Stabilizing an atomically thin quantum spin Hall insulator at ambient conditions: Graphene-intercalation of indenene

With the promise of dissipation-less spin-polarized boundary modes, QSHIs could initiate a paradigm shift in future spintronics technologies. The conceptual application perspective is bright and ranges from spin-transistors [10, 11], to low-power consumption devices [12, 13], to QSHI based quantum computing [14]. However, finding suitable materials for practicable device realization faces major challenges. The band-inverted narrow-gap semiconductors for which the quantum spin Hall effect had first been demonstrated [15, 16] do not lend themselves to room-temperature (RT) applications. 2D Dirac semimetals formed by atomic honeycomb monolayers as motivated by the seminal work of Kane and Mele [17] are a promising alternative [18]. But while spin-orbit coupling (SOC) in graphene is too weak to open an appreciable band gap, QSHI monolayers built from heavier group IV elements such as silicene, germanene, and stanene [19, 20] could experimentally only be synthesized on metal surfaces, preventing their use in actual transport devices, or failed to display a large non-trivial bandgap when placed on a semiconducting substrate [21].

In contrast, band-inverted large gap 2D Dirac semimetals have been successfully realized in group III and V monolayers on SiC(0001), specifically bismuthene [6] and the recently discovered indenene [7], and were experimentally confirmed as QSHIs. They could potentially solve the device challenge, yet, are inherently unstable to environmental factors outside their ultra-high vacuum (UHV) birthplace. This bottleneck has made serious transport device fabrication strategies elusive, and hitherto characterization is mostly bound to UHV-based surface science techniques such as angle resolved photoemission (ARPES) and scanning tunneling microscopy (STM).

Here, we design an extravehicular space suit to make these quantum materials operational in air, by placing quasi-freestanding graphene as protective sheet atop the QSHI monolayer via intercalation. Graphene’s resilience to ambient conditions provides an efficient protection against oxidation, while it leaves the intercalated material unaffected as was shown for a variety of few-layer quantum materials [22, 23]. With respect to topological physics, intercalation was suggested as a means to tailor the spin-orbit gap of graphene [24]. In contrast, here we reverse the roles of graphene and the intercalant, by using the former to stabilize the latter as a QSHI. For this purpose we employ indenene, the triangular monolayer phase of indium that can be grown routinely in high quality monodomains on large areas of SiC [9]. It is particularly suited for wafer-sized intercalation, which not only protects both its structure and its topological character but also ensures its chemical integrity upon exposure to environmental conditions, as we demonstrate below.

In its pristine form, the topological electronic structure of indenene is the result of a synergetic interplay of the indium monolayer and its underlying SiC substrate. The latter breaks the surface mirror plane and gaps out the metallic indium $sp$ states, leaving a set of Dirac bands of in-plane $p$-orbital character located at the K-point of the Brillouin zone (see Fig. 1a). The degeneracy of the Dirac point is lifted by two counteracting mechanisms [7, 8]. While in-plane inversion symmetry breaking (ISB), induced by the topmost carbon atoms of the substrate (see Fig. 1c), promotes a trivial band gap, atomic SOC drives band inversion and hence a large QSHI gap. As the bonding distance d${}_{\text{In-Si}}$ between indium and the topmost Si-layer controls the ISB strength felt by the In monolayer and consequently determines its topology and gap size, it has been used as one among several experimental indicators to measure indenene’s topology. We thus find the pristine form to lie deep within the QSHI regime (Fig. 1c, blue data point) [7].

Intercalating indenene into the graphene/SiC interface, the massive Dirac bands are found to be well preserved, yet, significantly depopulated with $E_{F}$ shifted from $n$- to $p$-type indenene (Fig. 1b). At the same time, the slight increase in the measured bonding distance d${}_{\text{In-Si}}$ indicates that graphene pulls indenene away from the substrate and thus points to a further reduction of the ISB strength $\lambda_{\text{ISB}}$ with respect to the pristine case, preserving SOC as the dominating factor, and stabilizing the topological gap along with the QSHI state (Fig. 1c, yellow data point).

The virtue of this graphene-covered QSHI relies on its resilience against oxidation, which we study by controlled oxygen exposure and subsequent X-ray photolelectron spectroscopy (XPS) on the pristine (Fig. 1d) and intercalated indenene (Fig. 1e). In both cases, the as-grown material (black spectra) reveals identical In $3d_{3/2}$/$d_{5/2}$ doublets. Exposing pristine indenene to large doses of oxygen (red) causes these peaks to broaden and display a chemical shift to higher binding energies, indicating strong indium oxidation [27]. In contrast, exposing intercalated indenene to the same dose of pure oxygen (red), ambient air (green) or even water (blue) has virtually no impact on the indium oxidation state as well as its band structure (shown in Fig. 4c,d after comprehensive discussion) and thus confirms the protective function of the graphene overlayer.

