Direct observation of the Mottness and p-d orbital hybridization in epitaxial monolayer α-RuCl3

α-RuCl 3 , with abundant studies in its bulk phase, has shown the promising potential to approach the two-dimensional Kitaev honeycomb model and to realize the consequential quantum spin liquids. In this material, some ingredients spark off the hunting of quantum spin liquid states: the localized magnetic moments on each Ru 3+ ion guaranteed by the Mottness, the Kitaev-type interaction originating from the superexchange path over the p-d bonds, and the nearly two-dimensional nature of the van der Waals coupled honeycomb layers. Here, we worked out the growth art of α-RuCl 3 monolayer on highly oriented pyrolytic graphite substrate for the rst time, and then studied its electronic structure, particularly the delicate orbital occupations. Through scanning tunneling microscopy and spectroscopy study, the bonding congurations are justied by the features of pronounced t 2g -p π and e g -p σ hybridization, and the Mott nature is unveiled by an ~ 0.6 eV full gap at the Fermi level located in the t 2g -p π level. Our experimental results agree well with the density functional theory calculations of the monolayer system. In accordance with previous theoretical research, the epitaxial monolayer α-RuCl 3 system holds high tunability comparing to its bulk phase and provides a novel platform to explore the Kitaev physics.

Comparing to the bulk, monolayer α-RuCl 3 is closer to the two-dimensional Kitaev model since the stacking faults in bulk may cause additional magnetic transitions at 8-14K 15,16 . In addition, the electronic and magnetic properties of monolayer are more tunable by the application of strain, doping, and interfacial effect which were recently predicted to be promising routes in searching for novel states of matter [17][18][19][20] . However, it has been di cult to synthesize high-quality, high-coverage, and chemically pure monolayer α-RuCl 3 which enables access to its intrinsic properties, and the study of monolayer α-RuCl 3 remains scarce and challenging.
In this work, we successfully synthesized high-quality monolayer α-RuCl 3 on highly oriented pyrolytic graphite (HOPG) substrate by molecular beam epitaxy (MBE). Through low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS) studies, we found an in-plane lattice expansion in the α-RuCl 3 monolayer compared to bulk and the persistence of the Mott nature as evidenced by an ~ 0.6 eV full Mott gap. Noting that the previous STM work on the α-RuCl 3 thin lm (≈ 15-30 layers) shows añ 0.25eV gap 21 , the gap size of the monolayer is signi cantly magni ed, which could result from the enhancement of the Coulomb correlation due to the reduced electronic screening in a two-dimensional system [22][23][24] . The observed electronic states agree with the distinct features of t 2g -p π and e g -p σ bonds.
Both the energy spectroscopy and the real-space images are in good agreement with density functional theory (DFT) calculations. The Mott gap in the t 2g manifold is justi ed by a comprehensive study of experiment and theory. Our attempts of the structural modi cation via interfacial effect on the monolayer scale are a rehearsal of tuning the relevant electronic/magnetic properties and exploring the Kitaev physics in α-RuCl 3 17,25−27 .

Results
Synthesis and topography of RuCl 3] Two structural phases of RuCl 3 thin lms were found in the growth process. First, β-RuCl 3 chains and disordered α-RuCl 3 fragments are self-assembled on the surface. Highly ordered α-RuCl 3 monolayer appears and proliferates gradually in the annealing process. Figure 1 Mott gap is consistently given by both the experiment and calculation as marked in Fig. 2(a). In Fig. 2(b), the calculated partial density of states (PDOS) graph exhibits an ~ 2.0 eV splitting of t 2g and e g orbitals due to the octahedral crystal eld. The Cl-3p orbital occupies the valence band below ≈ -2.0 eV, while the Ru-4d orbital resides between ≈ -2.0 eV and ≈ 3.0 eV. Meanwhile, the orbital hybridization induces the mixture of p and d components in the whole energy scale. We projected the p orbitals onto the degeneracy-lifting basis of p π and p σ orbitals and found that, speci cally, the hybridization undergoes in the manner of t 2g -p π and e g -p σ bonding in Fig. 2(b). In the energy range of t 2g orbitals, the PDOS of the p π component is much larger than the p σ one due to the dominant pdπ bonding. In the energy range of e g orbitals, instead, the p σ component is much larger due to the pdσ bonding.
As expected, we observed distinct STM patterns in the energy ranges of different orbitals. Figure 3(a-f) are the typical constant-current STM images at indicated bias voltages. In the t 2g and p π dominating energy range (-3.0 to 1.5 eV), three protrusions are resolved in each surface unit cell forming a "Kagomelike" lattice. However, in the energy range of e g orbital, only one protrusion is observed appearing as a cluster of three, forming a triangular lattice of the trimers. Similar phenomena were observed in the STM images of CrI 3 thin lm 33 . Figure 3(g, h) show the simulated constant-current STM images, i.e. the isosurface of DOS integrated from Fermi level to the bias energy, based on Tersoff-Hamann model 34 . with respect to the Cl atom sites (blue balls) as marked in Fig. 3(g, h). Thus, Cl-p π and Cl-p σ orbitals directly link to the t 2g and e g orbitals surrounding the Ru atoms, respectively. The same t 2g -p π textures across the fermi level clearly illustrates the monolayer system remains in Mott phase.

Conclusions
In conclusion, the strained α-RuCl 3 monolayer interfacing graphite was fabricated by the method of MBE.
The p-d hybridization was directly visualized and understood and the Mott insulating behavior of α-RuCl 3 monolayer was validated by the accordant STM measurements and DFT calculations. The monolayer system enables the local tunneling probes to join the search of topological quantum magnets as a powerful weapon targeting the atomic-scale structure, electronic properties, and correlations, microscopic magnetic order as well as the excitation of unusual quasiparticle [35][36][37] . The strained α-RuCl 3 would de nitely make the spin-orbital structure, as well as inherent magnetic interactions, differ from the bulk system. Besides the stretched lattice (and the widened Ru-Cl-Ru bond angle) which may be advantageous for the advancement toward Kitaev limit 17,26,27,38,39 , the magnetic anisotropy of the system could have a favorable out-of-plane easy axis. Thus, it's intriguing and worth more studies that what the exact magnetic ground order is.

Methods
The α-RuCl 3 monolayer was grown on cleaved HOPG by MBE at a base pressure of ~ 1×10 − 9 mbar. The   Spectrum and DFT results. (a) STS of α-RuCl3 monolayer (solid black line, U=2.2 V, I=5.8 nA, bias modulation amplitude ΔU=20 mV at frequency f=983 Hz) and calculated total DOS for the ground state of the α-RuCl3 monolayer by LSDA+SOC+U, the dashed green (orange) curve describes the majority (minority) spins. The size of the full gap and the peak-to-peak gap is indicated. (b) The orbital PDOS of the α-RuCl3 monolayer. The green (orange) curves describe the majority (minority) spins and the Fermi level is set to the middle of the gap. The representative constant-current-image simulations at 0.9 V with the distorted "Kagome" lattice and 2.8 V with the triangularly arranged trimers, respectively. The Ru-hexagon (gray balls) and topmost Cl ions (blue balls) are put at the right positions in the lattice. The orange and green arrows represent the displacement from Cl sites to the bright protrusions.