Interplay of paramagnetism and topology in the Fe-chalcogenide high-$T_c$ superconductors

The high-$T_c$ superconductor, $\mathrm{FeT}{\mathrm{e}}_{0.55}\mathrm{S}{\mathrm{e}}_{0.45}$, has recently been shown to support a surface state with topological character. Here we use low-energy laser-based angle-resolved photoemission spectroscopy with variable light polarization, including both linear and circular polarizations, to reexamine the same material and the related $\mathrm{FeT}{\mathrm{e}}_{0.7}\mathrm{S}{\mathrm{e}}_{0.3}$, with a larger Te concentration. In both cases, we observe the presence of a surface state displaying linear dispersion in a cone-like configuration. The use of circular polarization confirms the presence of a helical spin structure. These experimental studies are compared with theoretical studies that account for the local magnetic effects related to the paramagnetism observed in this system in the normal state. In contrast to previous studies, we find that including the magnetic contributions is necessary to bring the chemical potential of the calculated electronic band structure naturally into alignment with the experimental observations.

Figure 1

(a) ARPES measurement of the electronic structure around the Γ point of $\mathrm{FeT}{\mathrm{e}}_{0.55}\mathrm{S}{\mathrm{e}}_{0.45}$ using $p$-polarized light; (b) same measurement as in (a), but now $\mathrm{FeT}{\mathrm{e}}_{0.7}\mathrm{S}{\mathrm{e}}_{0.3}$ using $p$-polarized light; (c) same measurement as in (b), but using $s$-polarized light. (d)–(f) Cuts through the spectral maps in (a)–(c) showing EDCs in the vicinity of the Γ point. The temperatures associated with the different measurements are indicated in (a)–(c).

Figure 2

The Dirac cone as seen on $\mathrm{FeT}{\mathrm{e}}_{0.55}\mathrm{S}{\mathrm{e}}_{0.45}$ using (a) left-circularly polarized light and (b) right-circularly polarized light. The Dirac point is located at approximately 8.5 meV below the chemical potential. (c) MDC cuts through spectra measured with left-polarized (red) and right-polarized (blue) light as a function of binding energy (meV) as indicated. In all cases, the sample is held at 15 K in the normal state.

Figure 3

Calculated $k$-projected band structures along $\mathrm{\Gamma }-Z$. (a) Nonmagnetic bands with (lower panel) and without (upper panel) spin-orbit coupling. The SOC-induced gap is indicated by the circle. (b) Magnetic bands without SOC and with SOC for in-plane ($x$) and perpendicular ($z$) moments. Note the different energy scale (factor of 2) between (a) and (b) and the position of the zero energy (set to the calculated Fermi level).

Figure 4

Calculated $k$-projected bands for $k_{\left|\right|}$ in $k_z$ planes at the band maxima about $Z$ for (a) perpendicular ($z$) and (b) in-plane ($x$) moments along different directions as shown in the schematic in the upper right panel. The color corresponds to the calculated spectral weight; since bands of similar character (determined by the overlap with respect to $k$) are found to have similar spectral weight, the spectral weight becomes a proxy for wave-function character in the plots. (c) Bands for perpendicular moments over a $0.08\times 0.08{\AA }^{-1}$ region for $k_z$ at $\sim 0.4Z$, at $Z$, and at $\sim 0.6Z$. Note the two maxima in the lower band, and that the gap remains for each $k_z$.