# Realizing nearly-free-electron like conduction band in a molecular film through mediating intermolecular van der Waals interactions

## Abstract

Collective molecular physical properties can be enhanced from their intrinsic characteristics by templating at material interfaces. Here we report how a black phosphorous (BP) substrate concatenates a nearly-free-electron (NFE) like conduction band of a C60 monolayer. Scanning tunneling microscopy reveals the C60 lowest unoccupied molecular orbital (LUMO) band is strongly delocalized in two-dimensions, which is unprecedented for a molecular semiconductor. Experiment and theory show van der Waals forces between C60 and BP reduce the inter-C60 distance and cause mutual orientation, thereby optimizing the π-π wave function overlap and forming the NFE-like band. Electronic structure and carrier mobility calculations predict that the NFE band of C60 acquires an effective mass of 0.53–0.70 me (me is the mass of free electrons), and has carrier mobility of ~200 to 440 cm2V−1s−1. The substrate-mediated intermolecular van der Waals interactions provide a route to enhance charge delocalization in fullerenes and other organic semiconductors.

## Introduction

The degree of electron delocalization in organic semiconductors is critical for their adoption in electronic and optoelectronic applications1,2,3. Electron transport, however, is usually facile through chemical bonds in conjugated organic materials, but is rarely optimal when the noncovalent intermolecular van der Waals (vdW) forces define the self-assembly and consequently, the intermolecular electronic coupling4. C60 molecules, which have uncommonly large electron affinity and suitable electronic band gap, have been extensively investigated as zero- to three-dimensional (0-3D) organic semiconductors5,6,7,8,9. As a typical vdW material, C60 molecules form solids through a balance of the Pauli type, electrostatic repulsive force and the attractive vdW force10, which, however, does not enhance intermolecular electronic hybridizations. C60 solids are characterized by  flat electronic bands with inconsequential dispersions and hopping transport. Functionalization of C60 by synthesizing fullerene derivatives has been investigated as a means to improve its electron transport, but the improvement was limited as the dispersions of the electronic bands were not effectively modified11,12,13,14. A radical improvement of electron transport, however, might be achieved if the assembly of C60 molecules could increase the intermolecular electronic hybridizations.

Even though the vdW forces are weak compared to other bonding mechanisms, it can have a profound impact on the electronic properties. For example, a recent study has demonstrated that by controlling the vdW interactions in a bilayer graphene, it is possible to transform a nominally semiconducting material into a superconductor15. Our method to mediate the vdW interactions between C60 molecules is through a substrate control of intermolecular interactions. It has been demonstrated that epitaxial growth of CO molecules on metals can impose an in-plane molecular compression that affects the intermolecular electronic interactions16,17. On metal surfaces, however, the high electron affinity of C60 enables it to naturally draw electrons from its substrates and thereby to become metallic18,19. Thus, to retain and enhance its semiconducting properties, it is far more desirable to impose intermolecular interactions on C60 molecules with an electronically inert substrate. From this point of view, black phosphorous (BP)20,21, composed of atomic sheets that are held by vdW forces with alternating projecting “ridge” and subsiding “notch” atoms in a single layer, provides a unique adsorption platform for C60 molecules with yet unknown consequences.

Here we show by scanning tunneling microscopy (STM) and theory that the BP substrate organizes C60 molecules into a compressed monolayer and imposes a favorable orientation that optimizes the intermolecular π-π couplings, resulting in a nearly-free-electron (NFE) like lowest unoccupied molecular orbital (LUMO) band in C60 monolayers. Such NFE-like LUMO band would dominate charge transport in C60 assemblies. An NFE band in C60 nanostructures has been attested through discovery of the superatom molecular orbitals (SAMOs)22, and their strong hybridization. But SAMOs and their NFE bands are too high in energy to participate in charge transport unless C60 molecules are endohedrally doped with metallic atoms23. NFE dispersion has been attributed to π orbitals of a molecular monolayer on metallic substrates, but its origin has later been reassigned to quantum confinement of a metal surface state, rather than the electronic hybridization among organic molecules24,25,26,27,28. The NFE conduction formed by π-π interactions is worthy of further exploration in C60 or other organic molecules on inert substrates, because it realizes a long sought mode for charge transport for high-performance organic electronics and optoelectronics4.

