Electronic coupling between a FeSe monolayer film and ${\mathrm{SrTiO}}_3$ substrate

Several experimental groups have reported superconductivity in single unit cell layers of FeSe on ${\mathrm{SrTiO}}_3$ and a few other substrates, with critical temperature $T_c$ reports ranging up to 100 K, and a variety of theoretical work has been done. Here we examine more closely the interaction of a single FeSe layer with a ${\mathrm{TiO}}_2$ terminated ${\mathrm{SrTiO}}_3$(001) (STO) substrate. Several situations are analyzed: the underlying ideal interface, the effect of $z$-polarized longitudinal optic $\left[\mathrm{LO}\right(\widehat{z}$)] phonons in STO, electron doping of the STO substrate, substitution of Se by the bordering chalcogenides S and Te, and doping by adsorption of K on the FeSe surface. These results complement earlier studies of O and Se vacancies. The O $p_y,p_y$ surface band of STO persists at the interface, and by sharing holes with the hole pocket of FeSe it plays a part in the behavior around the interface, initially by determining the Fe Fermi level lineup with the STO band gap. The $\mathrm{LO}\left(\widehat{z}\right)$ mode causes strong band shifts around the interface but the strength of coupling to the Fe bands cannot be obtained with our methods. Adsorption of 25% K (one K per four Fe) fills the small O interface hole pocket and donates the rest of the electrons to the Fe hole pockets, filling them.

Figure 1

The structure of the simulation cell of 1 unit cell of FeSe on a ${\mathrm{SrTiO}}_3$ substrate, with site designations as used in this paper. The marked interlayer distances are defined as $d_S=z_{\text{Fe}}-z_{\text{Ti}}$ and $d_X=z_{\text{Se}}-z_{\text{Ti}}$, where $z_i$ are the $z$ coordinate of the atom.

Figure 2

Calculated Fermi surfaces of (a) 1UC FeSe and (b) 1FeSeSTO, the difference is at the corner $M$ point. The electronic band structures and projected densities of states (pDOS) are shown for (c) 1FeSeSTO, (d) 1UC FeSe, and (e) STO. The valence band maximum of STO has been aligned with the two Fermi levels in (c) and (d), which is very near where the STO bands lie in (c). The bands of 1FeSeSTO are simply a overlay of those of the two parts, reflecting only how they align across the interface. The red arrows indicate the Fermi surfaces arising from the O1 interface band.

Figure 3

(a) Color plot of the difference density FeSeSTO $-$ (FeSe + STO), in ${10}^{-3}$ atomic units, with FeSe lying at the bottom. The color scale is at the left. (b) Atomic positions in the (110) plane shown in (a). The surface Se atom does not lie in this plane. The differences are rather small (see text) but the rearrangement of charge on the Re atom at the bottom is evident.

Figure 4

Atom projected densities of states (pDOS) of (a) the interface Ti1 and O1 ions, and (b) the bottom surface Ti3 and O5 ions of 1FeSeSTO in $z$-polarized LO mode. “up” refers to O ions moving toward the FeSe layer and cations moving oppositely; “dn” refers to displacement in the opposite direction. The pDOS for the undisplaced (reference) position are filled in.

Figure 5

Band structures for the frozen $\mathrm{LO}(\widehat{z}$) phonon: (a) up, (b) reference undisplaced, and (c) dn displacements, see text. Red circles indicate strong Ti1 character, while blue circles represent strong O1 character of the band. In all cases the Fermi level is pinned by the Fe $d$ bands, but some changes are nonmonotonic (viz. the O $p$ bands).

Figure 6

Difference density (in ${10}^{-3}$ a.u.) in 101 plane containing (a) the Fe-Se2-Fe chain, and (b) the Se1-Fe-Se1 chain. For the orbital re-occupation on Fe, see text.

Figure 7

Bands edges for Fe and Ti bands at $\mathrm{\Gamma }$ point, and O bands at the $M$ point, for VCA nuclear charge equal to 22.00, 22.05, and 22.10.

Figure 8

Difference density, in ${10}^{-3}$ a.u., of $\rho$(1FeSeSTO) minus cells with Se replaced by a fraction $x$ of S or Te, $x=0.5$ and 1.0, as noted. The horizontal black separating line denotes where the color scale has been changed, because the differences are so much larger in the lower subpanels. Left color scale on the left is for upper subpanels, the one on the right is for the lower subpanels containing the Fe-$X$ chain.

Figure 9

(a) Orbital occupation differences, in ${10}^{-3}$, versus a normalized mean electropositivity difference $x$, supposing $x=-1$ for S, 0 for Se, and +1 for Te, and (b) the net change of charge in all Fe $d$ orbitals.  The nonlinearities are discussed in the text.

Figure 10

Bands of (a) 1FeSeSTO and (b) for a 25% K overlayer 1FeSeSTO. The Fermi level (set to zero in each figure) increases by 0.2 eV, just enough to fill the hole bands at $\mathrm{\Gamma }$.