Detection of Image Potential States above the vacuum level in GeTe

TL;DR

This work reveals, for the first time in a semiconductor, image-potential states (IPS) that extend up to $0.8\ \mathrm{eV}$ above the vacuum level on the ferroelectric GeTe(111) surface. By combining time- and angle-resolved photoemission spectroscopy (TR-ARPES) with Bloch spectral-function calculations, the authors resolve three IPS with parabolic in-plane dispersions, extract their binding energies, and show they follow a hydrogen-like Rydberg series $E_B(n)=\frac{\epsilon-1}{\epsilon+1}\cdot\frac{0.85\ \mathrm{eV}}{(n+a)^2}$. The unusually large extension above the vacuum is explained by a strong dipole coupling and a large reservoir of initial states that populate the IPS, together with a $1/z$-converging surface barrier that sustains the IPS in the vacuum region. These findings highlight the role of ferroelectric polarization in IPS formation and open avenues for spin-resolved and time-resolved studies of IPS dynamics in polar semiconductors.

Abstract

The ferroelectric semiconductor α-GeTe(111) has attracted significant attention in the last decade due to its unique properties, with extensive studies focusing on its occupied electronic bandstructure. In contrast, its unoccupied states - particularly those near the conduction band minimum - remain largely unexplored. In an effort to characterize those states, we surprisingly observe three image potential states (IPS) in α-GeTe(111) extending up to 0.8 eV above the vacuum level. Using time and angle-resolved photoemission spectroscopy, we resolve the full parabolic dispersions of the first three IPS and determine their binding energies. Our analysis, combined with Bloch spectral function calculations, reveals that the unexpected persistence of IPS above the vacuum level originates from strong dipole transitions and the presence of large electron reservoirs in GeTe.

Figures (9)

• Figure 1: Bandstructure of $\alpha$-GeTe(111). (a) ARPES measurements along $\overline{K\Gamma K}$ at 50 K with a probe photon energy of 21.2 eV with highlighted bulk (B1), surface resonance (SR) and surface states (SS). The photoemission intensity is plotted against the wavevector $k_{\parallel }$ and initial state energy $E-E_F$. (b) Snapshot of a TR-ARPES measurement along the $\overline{\Gamma K}$ direction (in the red area in (a)) at 90 K, taken with a UV photon energy of 6.3 eV and an IR photon energy of 1.55 eV obtained at negative IR-UV delays (integrated between $-50$ fs and $-250$ fs). (c) Same than (b) but integrated between $+50$ fs and $+275$ fs).
• Figure 2: Time-Resolved evolution of the Bandstructure of $\alpha$-GeTe(111) : Difference map of the intensity at normal emission between every delay and the one at $t_{IR}-t_{UV}=650$ fs, assumed to be close to equilibrium. Red and blue colors indicate an increase or loss in spectral weight with respect to equilibrium, respectively. Inset : Bulk Brillouin zone of GeTe and its surface projected plane along the [111] direction.
• Figure 3: Evolution of the IPS as a function of IR photon energy. Collection of time-resolved ARPES measurements along the high-symmetry line $\overline{K\Gamma}$, taken with an UV photon energy of 6.3 eV and for different IR energies as indicated at zero time delay. The IPS and replica are highlighted. The energy axis refers to the energy of the intermediate state in the two-photon transition with respect to the vacuum level. The energy axes are aligned such that the initial state energy is at constant height, as can be seen from the occupied surface states. The dashed line in panel (a) represents the parabolic curves used to extract the effective mass of the IPS.
• Figure 4: Evolution of the IPS below and above the vacuum level. (a) Collection of time-resolved ARPES measurements along the high-symmetry line $\overline{K\Gamma}$, taken with an UV photon of energy 6.3 eV and an IR photon of energy 1.55 eV that arrive simultaneously at $t_0$ to follow the whole dispersion of the $n=2$ and $n=3$ IPS above and below the vacuum level. (b) Exemplary time trace of the $n=2$ IPS (at $E-E_{Vac}=0.12$ eV - see purple box C in (a)) as a function of IR-UV delay with a fitting procedure (black) to decompose the dynamical background (gray) and the IPS contribution from the signal (dark red). (c) Evolution of the fitted intensity of the $n=2$ IPS as a function of its energy to vacuum level. (d) Collection of Intensity time traces of the $n=2$ at different $E-E_{\text{Vac}}$ (see boxes in (a) labelled from A through E) after dynamical background subtraction. Note that the green curve has been multiplied by a factor of $0.7$ for the sake of comparison. (e) Evolution of the fitted depopulation time of the $n=2$ IPS as a function of energy to the vacuum level.
• Figure 5: Comparison between the experimentally observed bandstructure (same parameters as in Fig. \ref{['fig:1']}), theoretical calculations, and projected IPS. Pink arrows indicate the different reservoirs and population pathways feeding the intermediate IPS states.