SmO thin films: A flexible route to correlated flat bands with nontrivial topology

Using density functional theory based calculations, we show that the correlated mixed-valent compound SmO is a three-dimensional strongly topological semimetal as a result of a $4f\text{−}5d$ band inversion at the $X$ point. The [001] surface Bloch spectral density reveals two weakly interacting Dirac cones that are quasidegenerate at the $\overline{M}$ point and another single Dirac cone at the $\overline{\mathrm{\Gamma }}$ point. We also show that the topological nontriviality in SmO is very robust and prevails for a wide range of lattice parameters, making it an ideal candidate to investigate topological nontrivial correlated flat bands in thin-film form. Moreover, the electron filling is tunable by strain. In addition, we find conditions for which the inversion is of the $4f\text{−}6s$ type, making SmO to be a rather unique system. The similarities of the crystal symmetry and the lattice constant of SmO to the well studied ferromagnetic semiconductor EuO, makes SmO/EuO thin film interfaces an excellent contender towards realizing the quantum anomalous Hall effect in a strongly correlated electron system.

Figure 1

Phase diagram (d) of SmO as a function of the fcc lattice parameter within LDA+SO+$U$ $(U=6$ eV, $J_{\mathrm{H}}=0$ eV) along with representative FPLO band structures for the (a) nontrivial $d\text{−}f$ band inversion, (b) trivial insulator, and (c) nontrivial $s\text{−}f$ band inversion scenarios. The $4f,5d$, and $6s$ orbital character derived bands are represented by red, blue, and green colored symbols, respectively. The size of the symbols represent the weight of the various orbital contributions to the underlying bands. The Brillouin zone of an fcc lattice is displayed along with the eight time reversal invariant momenta (TRIM) points.

Figure 2

Left: Surface Bloch spectral density $\left[A_{\mathrm{Bl}}\left(k\right)\right]$ of the first 12 SmO layers of a semi-infinite solid with [001] surface. Note that there are two Dirac cones at the $\overline{X}$ point, while the one at the $\overline{\mathrm{\Gamma }}$ point falls into the bulk projected band structure and hence forms a surface resonance (see right panel). Right: $A_{\mathrm{Bl}}\left(k\right)$ with a downward shifted $4f$-electron pocket around the $\overline{\mathrm{\Gamma }}$ point to reveal the third Dirac cone.

Figure 3

Maximum possible $f$ valence due to $f⟶d$ or $f⟶s$ promotion in SmO while retaining the nontrivial topology as a function of lattice parameter. The color map follows that of Fig. 1: light blue = nontrivial topology from $d\text{−}f$ inversion, light green = nontrivial topology from $s\text{−}f$ inversion, light pink = trivial topology. The equilibrium lattice parameters for a high-spin 3+ and 2+ state are computed using the L(S)DA+SO+$U$ scheme (dashed red line). The estimates from an empirical extrapolation for the limiting cases are obtained from Ref. [43] (dashed green line). The filled green circle denotes the experimental bulk SmO. SmO remains a topological semimetal for a wide range of tensile strain $(\ge 1\%)$, since the calculated maximum valence is above both the empirical extrapolation and L(S)DA+U+SO estimates.

Figure 4

The calculated FPLO band structure of SmO $(a=4.941\AA )$ within a nonspin polarized, full-relativistic approximation including strong Coulomb correlation (LDA+SO+$U)$. A $U$ and $J_H$ value of 6 and 0 eV have been used, respectively. The size of the symbols represent the weight of the various orbital contributions to the underlying bands. The numbers within parentheses are band indices to assist in assigning the various topological indices in Table 1.

Figure 5

Band structure of SmO with orbital character using MBJLDA+SO approximation as implemented in WIEN2K. The topology and order of the bands are consistent to the ones obtained using the LDA+SO+$U$ scheme. The blow-up in the bottom panel clearly shows the opening of the warped band gap along $\mathrm{\Gamma }\text{−}X$, but smaller in size compared to FPLO. For clarity we have plotted the bands without any band character.

Figure 6

Bulk and surface Brillouin zone of an fcc lattice.