Manipulating single excess electrons in monolayer transition metal dihalide

Polarons are entities of excess electrons dressed with local response of lattices, whose atomic-scale characterization is essential for understanding the many body physics arising from the electron-lattice entanglement, yet difficult to achieve. Here, using scanning tunneling microscopy and spectroscopy (STM/STS), we show the visualization and manipulation of single polarons in monolayer CoCl2, that are grown on HOPG substrate via molecular beam epitaxy. Two types of polarons are identified, both inducing upward local band bending, but exhibiting distinct appearances, lattice occupations and polaronic states. First principles calculations unveil origin of polarons that are stabilized by cooperative electron-electron and electron-phonon interactions. Both types of polarons can be created, moved, erased, and moreover interconverted individually by the STM tip, as driven by tip electric field and inelastic electron tunneling effect. This finding identifies the rich category of polarons in CoCl2 and their feasibility of precise control unprecedently, which can be generalized to other transition metal halides.


STM contrast for different types of polarons
In principle, polarons should be visible if their presence perturbs the local density of states at the polaron sites. STM images of the polarons that appear as depressions or protrusions, depending on their electronic states. Since all kinds of polarons are electron type, they all induce upward local band bending, which allow them to be visualized as depressions at energies associated with the band bending, because their presence deleted the local density of states. At negative bias, type-II polarons are visualized as protrusions at energies of their polaronic states, but type-I (down) and type-I (up) polarons become invisible because their polaronic states are not discernible.
To depict the dependence of STM contrast of different polarons on their electronic states, we show a data set in Supplementary Fig. 8 as a typical example. Supplementary Fig. 8(a) is an STM image of three polarons with different types at 1.2 V. The type-I (down) and type-I (up) polaron appear as a shallow and deep depression, respectively. However, the type-II polaron appears as a protrusion. Line spectra surpassing all the three kinds of polarons indicate that the type-I (up) polaron has more depleted electron density at 1.2 V than that of the type-I (down) polaron, and the type-II polaron has enhanced electron density compared to the polaron-free region [Supplementary Figs. 8(b,c)].

Localized polaronic states
Our calculations reveal a very localized (narrow) charge distribution of polaronic states along the out-of-plane direction (z-direction), due to the d-orbital nature of these states. As the STM tip is ~5 Å higher than the top Cl layer in experiments, much larger than the extent of 3d-orbitals, the sample-to-tip tunneling is dominated by the wavefunction "tail" of polaronic states, which decays exponentially into the surface region. Supplementary Fig. 13 shows the charge density of Co-and Cl-centered polarons along a line in the out-of-plane direction passing through the polaron center.
Here it can be seen that while the charge densities of both states decay exponentially in the vacuum region, the charge density associated with the Cl-center polaron (and hence the tunneling current) is orders of magnitude larger that of the Co-centered polaron. As such, in-gap states associated with type-I (down) and type-I (up) polarons (Co-centered) are inherently more difficult to see from STS than the type-II polaron (Cl-centered).

Model of tip electric field
We modelled the electric field between the tip and the substrate, which were considered as a point charge and a semi-infinite metal, respectively, for simplicity. The metallic substrate creates an image charge with opposite polarity in the presence of the point charge [ Fig. 5(a), inset]. The electric filed of the surface location beneath the tip reads = 2 0 (∆ + 0 ) 2 , where the tip charge = ( + ∆ ) with the capacitance between tip and sample C, the applied voltage V, and the work function difference between tip and sample ΔW. Z0 and Δz represent the initial tip height and decreasing tip height, respectively. In the situation of constant critical electric field, the above

Polaron conversion conditions
Type Supplementary Fig. 13. Polaronic charge density of Co-centered (black) and Cl centered (red) states along a line in the out-of-plane direction passing through the polaron center. The position of Co layer is chosen as the zero of horizontal axis. The two blue dashes lines are given as guide to the eye, which shows that the Cl-centered polaronic state has larger charge density and decays slower than Co-centered one in the surface range.