Topological band inversion in HgTe(001): Surface and bulk signatures from photoemission

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular, due to coupling of the Te $5p$-derived valence electrons to Hg $5d$ core states at shallow binding energy. We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of: (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg $5d$ states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its nontrivial band topology.

Figure 1

(a) Bulk Brillouin zone with high-symmetry points. The $k$-space path for the panels (d)–(f) is indicated in red. (b) $k_x\text{−}{k}_z$ ARPES data sets obtained from $h\nu$-dependent measurements. (c) ARPES data set for HgTe(001) around the $\mathrm{\Gamma }$ point ($h\nu =123\mathrm{eV}$) and corresponding calculation of the bulk band structure. (d) ARPES data along high-symmetry directions. For maximal visibility we plot the sum of data sets for $p$- and $s$-polarized light (cf. Fig. 3). (e) and (f) Calculations of the (001)-projected surface and bulk spectral functions.

Figure 2

(a) Angle-integrated photoemission data of the Hg $5d$ states in comparison to DFT calculations based on different exchange-correlation functionals. (b) Calculated and measured band dispersion of the Hg $5d_{\frac{5}{2}}$ states.

Figure 3

(a) and (b) Constant-energy ARPES datasets obtained with $p$- and $s$-polarized light. The boundaries of the bulk BZ are indicated. (c) and (d) ARPES data along the $K-\mathrm{\Gamma }-K$ direction for $p$- and $s$-polarized light. (e)–(g) Calculations of the (001)-projected surface spectral function along $\mathrm{\Gamma }K$ projected on different Te $5p$ orbitals. (h) Schematic of the experimental geometry. The datasets in all panels were taken with $h\nu =123\mathrm{eV}$.

Figure 4

(a) ARPES data near the $\mathrm{\Gamma }$ point taken with $h\nu =123\mathrm{eV}$ and $p$-polarized light. The inset shows ARPES data obtained with with He $I_{\alpha }$ line ($h\nu =21.2\mathrm{eV}$) for which the cross section of the topological surface state is much larger than for the bulk bands. (b) Calculated bulk band structure projected on Te $5p_z$ and Hg $6s$ orbitals. (c) and (d) ARPES datasets measured at (b) $T=40\mathrm{K}$ and (c) $300\mathrm{K}$ ($h\nu =21.2\mathrm{eV}$).