repulsion $U$. The transition occurs at $U=2t$.