Emergence of Dirac-like bands in the monolayer limit of epitaxial Ge films on Au(111)

After the discovery of Dirac fermions in graphene, it has become a natural question to ask whether it is possible to realize Dirac fermions in other two-dimensional (2D) materials as well. In this work, we report the discovery of multiple Dirac-like electronic bands in ultrathin Ge films grown on Au(111) by angle-resolved photoelectron spectroscopy. By tuning the thickness of the films, we are able to observe the evolution of their electronic structure when passing through the monolayer limit. Our discovery may signify the synthesis of germanene, a 2D honeycomb structure made of Ge, which is a promising platform for exploring exotic topological phenomena and enabling potential applications.


Introduction
Since the discovery of the extraordinary physical and electronic properties of graphene, there has been an intense effort to synthesize two-dimensional (2D) honeycomb structures based on heavier elements than carbon, in order to realize new topological phenomena that are driven by spin-orbit coupling (SOC), such as the quantum spin-Hall (QSH) [1][2][3] or quantum anomalous-Hall (QAH) [4,5] effects. One promising family of materials to host these exotic effectssilicene [6], germanene [6,7], and stanene [7,8] is built out of the group IV elements Si, Ge and Sn, which are predicted to form buckled honeycomb structures. Similar to graphene, these structures are expected to host Dirac fermions with a linear dispersion relation in the vicinity of the K/K' points of their hexagonal Brillouin zones. However, unlike graphene, for which SOC is too small to induce a measureable band gap, silicene, germanene, and stanene are predicted to open a gap at K/K' on the order of ~1.6 meV [6], ~24 meV [6], and ~100 meV [8], respectively, which is crucial to observe and utilize the QSH and QAH effects at elevated temperatures, and may pave the way for future applications. It should be noted that Dirac fermions can also be realized in other 2D materials, such as binary honeycomb structures [9] or non-symmorphic 2D materials [10].
For the cases of silicene and stanene, a large number of experimental studies investigated the electronic structure of ultra-thin films of Si and Sn on various metallic and insulating substrates [11][12][13][14][15]. Although initial reports claimed the existence of Dirac dispersions for silicene on Ag(111) [11], more recent studies found that these are likely to be caused by substrate interactions [16][17][18][19][20].
Scanning tunneling spectroscopy (STS) studies found evidence for a Dirac dispersion in some of these systems [14] , but due to the lack of momentum resolution, it was not possible to disentangle the signal from the Dirac fermions and other bands in the vicinity of the Fermi level. An angle-resolved photoelectron spectroscopy (ARPES) study on a thick film of Ge grown on Au(111), corresponding to about ~4.5 monolayers (ML) of germanene, reported the appearance of a quasi-linear band that crosses the Fermi level close to the point of the underlying Au(111) substrate surface Brillouin zone [26]. However, further investigations are required to determine how this additional band is related to the predicted Dirac fermions in single-layer germanene, or whether it may be induced by the underlying metallic substrate, as was suggested for similar bands found in silicene. For the growth of germanene on Al(111), a buckled structure with a relatively simple registry between 2x2 monolayer Ge on a 3x3 Al (111) substrate was shown by Derivaz et al. [22]. However, ab-initio calculations have suggested that a strong hybridisation between the Ge and the Al metallic substrate bands would wash out any sign of the Dirac dispersions [27]. On the other hand, some ab-initio calculations would suggest that Ge on Ag or Au(111) could be a more promising route to realise Dirac dispersions [27,28], while others suggest that interactions with the substrate Au d bands will destroy germanene's Dirac dispersion for Ge on Au(111) [29]. Thus, the presence of Dirac fermions in grapheneanalogues supported by metallic substrates requires experimental confirmation.
In the present work, by performing comprehensive ARPES measurements, we study the electronic structure of ultra-thin Ge films grown on Au(111). By tuning the thickness of the Ge layer, we are able to track the evolution of the resulting band structure from a sub-ML to the trilayer regime, which allows us to identify bands that are replicated from the Au(111) substrate.
In the ML limit, by tuning the incident photon polarization, we are able to unmask a number of previously unreported linearly dispersing Dirac-like bands, which may originate from rotationally disordered germanene.