## Results

### Topography of C60 monolayer on BP

Figure 1a shows a topographic reconnaissance STM image of a C60 monolayer island on BP, where C60 molecules aggregate into a compact, highly ordered film. The top inset in Fig. 1a shows a topographic STM image, with atomic resolution, of the BP substrate where only the topmost ridge atoms are resolved while the lower notch atoms remain undetected within the dark waving lines. A rectangular surface unit cell is marked in the image with lattice constants l1 and l2 along the zig-zag and arm-chair directions, respectively. By analyzing the central position of C60 molecules at the island edge (bottom right inset in Fig. 1a), we establish that they assemble above notches of the BP layer (noted by white dashed lines), while the exact adsorption sites will be elaborated later. Figure 1b presents a close-up STM topographic image of unoccupied states (Vbias = +1.05 V) of the C60 monolayer, where each molecule appears as two bright lobes. As established in previous studies18,29,30, the characteristic two-lobe structure corresponds to the unoccupied π-orbitals of two pentagons that are joined by a C = C bond (see Fig. 1c). Here, we mark the C = C bond with “h:h” (The “h:h” designation represents C = C bonds shared by the two side-by-side hexagons)31. This two-lobe intramolecular feature establishes that C60 molecules sit on the surface in a highly ordered structure, where its two side-by-side hexagons and h:h joined pentagons point up (Fig. 1c).

In Fig. 1b, it is clear that along the zig-zag direction of the substrate, the h:h bonds are oriented in the same direction forming an equivalently oriented C60 chain over the BP notches. In the adjacent C60 chain, the h:h bonds are again oriented parallel to each other, but the h:h-h:h angle (indicated by φ in Fig. 1d) with respect to the original chain is 99.2 ± 0.4°, i.e., the h:h bonds orientation alternates between C60 molecules in the arm-chair direction. The alternation of the h:h bonds are highlighted in Fig. 1d, where ball-stick models of C60 are superimposed on the topography image with the h:h bonds marked in red. With this molecular arrangement, C60 molecules form a centered supercell, which contains two molecules of different h:h orientations with lattice constants a = 9.9 ± 0.2 Å (zig-zag) and b = 17.2 ± 0.2 Å (arm-chair), corresponding to three and four times the substrate lattice constants along the zig-zag and arm-chair directions, respectively. The obtained intermolecular distances d1 is nearly identical to d2 with values of 9.9 ± 0.2 Å, and d3 is of 10.0 ± 0.2 Å (Fig. 1d). These distance values imply a tighter packing of C60 molecules in the monolayer than that in molecular crystals where the vdW distance is 10.04 Å. The distance is also smaller than commonly found in C60 monolayer on most metal surfaces29,32,33,34,35,36. The STM image shown in the inset of Fig. 1b identifies six positions with weak, bright contrast around each C60 molecule, as marked by arrows; two arrows belong to interfaces between C60 molecules along the zig-zag direction (blue) and the rest are along the arm-chair direction (black). We will elucidate later how this interface contrast relates to strong intermolecular interactions unique to the C60 monolayer on BP surface.

Figure 1e presents the most stable adsorption structure of an isolated C60 molecule on a BP tri-layer based on DFT structural optimization. Consistent with the experiment, the bottom h:h bond (depicted in deep blue) lays over the BP notches such that each C atom interacts with two of the closest P atoms (dark pink). The relative orientation of the bottom h:h to the interacting P-P bond direction has an angle of θ = 11.0° (Fig. 1e). To get more insight into C60-BP interactions, we calculate the differential charge density [DCD, total – (BP + C60)] between C60 and BP. The largest DCD of 0.0029 eÅ−3 is about 0.001 of the largest pre-adsorption density of 2.1925 eÅ−3, implying there is negligible charge transfer between BP and C60 and the interaction mainly occurs through vdW forces. The adsorption gains −1.24 eV energy per C60 molecule and the C–P distances are 3.42~3.46 Å, consistent with the vdW force mediated adsorption energy of C60 on graphene37.

Figure 1f shows the most stable molecular configuration of the C60 monolayer predicted by DFT. The orientation of C60 molecules within the monolayer is similar to that of isolated C60 molecules on BP, with the bottom h:h bond almost parallel to the substrate P-P bond with an angle of 1.6° between them. These results indicate that condensing C60 into a monolayer does not strongly alter the local adsorption structure with respect to that of single C60 molecules, implying that C60-BP interactions dominate the monolayer formation. This assertion can also be quantified from an energetic perspective. The obtained absorption energy of −1.36 eV per C60 molecule in the monolayer on BP is only 0.12 eV larger than that for an isolated C60. The adsorption energy difference can be regarded as the energy gain due to inter-C60 interactions, which are much weaker than that for the BP–C60 interaction. Our calculations also reproduce the observed molecular arrangement with identical h:h bonds orientation along the zig-zag direction and alternating h:h bonds along the arm-chair direction. The theoretical lattice constants a and b of 9.90 Å (d1) and 17.20 Å and φ of 97.3° reaffirm the compressed C60 structure. We calculate that such in-plane lattice compression corresponds to an effective pressure of 1.8–2.2 GPa on a C60 monolayer by the BP–C60 interaction.

