Unveiling the complete dispersion of the giant Rashba split surface states of ferroelectric $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ by alkali doping

$\alpha \text{−}\mathrm{GeTe}\left(111\right)$ is a noncentrosymmetric ferroelectric material for which a strong spin-orbit interaction gives rise to giant Rashba split states in the bulk and at the surface. The detailed dispersions of the surface states inside the bulk band gap remains an open question because they are located in the unoccupied part of the electronic structure, making them inaccessible to static angle-resolved photoemission spectroscopy. We show that this difficulty can be overcome via in situ potassium doping of the surface, leading to a rigid shift of 80 meV of the surface states into the occupied states. Thus, we resolve, in great detail, their dispersion and highlight their crossing at the $\overline{\mathrm{\Gamma }}$ point, which, in comparison with density functional theory calculations, definitively confirms the Rashba mechanism.

Figure 1

(a) Crystal structure of $\alpha \text{−}\mathrm{GeTe}$ along the [111] crystallographic direction (right) and the corresponding projection on the (111) atomic plane (bottom left). The 2D unit-cell (green rhombus) parameter is extracted from x-ray-diffraction measurements [41]. (b) Corresponding three-dimensional BZ and its 2D projection on the (111) plane (blue). (c) STM image of the bare $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ surface ($U=-1.5\mathrm{V},I=0.15\mathrm{nA}$) and associated LEED pattern in the top right corner. The 2D unit cells in real and reciprocal spaces are indicated in green. (d) STM image of the $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ surface covered by 0.09 monolayer (ML) of K ($U=-1.5\mathrm{V},I=0.15\mathrm{nA}$) and the associated LEED pattern in the top right corner.

Figure 2

ARPES spectra along the $\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ high-symmetry line of the 2D BZ (left) and the corresponding energy-distribution curve (EDC) taken at $k=0$ (right) for (a) bare $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and (d) $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$. Associated constant energy surfaces taken at $E-E_F=0$ and $E-E_F=50\mathrm{meV}$ for (b) and (c) bare $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and (e) and (f) $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$.

Figure 3

(a) Fermi-Dirac distribution divided (at RT) ARPES spectrum along the $\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ high-symmetry line of the 2D BZ for the $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$ surface. The dashed-blue and red lines correspond to guides to the eye showing the full dispersions of ${\mathrm{SS}}_1$ and ${\mathrm{SS}}_2$. (b) BSF calculations of Te-terminated $\alpha \text{−}\mathrm{GeTe}\left(111\right)$. (c) and (d) ARPES spectra of $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and $\alpha \text{−}\mathrm{GeTe}\left(111\right)$. The solid red and blue lines are shifted by 80 meV up to $E_F$ in (d) compared to panel (a). (e) Momentum distribution curves (MDCs) associated with the horizontal colored-dashed lines in panels (c) and (d).

Figure 4

XPS spectrum of the $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ surface obtained after the initial desorption procedure to remove the capping layer. The photon energy is $h\nu =1486.6\mathrm{eV}$.

Figure 5

Series of LEED patterns (top) and ARPES spectra (bottom) along the $\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ high-symmetry line of the 2D BZ for (a) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$, (b) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ with 1 min of K deposition, (c) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ with 10 min of K deposition, and (d) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ with 10 min of deposition followed by an annealing at 500 K. Note that the spectra from panels (a) and (d) have been measured with better statistics and with a smaller energy step compared to panels (b) and (c). (e) Corresponding low-energy cutoff of the secondary electrons as probed by ${\mathrm{HeI}}_{\alpha }$ photoemission by applying a voltage bias of $-8\mathrm{V}$ to the sample surface.

Figure 6

Temperature-dependent ARPES measurements along the $\overline{K}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ high-symmetry line of the 2D BZ at RT for (a) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and (b) $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and at $T=80\mathrm{K}$ for (c) $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ and (d) $K/\alpha \text{−}\mathrm{GeTe}\left(111\right)$.