Results and discussion 2.1. Film characterization
To experimentally determine the thickness of the Ge films, we exploited a shift in the binding energy of the Ge 3d doublet peak for different chemical environments of the Ge atoms. As shown in Figure 1(a), for a Ge film of nominal 1.0 Å thickness (upper panel), the photoemission intensity is dominated by the Ge 3d doublet at higher binding energies, similar to previous reports [15] . When substantially increasing the film thickness to 7.2 Å (lower panel), the photoemission intensity, which is extremely surface-sensitive, is instead dominated by a doublet at lower binding energies, since the chemical environment of Ge in an epitaxial multilayer sample is distinct from the sub-ML case of the Ge-Au interface. At a nominal deposition of 2.6 Å, the two doublets are observed to coexist, supporting that this sample is close to the ML limit. We furthermore performed scanning tunneling microscopy measurements to confirm that a Ge monolayer is approximately 2.5 Å thick, which can be found in the supplementary material. The formation of a ML of Ge is also evident as a structural transition in the low-energy electron diffraction (LEED) images shown in Figure 1 This 8x8 reconstruction is always observed in samples with a thickness from ~1 to at least 3 MLs (as can be seen in Figure 1(d)), indicating epitaxial growth in this regime and no further structural phase transitions.

Band structure evolution with film thickness
In Figure  However, as we will show below, there is strong evidence that these bands may actually originate from the Ge layers. linear-vertical, which will be discussed in the next section. Increasing the nominal film thickness to 7.2 Å leads to a broadening of these new bands, which can be seen in Figure 3(d), as well as the disappearance of the replica bands from Figure 3(b).

Emergence of multiple Dirac-like bands in the monolayer limit
In Figure 4 we present evidence that the new bands emerging at the ML-limit may originate from the formation of germanene, rather than the metallic substrate. By switching the polarization of the incident photons with respect to the sample plane, we can unmask a set of bands that were previously hidden due to photoemission selection rules [30]. surface BZ. Although previous ab-initio calculations concluded that the strong hybridization between the substrate bands and the germanene bands will destroy any linear bands close to the Fermi level [16] , the 8x8 superstructure observed in the LEED image in Figure 1 m/s, which is similar to the order of magnitude reported in graphene [33].
We would like to note that, although there are currently no ab-initio calculations for germanene/Au(111) that include the large experimentally observed 8x8 superstructure, the folding of germanene's Dirac cone to the -point of the reconstructed BZ has recently been proposed for smaller superstructures based on ab-initio calculations [27]. Because of the folding, a strong hybridization with the substrate bands was avoided and the Dirac dispersion was preserved. It is therefore a plausible assumption that a similar mechanism can also exist for the larger 8x8 reconstruction, which needs to be confirmed by future theoretical work.

Conclusion
In summary, we have reported detailed core-level, LEED, and ARPES measurements of ultrathin Ge films grown on Au(111), with nominal thicknesses between 1.0 Å and 7.2 Å. Our ARPES spectra reveal Au(111) replica bands for the thinnest films, and the emergence of Diraclike dispersions at the ML limit, which persists for thicker films up to at least 7.2 Å. These bands may be caused by the folding of germanene's Dirac cones to other positions in momentum-space, due to the presence of an 8x8 surface superstructure, which prevents their hybridization with the substrate bands, similar to what has been proposed by recent ab-initio calculations for smaller reconstructions [27]. This is a remarkable finding since the interaction with metallic substrates was previously considered to preclude the existence of Dirac fermions in germanene on Au(111). Our results provide a strong motivation for future experimental studies investigating the precise microscopic structure of ultra-thin Ge films on Au(111), for instance by grazing incidence XRD. Such a structural determination will be necessary as an input for ab-initio band structure calculations that can consider the large 8x8 superstructure that we found experimentally. It will be furthermore interesting to probe the unoccupied states of the Dirac-like bands to observe the upper half of the Dirac cone that was proposed in the present work, which may be achieved via electron doping or pump-probe ARPES experiments.
Moreover, it will be interesting to try to reduce the influence of the Au(111) substrate on the band structure of the Ge thing films, e.g. by decoupling via hydrogen intercalation.