Having summarized the phenomenology, let us now focus on detailed aspects of indium intercalation [22, 28, 29], especially the large area growth of monolayer indenene and the identification of its non-trivial topology. Following the well-established recipe of Ref. 25, the synthesis is initiated by sublimating the topmost Si atoms off the SiC(0001) substrate, leaving a C-rich buffer layer referred to as zero-layer graphene (ZLG, Fig. 2a). Low energy electron diffraction (LEED, Fig. 2a₁) reveals a characteristic ($6\sqrt{3}\,\times\,6\sqrt{3}$)R30^∘ fingerprint relative to the SiC(0001) ($1\,\times\,1$) surface unit cell signalling a homogeneous ZLG coverage of the substrate. Corresponding ARPES measurements (Fig. 2a₂) show a broad and non-dispersive valence state at the K-point of the graphene Brillouin zone, affirming the covalent bonding (Fig. 2a₃) to the underlying SiC that prevents ZLG from developing linear $\pi$-bands [25].

In a cyclic process of indium deposition and subsequent annealing, we replace the top layer carbon for indium as bonding partner to the substrate, hereby lifting the ZLG template from the subjacent SiC to form quasi-freestanding monolayer graphene (QFMG). The ($6\sqrt{3}\,\times\,6\sqrt{3}$)R30^∘ LEED signature of ZLG weakens significantly, while the diffraction spots of QFMG intensify and mark its decoupling from the substrate (Fig. 2b₁ and inset). ARPES now exhibits the characteristic $\pi$-band crossing of graphene (Fig. 2b₂), with the Dirac point (DP) at K (-0.5 eV) lying at slightly ($\sim$80 meV) higher energies as compared to non-intercalated graphene on a ZLG buffer layer [25]. Representative scanning transmission electron micrographs (STEM) (Fig. 2d) show two projected indium layers, each containing one In atom per Si site of the SiC surface. This puts forward a $(1\,\times\,1)$ adsorption geometry of 2 ML In on SiC(0001) as illustrated in Fig. 2b₃ and is corroborated by the absence of higher order diffraction spots in LEED (Fig. 2b₁).

At this point, our experimental results are reminiscent of recent experimental work on 2 ML In intercalated into a graphene-SiC interface with three graphene top layers instead of one [22]. By thermal removal of In (550$\,{}^{\circ}$C, 30 min) we now convert indium into monolayer indenene, pushing this material into the QSHI phase. STEM in Fig. 2e exposes the indenene/graphene sandwich, with In adsorbed directly above the topmost Si species of SiC (Fig. 2c₃) [7]. The corresponding LEED in Fig. 2c₁ again shows $(1\,\times\,1)$ periodicity, clear-cut evidence for intercalated indenene to arrange in the same triangular lattice as its pristine counterpart. Quite remarkably, the transformation from 2 ML indium to 1 ML indenene redistributes charge within the heterostructure, shifting the graphene Dirac bands by 0.28 eV higher in energy compared to the 2 ML film as revealed by ARPES. (Fig. 2b₂ and c₂). Similar band fillings upon post-annealing were already observed in Ref. 28, yet, were tentatively assigned to incomplete intercalation and a 2 ML phase, respectively. In contrast, we identify graphene doping as clear-cut fingerprint to distinguish bi- from monolayer indium.

To further elaborate on this link, we recapitulate the experimental band structures of pristine 1 ML and 2 ML In films in Fig. 3(a,b) [9], and compare them to their intercalated counterparts in Fig. 3(c,d). ARPES at the $\Gamma$-point of both pristine phases (a,b) shows the intense SiC valence band maximum as well as an indium-related band dispersing upwards in energy, the latter exposing distinct maxima along the $\Gamma\text{M}$ and $\Gamma\text{K}$ paths (blue arrows). These maxima arise from the substrate-induced breaking of mirror symmetry that fosters hybridization between in- and out-of-plane In $p$ orbitals [7], and gaps out the metallic $sp$ bands observed close to the M-point of 2 ML In, exposing the Dirac states at K that we discussed in Fig. 1a [9].

