Rich nature of the topological semimetal states in InBi

Spin-orbit coupling (SOC) plays a significant role in the development of topological physics. For example, considering the SOC effect would lead to the formation of a topological insulator with band inversion in a time-reversal symmetry-preserved system and the realization of a Chern phase in a time-reversal symmetry-broken system. Here, by using angle-resolved photoemission spectroscopy combined with first-principles electronic structure calculations, we report SOC-induced “hidden” Dirac bands near the Fermi level in the nonsymmorphic topological semimetal InBi. We clearly observe Dirac-like bulk band crossings located at the corner and boundary of the Brillouin zone, providing compelling evidence for three-dimensional Dirac semimetal states. By means of in situ potassium dosing on the crystal surface, we are able to reveal a partial Dirac nodal line along the $k_z$ direction formed by Dirac fermions close to the Fermi level. Our results not only demonstrate the rich topological states in InBi but also offer a good platform for engineering topologically nontrivial phases.

Figure 1

Crystal structure and electronic structures of InBi. (a) Schematic crystal structure of InBi with space group $P4/nmm$ (No. 129). InBi has a preferred cleaving plane between ${\mathrm{InBi}}_4$-tetrahedron layers. (b) 3D and (001)-projected BZs of InBi with marked high-symmetry points and lines. Cuts 1–4 indicate the locations of the experimental band structures in Fig. 2. (c) Calculated band structure without the SOC effect along high-symmetry lines. (d) Same as (c) with the SOC effect. Insets: Zoomed-in electronic band structure near $E_{\mathrm{F}}$ at the $R$ and $M$ points, respectively. (e) Core-level photoemission spectrum of InBi recorded by 200-eV photons with peaks from each element indicated. (f) Photoemission intensity plot with $h\nu =17\mathrm{eV}$ at $E_{\mathrm{F}}$ measured in the $k_z\sim 0$ plane. (g) Same as (f) measured with $h\nu =25\mathrm{eV}$ in the $k_z\sim \pi$ plane. The blue solid lines in (f) and (g) indicate the (001)-surface BZs.

Figure 2

Near-$E_{\mathrm{F}}$ band structures along high-symmetry lines. (a) Photoemission intensity plot and corresponding second derivative intensity plot along the $Z\text{−}R$ direction [cut 1 in Fig. 1]. (b) Same as (a) along the $\mathrm{\Gamma }\text{−}M$ direction [cut 2 in Fig. 1]. The appended red solid curves are the bulk band calculations considering the SOC effect. (c), (d) MDC plots around the $R$ and $M$ points, respectively. The blue dashed lines indicate the linear band dispersions. (e), (f) Photoemission intensity plots along the $\mathrm{\Gamma }\text{−}X$ and $Z\text{−}A$ directions [cuts 3 and 4 in Fig. 1], respectively.

Figure 3

Photon-energy-dependent measurements of InBi. (a), (b) ARPES intensity plots of the pristine InBi (sample No. 1) in the $k_z\text{−}{k}_{\parallel }$ plane at $E_{\mathrm{F}}$ and 0.75 eV below $E_{\mathrm{F}}$ with $k_{\parallel }$ oriented along the $\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ direction, respectively. (c) Intensity plot of pristine InBi taken along the $X\text{−}R$ direction, as indicated by the red solid line in (a). (d) Photoemission intensity plots measured with variable photon energies along the $\overline{X}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{X}$ line after potassium dosing on sample No. 2, where DP1 sinks below $E_{\mathrm{F}}$ at the $R$ point (leftmost panel). The appended red dashed lines are guides to the eye for the linear band crossings. The Dirac nodal line is indicated by the white solid curve. (e) MDC plots of (d)(i)–(d)(v). The momentum range is indicated by the red solid rectangle in (d). The black dashes indicate the linear bands forming DP1.