Methods
The ARPES measurements were performed on beamline I05 (Diamond Light Source, UK) [34].
The Au(111) substrate and Ge films were prepared and grown in-situ. The layer thickness was determined via the calibration of the deposition rate with a quartz crystal microbalance, and the observation of core level chemical shifts. Before the deposition of the Ge layers, a Bi layer of 0.8 Å nominal thickness was deposited as a surfactant. ARPES measurements were taken with a photon energy of 120 eV with linear horizontal and vertical polarization. The photoelectron energy and angular distributions were analyzed with a SCIENTA R4000 hemispherical analyzer. The measurement temperature was 10 K and the sample remained in a vacuum of <5x10 -10 Torr throughout the measurements. The angular resolution was 0.2°, and the overall energy resolution was better than 25 meV. The ab-initio calculations were performed using the generalized gradient approximation and the full-potential linear augmented plane-wave basis within the Wien2k package [35].

Au 4f peaks: suppression of Au(111) surface state and formation of new interface environment
The 4f core levels of pristine Au(111) surfaces display splittings within the 4f7/2 and 4f5/2 peaks due to the different chemical shifts in the bulk and on the surface, as can be seen in Figure S1.
However, the Au(111) surface peak is completely suppressed by the time the first ML of Ge is deposited, as a new Au-Ge interface environment develops. This interface layer has its own signature (labelled Int) as a shoulder at higher binding energy than the bulk peaks. The overall intensity of the Au substrate core levels is reduced as additional Ge is deposited on top, but the interface layer becomes relatively more pronounced compared to the bulk contribution as the Figure S1: Stacked XPS spectra covering the Au 4f core levels, obtained with 120 eV photon energy at 10 K in normal emission. Intensities are normalized to background at 80 eV binding energy.

The role of Bi as a surfactant
The role of a surfactant in thin-film growth is to encourage a change in the growth mode from 3D to epitaxial 2D growth. Sb (isovalent to Bi) was shown to be an effective surfactant for Ge film growth on Si(111) (T. Schmidt, R. Kröger, T. Clausen, J. Falta, A. Janzen, M. Kammler, P. Kury, P. Zahl, M. Horn-von Hoegen, Appl. Phys. Lett. 2005, 86, 111910), thus Bi is likely to play this role in germanene growth as well.

Bi 4f core levels: Bi rises to the top
A well-calibrated small quantity of Bi surfactant is deposited first onto the Au substrate, before the Ge deposition. However, it seems that after the growth, Bi is always found on the top surface of the sample, once the few-layer germanene is grown. The evidence for this is that the Ge 4f peak height is completely independent of germanene thickness, as shown in Figure S2. This is in contrast to the suppression of the underlying substrate Au 4f peaks, which occurs due to the surface-sensitivity of photoemission. Figure S2: Core level photoemission spectrum containing Bi 4f and Ge 3d peaks. The intensity of the Bi 4f peaks is independent of thickness. Data obtained with 120 eV photon energy. The data is normalized to the background. Figure S3: a) LEED obtained at ∼55 eV incident energy, on different samples. Red hexagons are used to indicate the first order Au(111) substrate peaks. Note that due to small distortions in the LEED images, in some places the spots deviate slightly from a perfect hexagon. Apart from the sub-ML coverage, all subsequent layers display qualitatively equivalent spectra, although the quality of the spectra is sample dependent (for a mixture of intrinsic and extrinsic reasons). The 2 ML* sample was not used for ARPES measurements. e-g) LEED at various energies on the 2 ML* sample; some prominent peaks associated with the dominant 8×8 reconstruction are circled in red. h) Detail of the 56 eV data from panel d). Orange and green circles highlight spots which do not conform to the 8×8 reconstruction, as discussed.

Submonolayer case: linking the LEED pattern with replica bands observed by ARPES
For the sub-ML case, the LEED pattern is qualitatively different to both the pristine Au (111) and the epitaxial few-layer films. One study (M. E. Dávila, G. Le Lay, Sci. Rep. 2016, 6, 20714) indexed a sub-ML LEED pattern of Ge on Au(111) to a combination of 19×19R(23.4°), 5×5, and 7×7R(19.1°) reconstructions, suggesting a number of variants are possible depending on the coverage; here the inclusion of Bi is also likely to play a role. In our sub-ML sample, a few weaker spots in the LEED pattern might be associated with a 5×5 pattern, but the most prominent spots are found as a regular hexagon around the first order substrate peak, which could be indexed to approximately a 15×15 surface reconstruction. Due to this surface superstructure, it is to be expected that replica substrate bands could be observed in ARPES measurements, with the magnitude of the shift in momentum space being linked to the periodicity of the of the superstructure, as is discussed in the main text.