### Delocalized LUMO state of C60 on BP surface

Next, we examine the electronic structure that emerges from the C60 monolayer compression. Figure 2a shows an exceptional STM topographic image acquired at a bias of approximately +0.80 V, where the intramolecular contrast of C60 vanishes to be replaced by a wave-like supramolecular contrast. The STM image has a herringbone stich knitted fabric pattern with electron density distribution extending deep between the molecules, indicating that the contrast at this energy is dominated by intermolecular electron delocalization. The vanishing of the intramolecular contrast in delocalized 0D, 1D, and 2D structures has been observed for SAMOs of C6022,23, but such images have not been reported for π-orbitals forming the electronic gap.

We establish the origin of the delocalized electronic structure by recording scanning tunneling spectroscopy (STS) spectra. The inset in Fig. 2b shows a spectrum measured between the valence and conduction bands. It indicates that the C60 monolayer is semiconducting with a bandgap of 2.88 eV, very close to that of a C60 bilayer or multilayer38. The band gap value and the location of the Fermi level within it confirms that the C60 monolayer experiences negligible charge transfer upon adsorption on BP. Figure 2b provides STS spectra of the LUMO region, which are measured at four different positions on and around an individual C60 molecule selected by considering the symmetry of the adsorption structure (Fig. 2b inset). The spectra are similar at these four sites and show a shoulder peak at the bottom of the LUMO resonance (from 0.67 to 0.82 eV), which distinguishes them from previous measurements. The two sharp peaks, residing at 1.05 and 1.33 eV, respectively, are typical in previously reported LUMO bands for metal supported C60 bilayers38. The less intense shoulder feature, to which we attribute the herringbone structure of the STM topographic image at 0.8 eV in Fig. 2a, is, however, exceptional to the C60 monolayer on BP.

This newly observed shoulder feature in Fig. 2b originates from the electronic hybridization between π-orbitals of C60 molecules, as established by a series of spectra measured over single C60 molecules in Fig. 2c. The shoulder intensity gradually diminishes as the measuring location approaches the island edge and grows back when the tip returns to the island interior. STS spectra are also acquired on the locations across the C60/BP island edge, as shown in Fig. 2d. It is evident that the spectroscopic shoulder feature of C60 within the island terminates at the edge C60 molecules; after leaving the C60 island edge, the spectra show the typical bare BP character21. These spectra, thus, compellingly establish that the shoulder belongs to a C60 bonding LUMO band, whose density is expected to be maximum within the island bulk and to decrease upon approaching the edge. This conclusion is further confirmed by the spectroscopic dI/dV map recorded at 0.80 eV (Fig. 2e), where there are appreciable electron densities around the edges of the herringbone topographic contrast. Specifically, the contrast involves four extended arms of C60, two to the left and two to the right along the arm-chair direction (indicated by the black circles in the inset of Fig. 2e). These arms link four adjacent C60 molecules in the arm-chair direction. In the zig-zag direction, there is also a high intensity contrast (indicated by the blue circles in the inset of Fig. 2e) that links two vertically adjacent C60 molecules with one arm on each side. These six arms are responsible for the weak bright contrast observed around single C60 molecules mentioned in Fig. 1b. Importantly, the electronic interaction corresponding to the arms form a delocalized 2D electron density network, in sharp contrast to the dI/dV mapping images of the two commonly observed 1.05 and 1.33 eV LUMO states (Supplementary Fig. 1) where electron densities are localized on single molecules.