Albeit considerably damped and broadened by the graphene cover, we recognize all ARPES features of the pristine phases to reappear in their intercalated counterparts of Fig. 3(c,d). Here, we chose a different photon energy at which the indium 2D bands around $\Gamma$ are more prominent while SiC bands appear suppressed. We also identify the intense $\pi$-band characteristic of graphene, faintly replicated by final state scattering via higher order reciprocal lattice vectors – an effect known from well-ordered intercalated materials [30] that is also seen in our LEED data, see red marks in Fig. 2 b₁, c₁ and Ref. [26].

With respect to pristine indenene, the intercalated indenene bands are shifted up by approximately 250 meV (horizontal lines in Fig. 3), corresponding to an overall charge carrier depletion of $\Delta n_{\text{In}}\approx-3\times 10^{12}$ carriers per cm² that we estimate from the Fermi surface area (see Methods) and is in qualitative agreement with the n- to p-type transition in Fig. 1(a,b). At the same time, Fig. 2c₂ suggests the graphene layer to accumulate $\Delta n_{\text{Gr}}\approx+3.4\times 10^{12}$ cm^-2 with respect to charge neutral graphene, indicating a dominating electron transfer from indenene to graphene that is balanced by the underlying SiC substrate [31].

Irrespective of the exact mechanism, the observed charge transfer indicates non-negligible interaction between indenene and graphene that could potentially affect indenene’s topology, for instance by modulating $\lambda_{\text{ISB}}$. On top of that, the very presence of graphene tends to increase the distance d${}_{\text{In-Si}}$ (see Fig. 1c) hence enhancing the dominance of SOC over ISB. To quantify these effects, we add one relevant parameter to our analysis, namely the distance between indium and graphene d${}_{\text{In-Gr}}$. Both d${}_{\text{In-Si}}$ and d${}_{\text{In-Gr}}$ can experimentally be accessed by X-ray standing wave (XSW) photoemission that utilizes Bragg scattering off the bulk substrate lattice to generate a modulated wave-field along the surface normal. The photoelectron yields of the In and C core levels get strongly enhanced when the field maxima coincide with the corresponding atomic layer (for details see Methods) [32]. Tuning the photon energy and thus the phase of the standing wave, we measured the layer distances of intercalated indenene and found d${}_{\text{In-Si}}=(2.74\pm 0.04)\,\text{\AA}$ and d${}_{\text{In-Gr}}=(3.35\pm 0.04)\,\text{\AA}$. The latter amounts to about 92$\%$ of indium’s van der Waals bonding length [33], underlining graphene’s quasi-freestanding character [34]. In order to disentangle the effect on $\lambda_{\text{ISB}}$ induced by the SiC-substrate underneath from that of the graphene capping on top, we perform density functional theory (DFT) calculations for indenene without and with graphene cover as shown in Fig. 4a and b for the same d${}_{\text{In-Si}}$. The results clearly indicate that the bands at the valley momenta preserve their non-trivial sequence. The splitting due to SOC strength $\lambda_{\text{SOC}}$ gets slightly renormalized but is roughly compensated by a concomitant reduction of the $\lambda_{\text{ISB}}$, effectively leaving the band gap unchanged (see arrows). For this reason we conclude that the variation of the In-Si distance d${}_{\text{In-Si}}$ induced by the presence of graphene is the main factor determining $\lambda_{\text{ISB}}$, as indicated in Fig. 1c. This completes the proof of intercalated indenene to be topologically robust and clearly placed within the QSHI regime.

Combined with its remarkable resilience against ambient conditions, this opens up a wealth of experimental possibilities to characterize and manipulate this 2D topological insulator ex-situ. While the conductive nature of the graphene cap may still interfere with meaningful edge transport measurements, its effective protection of the monolayer QSHI certainly paves the way for (nano)fabrication of device structures, e.g., for field effect gating. It also greatly facilitates optical or infrared experiments such as Raman and Landau level spectroscopy in non-vacuum settings, techniques that will give further insight to the physics of this intriguing QSHI. We underline that – quite remarkably – intercalated indenene remains inert even upon immersion in water (see Figs. 1e and 4). Beyond the specific case of indenene, this suggests graphene intercalation as a promising route towards the application of atomic monolayers as functional quantum materials, even in rough chemical environments [35].

Data Availability The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

We are grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (Project ID 258499086). We acknowledge Diamond Light Source for time on beamline I09 and I05 under proposals SI31808-1, SI25151-4 and SI30583-1. We gratefully acknowledge the Gauss Centre for Supercomputing e.V. (https://www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC-NG at Leibniz Super- computing Centre (https://www.lrz.de).