Basic electronic properties of iron selenide under variation of structural parameters

Since the discovery of high-temperature superconductivity in the thin-film $\mathrm{FeSe}/{\mathrm{SrTiO}}_3$ system, iron selenide and its derivates have been intensively scrutinized. Using ab initio density functional theory calculations we review the electronic structures that could be realized in iron selenide if the structural parameters could be tuned at liberty. We calculate the momentum dependence of the susceptibility and investigate the symmetry of electron pairing within the random phase approximation. Both the susceptibility and the symmetry of electron pairing depend on the structural parameters in a nontrivial way. These results are consistent with the known experimental behavior of binary iron chalcogenides and, at the same time, reveal two promising ways of tuning superconducting transition temperatures in these materials: on one hand by expanding the iron lattice of FeSe at constant iron-selenium distance and, on the other hand, by increasing the iron-selenium distance with unchanged iron lattice.

Figure 1

Crystal structure of FeSe (top) and summary of the four ways to increase the superconducting transition temperature $T_c$ (bottom) by changing lattice parameters $a,c$, and $d$, as described in the main text. Arrows indicate the change in lattice parameter. An up arrow represents enlargement, a down arrow represents shrinking, while a horizontal arrow represents keeping the parameter unchanged compared to the experimental pristine FeSe.

Figure 2

Electronic band structure with orbital weights indicated by colors for varied iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}$ and lattice parameter $a$. (a)–(c) $a=3.5\AA =0.93a_{\exp }$, (d)–(f) $a=3.8\AA =1.01a_{\exp }$, and (g)–(i) $a=4.1\AA =1.09a_{\exp }$. First row (a), (d), (g) $d_{\mathrm{Fe}-\mathrm{Se}}=2.35\AA =0.98d_{\exp }$, second row (b), (e), (h) $d_{\mathrm{Fe}-\mathrm{Se}}=2.37\AA =0.99d_{\exp }$, and third row (c), (f), (i) $d_{\mathrm{Fe}-\mathrm{Se}}=2.393\AA \equiv d_{\exp }$. Arrows mark points where changes in the band structure happen as a function of parameters.

Figure 3

Electronic band structure with orbital weights indicated by colors at constant lattice parameter $a=a_{\exp }$ and varied iron-selenium distance $d$. (a) $d_{\mathrm{Fe}-\mathrm{Se}}=2.447\AA =1.02d_{\exp }$, (b) $d_{\mathrm{Fe}-\mathrm{Se}}=2.348\AA =0.98d_{\exp }$, and (c) $d_{\mathrm{Fe}-\mathrm{Se}}=2.256\AA =0.94d_{\exp }$. Arrows mark points where changes in the band structure happen as a function of parameters.

Figure 4

Fermi surface with orbital weights indicated by colors for varied iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}$ and lattice parameter $a$. (a)–(c) $a=3.5\AA =0.93a_{\exp }$, (d)–(f) $a=3.8\AA =1.01a_{\exp }$, and (g)–(i) $a=4.1\AA =1.09a_{\exp }$. First row (a), (d), (g) $d_{\mathrm{Fe}-\mathrm{Se}}=2.35\AA =0.98d_{\exp }$, second row (b), (e), (h) $d_{\mathrm{Fe}-\mathrm{Se}}=2.37\AA =0.99d_{\exp }$, and third row (c), (f), (i) $d_{\mathrm{Fe}-\mathrm{Se}}=2.393\AA \equiv d_{\exp }$. Arrows mark points where changes in the Fermi surface happen as a function of parameters.

Figure 5

Fermi surface with orbital weights indicated by colors at constant lattice parameter $a=a_{\exp }$ and varied iron-selenium distance $d$. (a) $d_{\mathrm{Fe}-\mathrm{Se}}=2.447\AA =1.02d_{\exp }$, (b) $d_{\mathrm{Fe}-\mathrm{Se}}=2.348\AA =0.98d_{\exp }$, and (c) $d_{\mathrm{Fe}-\mathrm{Se}}=2.256\AA =0.94d_{\exp }$. Arrows mark points where changes in the Fermi surface happen as a function of parameters.

Figure 6

Nearest $\left(t_1\right)$ and next-nearest $\left(t_2\right)$ neighbor hopping parameters in the Fe $3d_{xy}$ orbitals (a) as function of lattice parameters $a$ at fixed iron-selenium distance (a) $d_{\mathrm{Fe}-\mathrm{Se}}=2.35\AA =0.98d_{\exp }$, (b) $d_{\mathrm{Fe}-\mathrm{Se}}=2.37\AA =0.99d_{\exp }$, and (c) $d_{\mathrm{Fe}-\mathrm{Se}}=2.393\AA \equiv d_{\exp }$. (d) The hoppings at fixed lattice parameter $a=3.76988\text{Å}\equiv a_{\exp }$ and varied iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}$.

Figure 7

Static susceptibility on a high-symmetry path as a function of the lattice parameter $a$. The iron-selenium distance is kept fixed at (a) $d_{\mathrm{Fe}-\mathrm{Se}}=0.98d_{\mathrm{Fe}-\mathrm{Se}\exp }$, (b) $d_{\mathrm{Fe}-\mathrm{Se}}=0.99d_{\mathrm{Fe}-\mathrm{Se}\exp }$, and (c) $d_{\mathrm{Fe}-\mathrm{Se}}=d_{\mathrm{Fe}-\mathrm{Se}\exp }$.

Figure 8

Static susceptibility on a high-symmetry path as a function of $d_{\mathrm{Fe}-\mathrm{Se}}$ at fixed lattice parameter $a=a_{\exp }$.

Figure 9

Pairing eigenvalues $\lambda$ as a function of the lattice parameter $a$ at fixed iron-selenium distance $d=0.98d_{\mathrm{Fe}-\mathrm{Se}\exp }$.

Figure 10

(a) Pairing eigenvalues $\lambda$ and (b) orbital-resolved density of states $\rho$ at the Fermi level as a function of the lattice parameter $a$ at fixed iron-selenium distance $d=0.99d_{\mathrm{Fe}-\mathrm{Se}\exp }$.

Figure 11

(a) Pairing eigenvalues $\lambda$ and (b) orbital-resolved density of states $\rho$ at the Fermi level as a function of the lattice parameter $a$ at fixed iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}=d_{\mathrm{Fe}-\mathrm{Se}\exp }$.

Figure 12

Pairing eigenvalues $\lambda$ as a function of the iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}$ at fixed lattice parameter $a=a_{\exp }$.

Figure 13

Pairing eigenvalues $\lambda$ as a function of the lattice parameter $c$ at fixed lattice parameter $a=a_{\exp }$ and fixed iron-selenium distance $d_{\mathrm{Fe}-\mathrm{Se}}=d_{\mathrm{Fe}-\mathrm{Se}\exp }$.