### Electronic hybridization among C60 on BP surface

We confirm the experimentally observed formation of the delocalized LUMO band by reproducing it with DFT calculations. The calculations are performed for both the C60 monolayers with BP substrate and without BP substrate using the supercell shown in Fig. 1f. As shown in Supplementary Fig. 2, the energies and dispersions of the LUMO bands of two C60 molecules in the supercell does not appreciably change upon the removal of BP substrate. Furthermore, removing the BP substrate does not cause appreciable change in the partial density of states of C60 monolayer (Supplementary Fig. 3). In light of these comparisons, we conclude that DFT results of the isolated C60 monolayer without BP substrate fully capture the essential features of the NFE band formation. As shown in Supplementary Fig. 2a, the inclusion of the BP substrate in the electronic structure calculation introduces several substrate bands in the proximity of the C60 LUMO bands, which may blur the NFE LUMO band we intended to present. Therefore, we only provide DFT results of the fully relaxed C60 monolayer without BP substrate in the following discussions.

Figure 3a plots the calculated density of states (DOS) of the unsupported C60 monolayer. The LUMO region spans an energy range of over 0.5 eV, and consists of a shoulder and two dominant peaks at higher energy; this well reproduces the three features observed in our dI/dV spectra (Fig. 2b). The band structure plot (Fig. 3b) establishes the band contributions to the DOS peaks. For an isolated C60, the LUMO orbitals are triply-degenerate (Supplementary Fig. 4)39. LUMO-a, -b, -c derive from the LUMO orbitals of a free molecule when the degeneracy is broken by nonisotropic environment such as caused by the intermolecular and molecule-substrate interactions. The LUMO-a, -b, -c label is normally used to identify the three orbitals that can be identified when the perturbations are sufficiently strong, to distinguish their origin from lowest energy state to the higher ones19. Figure 3b is the calculated band structure of C60 monolayer with the structures shown in Fig. 1f. Here, the supercell contains two C60 molecules and those LUMO orbitals thus form six LUMO bands (three pairs of bonding–antibonding bands) in the monolayer. The dispersion and the energy levels of those bands are determined by C60–C60 interactions within the monolayer. The lowest unoccupied energy at the Γ point belongs to the LUMO-a bonding band, which results into the shoulder in the DOS plot (marked with the violent circle in Fig. 3a) and corresponds to the shoulder (~0.78 eV) recorded in our dI/dV STS spectra (Fig. 2b). Those two higher-energy peaks marked with cyan and light orange circles in the DOS plot shown in Fig. 3a are ascribed to the LUMO-b, -c bonding bands and the LUMO-a, -b, -c antibonding bands, respectively, which reproduce the two major dI/dV peaks at 1.05 and 1.33 eV (Fig. 2b). More details on assignments of the two sharp peaks in the dI / dV STS spectra are presented in Supplementary Fig. 5.

The compelling result of the band structure calculation is that the LUMO-a bonding band is highly dispersive, characterized with the electron effective masses (m*) of 0.70 me and 0.53 me along the Γ-X (zig-zag) and Γ-Y (arm-chair) directions, respectively (Table 1). We further confirm the rather small DFT calculated m* in C60 monolayer by performing complementary tight binding calculations (Supplementary Note 1 and Supplementary Fig. 6). These calculations give a bandwidth of 0.64 eV for the LUMO-a band and m* values of 0.96 me along the Γ-X (zig-zag) and 0.32 me along Γ-Y (arm-chair) directions. These results indicate electrons excited or injected into the 2D delocalized LUMO-a band behave like free electrons, which is consistent with the 2D herringbone network appearance of the dI/dV image (Fig. 2e). A real-space plot of the wave function norm of the 0.57 eV shoulder state (Fig. 3c) reveals wave function overlaps among the four arms of each C60 molecule along the arm-chair direction and two arms along the zig-zag direction, accounting for the experimental observation (Fig. 2e). Figure 3d reveals that 2D delocalized charge distribution is a two-layer structure parallel to the surface in real space. The LUMO-b and LUMO-c bands have larger effective masses (Table 1) and their wave functions are more localized to the C60 molecules.

### Origin of the NFE LUMO-a band

A highly delocalized band, such as LUMO-a, is unprecedented for a molecular monolayer bound by vdW forces; it is also significant that it is specific to LUMO-a only. To pinpoint the origin of the NFE bands, in Fig. 3e we first examine the top and side views of probability densities of the LUMO-a, -b, -c orbitals of an isolated C60 molecule, with the molecular orientation that is related to experiments. The difference between the LUMO orbitals can be seen by their probability densities with respect to the molecular plane. Specifically, the LUMO-a orbital is primed to hybridize within the molecular plane (Fig. 3e), but the LUMO-b and -c have densities projecting above and below the plane, and hence their intermolecular hybridizations within the molecular plane are weak (Fig. 3e). The calculations show that the unique C60 lattice on BP surface favors the in-plane hybridization of probability density of the LUMO-a orbital resulting in the NFE band.