LEED patterns in the few-multilayer regime
In Figure S3b reconstruction. First, as seen most clearly in Figure S3d, the peak pattern seen around the main Au(111) substrate peaks is replicated at a 30 rotation, indicating the likely presence of 8×8R30 domains. Second, the spots marked in orange in Figure S3h, do not conform to any allowed 8×8 diffraction peak, but instead they may be attributed to a 6° rotation of the 8×8 structure (i.e., 8×8R6°). It seems probable that the azimuthal orientation of the Ge film is not strongly constrained, which may be related to the large size of the reconstruction. Third, the peaks marked in green in Figure S3h do not conform to the 8×8 structure. These may be tentatively associated with Bi surface ordering due to the fact that these peaks alone disappear in the range of 250-300°C (see below), as well as the fact that these peaks do not appear in the The as-grown 3 ML film features some spots consistent with an 8x8 reconstruction, but in place of the 8×8R6 peaks, a ring-like continuum of intensity from 6° to 24° rotation. It is likely that some rotational disorder of the growth occurs as the film thickness increases, which manifests as a ring-like structure. After annealing at 300°C, as shown in in Figure S4c, these rings disappear and instead 8×8R6 spots emerge. This indicates that the annealing process aids the azimuthal rotational ordering of the germanene structure on Au(111), though there may still be several preferred orientations. In addition, the main 8×8 peaks appear sharper after the annealing process, indicating that the film quality is increased by the annealing.
Additionally, a set of spots labelled with green rings disappear at temperatures between 250 and 300°C reversibly, since they are present again in the final cooled data. One possible explanation for this is that these peaks are associated with the Bi atoms which are likely to sit in an ordered arrangement on the top surface of the sample. We also note that this annealing procedure gave no significant difference to the XPS spectrum, i.e., no significant desorption occurred at these temperatures.
Annealing also influences the quality of our ARPES data, as can be seen in Figures S4e-h. While the ~2ML as-grown film without annealing shows to rotationally smeared LEED spots ( Figure 4e) and rotationally smeared Dirac bands (indicated by red arrows in Figure 4g), the ~3ML film after annealing shows a more discrete LEED pattern (Figure 4f) and band structure (Figure 4h), which suggests less rotational disorder.

Ge monolayer thickness determination via STM
We determined the thickness of a Ge film monolayer from preliminary STM measurements of a thick Germanium film (nominal thickness 3.3 Å) evaporated on Au(111), the topography of which is shown in Figure S5. The STM image shows a number of Ge islands that allowed us to determine a Ge monolayer thickness of ~2.5 Å. The coloured curves indicate the measured data, while the red solid lines are the fitting curves from which the island heights Δh were extracted. The measurements were performed with a commercial Omicron STM at room temperature.
The structural transition that is indicated by the LEED measurements shown in Figure 1b-c is a strong indicator that at least one full layer of Germanium is completed at the nominally 2.6 Å thick films. which is also corroborated by the Ge appearance of a bulk (i.e. germanene) contribution in the Ge 3d core level peaks (shown in Fig 1a and S2). Due to the possibility of island growth, the film may be slightly thicker than one monolayer in some parts of the sample, but it is unlikely that two layers were completed in this film, since the interface component in the Ge 3d core level spectrum is still clearly present in Fig 1a for the nominally 2.6 Å thick film, but only fully suppressed for a ~2 ML thick film (shown in Fig SM2). Based on the STM measurements, quartz microbalance rate calibration, and core-level spectroscopy, we therefore conclude that the film with nominal thickness of 2.6 Å measured during our ARPES experiments is approximately at the monolayer limit.

Influence of rotational disorder on the appearance of Dirac cones
We observed the appearance of parallel lines on the equal energy surfaces shown in Figure 4(d).
These lines can be understood from the suppositions of circular pockets with small rotational disorder, which will wash out the sides of the pocket, while leaving streaks of intensity tangential to the sense of the rotational disorder, as is illustrated by the simulation in Figure S6. Here the "perfect" cone is centered at (-1,0), while in the right panel we sum intensities after continuously rotating the cone over -2.5° to 2.5° (the centre of rotation is (0 0)).