Predicted electronic markers for polytypes of $\mathrm{LaOBi}{\mathrm{S}}_2$ examined via angle-resolved photoemission spectroscopy

The natural periodic stacking of symmetry-inequivalent planes in layered compounds can lead to the formation of natural superlattices; albeit close in total energy, (thus in their thermodynamic stability), such polytype superlattices can exhibit different structural symmetries, thus have markedly different electronic properties which can in turn be used as “structural markers”. We illustrate this general principle on the layered $\mathrm{LaOBi}{\mathrm{S}}_2$ compound where density-functional theory (DFT) calculations on the ($\mathrm{Bi}{\mathrm{S}}_2$)/(LaO)/($\mathrm{Bi}{\mathrm{S}}_2$) polytype superlattices reveal both qualitatively and quantitatively distinct electronic structure markers associated with the Rashba physics, yet the total energies are only ∼ 0.1 meV apart. This opens the exciting possibility of identifying subtle structural features via electronic markers. We show that the pattern of removal of band degeneracies in different polytypes by the different forms of symmetry breaking leads to Rashba “minigaps” with characteristic Rashba parameters that can be determined from spectroscopy, thereby narrowing down the physically possible polytypes. By identifying these distinct DFT-predicted fingerprints via angle-resolved photoemission spectroscopy (ARPES) measurements on $\mathrm{LaBiO}{\mathrm{S}}_2$ we found the dominant polytype with small amounts of mixtures of other polytypes. This conclusion, consistent with neutron scattering results, establishes ARPES detection of theoretically established electronic markers as a powerful tool to delineate energetically quasidegenerate polytypes.

Figure 1

(a) The layered structure of $\mathrm{LaOBi}{\mathrm{S}}_2$ with the unit cell indicated by the black frame. The green, red, purple, and yellow balls represent La, O, Bi, and S atoms, respectively. Note that there are two $\mathrm{Bi}{\mathrm{S}}_2$ layers in each unit cell. (b) Different stacking configurations of two $\mathrm{Bi}{\mathrm{S}}_2$ layers for unstable structure ${\mathrm{T}}_0$ and its three stable polytypes ${\mathrm{T}}_1–{\mathrm{T}}_3$. Compared with ${\mathrm{T}}_0$, the Bi-S1 2D networks of ${\mathrm{T}}_1–{\mathrm{T}}_3$ have an in-plane distortion showing displacement of the S1 atom along the $x$ or $y$ direction, and thus two different Bi-S1 bond lengths.

Figure 2

(a) Illustration of two types of band motifs (BM) classified by the degree of degeneracy (indicated by the number in parentheses) at the X (1/2, 0, 0) and Y (0, 1/2, 0) points. Type-I BM manifests the fourfold degenerate Dirac point, which breaks into a pair of twofold degenerate points with a minigap Δ (horizontal arrows) as type-II BM. Off high-symmetry points X or Y, type-II BM can have twofold degenerate bands (black) or single degenerate bands (red and blue) according to the presence of inversion symmetry. (b–e) Band structures of ${\mathrm{T}}_0–{\mathrm{T}}_3$ polytypes show different BM types at X and Y point, which act as an electronic marker. Beyond the X or Y points in either direction of these plots is the M point. The BM types are summarized in (f).

Figure 3

(a) Fermi map of lightly $n$-doped $\mathrm{LaBiO}{\mathrm{S}}_2$ in the first Brillouin zone. Electron pockets are found near the X/Y points, the zoomed-in version of which is shown in (b). ARPES spectra along high-symmetry cut Γ-Y/X-M (black arrows) are shown in (c) for conduction and valence bands. The data are raw and unsymmetrized, taken under 60 eV, circular-left polarized light coming along Γ-Υ with 45° incidence angle in Swiss Light Source beamline 9L. Similar data on five other samples were obtained at the Swiss Light Source beamline 9L as well as at the Advanced Light Source beamlines 4.0.3 and 10.0.1.

Figure 4

ARPES spectra of the valence band near (a) the X pocket and (b) the Y pocket. Data were taken at ALS beamline 10.0.1 with 60 eV, linear horizontal polarized light coming in at a glancing angle along the Γ-X/Γ-Y direction, with the sample's azimuth angle rotated by 90° from (a) to (b).

Figure 5

Experimental spectra of (a) conduction bands along M-X-M direction; (b) conduction bands along Γ-Y-Γ direction, (c) valence bands along M-X-M direction, and (d) valence bands along Γ-Y-Γ direction, to be compared with DFT calculations of ${\mathrm{T}}_0,{\mathrm{T}}_1,{\mathrm{T}}_2$, and ${\mathrm{T}}_3$, respectively. ARPES spectra were taken under 60 eV, linear horizontal polarized light coming along the Γ-Y direction, with 45° incidence angle in Swiss Light Source beamline 9L. Similar data on five other samples were obtained at the Swiss Light Source beamline 9L as well as at the Advanced Light Source beamlines 4.0.3 and 10.0.1.

Figure 6

ARPES spectra (left panel) of (a) conduction bands along M-X-M cut; (b) conduction bands along Γ-Y-Γ cut; (d) valence bands along M-X-M cut, and (e) valence bands along Γ-Y-Γ cut, compared with DFT calculations (right panel) for ${\mathrm{T}}_1$ (red dash), ${\mathrm{T}}_2$ (blue dot), and ${\mathrm{T}}_3$ (black solid), respectively. (c) EDC at the X/Y point, the local maxima of which should correspond to the dominant bands while the local minimum suggests the existence of gapping. The size of the minigap can be estimated from the distance between the two peaks.

Figure 7

Simulations of ARPES spectra for the ${\mathrm{T}}_1,{\mathrm{T}}_2$, and ${\mathrm{T}}_3$ polytypes (top three rows, respectively) compared with ARPES data (bottom row). Left two columns: CB spectra along M-X-M and along Γ-Y- Γ. Right two columns: VB spectra along M-X-M and Γ-Y- Γ. All spectra in the bottom row were taken with 60-eV circular left polarized light coming along the Γ-Y direction at the Swiss Light Source beamline 9L.