The detailed features of the in-plane hybridization can be recognized by plotting the intermolecular DCD of LUMO-a of the monolayer. Figure 4a shows how the delocalized band forms through intermolecular density sharing between C60 molecules. In particular, the hybridization occurs at interfaces between molecules along the arm-chair and zig-zag directions (indicated by black and blue circles). This is consistent with the total of six extended arms of C60 intermolecular interactions that are observed in dI/dV mapping image (Fig. 2e). The chirality of the arms along the zig-zag direction is also well reproduced.

### Dependence of the NFE LUMO-a band on C60 monolayer topography

The single molecule wave functions and their interactions give clues for the formation of the NFE LUMO-a band. To illustrate the roles of the unique compressive C60 molecular lattice that is imposed by the BP, i.e., the intermolecular distance and orientation within the 2D lattice, we calculate the DOS of a C60 monolayer, without the substrate, for different lattice constants, a and b, and mutual orientation angles, φ, that are indicated in Fig. 1f. The calculation results are presented in Fig. 4b–d. Figure 4b, c shows that the lattice constant compression along the arm-chair direction, b, is critical for enhancing the DOS of the NFE-shoulder state. The NFE-shoulder gradually fades out upon increasing b and disappears for 1.03 × b, and larger, corresponding to d2 of ~10.11 Å. The shoulder state is less sensitive upon elongating the lattice constant, a, because in the zig-zag direction the lattice is more heavily compressed than the arm-chair direction when the C60 monolayer lattice is constructed by the BP template.

Moreover, the calculations show that the lattice compression alone is not sufficient for producing the NFE band; the intermolecular orientation matters. Figure 4d shows the DOS of the monolayer upon varying the intermolecular orientation angle φ, while keeping the lattice at a constant a and b. Varying φ has a more complex effect on the distribution of the DOS amplitudes than for varying lattice constants. It is evident, however, that when φ is in the range from 90° to 120°, the LUMO peak distribution becomes much broader and small peaks clearly appear in the energy region below the noninteracting LUMO states. The NFE band features are only pronounced within a certain range of angles where the LUMO-a orbitals of adjacent C60 molecules have a stronger π-π wave function overlaps (Supplementary Fig. 7). For the C60 monolayer on BP, the theoretically and experimentally observed φ are 97.3° and 99.2°, respectively. These angles are within the angular window of an appreciable intermolecular interaction, indicating that BP substrate imposes a template that favors inter-C60 hybridization. This angle dependence also explains why within C60 bulk solids where the intermolecular distance of 10.04 Å is close to the critical distance34, the dispersive LUMO bands have not been found. In the case of C60 solids, molecules rotate at room temperature, resulting in a random orientation of adjacent molecules that does not support band formation and delocalization. The results explain how the relative C60 orientation and compression that are enforced by the BP substrate lead to the intermolecular electronic hybridization of the LUMO-a into the NFE band that is imaged in experiments.

### Carrier mobility

Next, we examine possible novel physical properties that are embodied in the dispersive band of the C60 monolayer. The discovery and imaging of the delocalized LUMO-a band suggest that it could enable band-like transport, rather than the well documented hopping mode found in C60 aggregates40. Table 1 shows the effective masses and calculated electron mobilities using phonon-limited band-like and carrier hopping transport models40,41. The actual carrier mobility is difficult to measure by conventional means because the conduction band minimum of BP is below that of C60. The theoretical mobilities of LUMO-a are 201 to 224 cm2 V−1 s−1 at 300 K along zig-zag and increase up to 339 to 440 cm2V−1s−1 in the arm-chair direction. These values are comparable to some covalent 2D inorganic solids such as MoS242, which is surprisingly high for an organic molecular monolayer that forms through vdW interactions. Carrier mobilities are affected by various processes, thus the predicted values can be different than the measured ones. Nevertheless, it is meaningful to compare theoretical values for a range of molecular layers. Both the calculated hopping (14.7 cm2 V−1 s−1) and the band-like mobility (201–223 cm2 V−1 s−1) of LUMO-a are several times the values calculated for pentacene mono- (hopping, ~10–15 cm2 V−1 s−1) and bi-layers (band-like, 9–65 cm2 V−1 s−1) transport40, where the molecular arrangement does not favor effective π-π interaction in the conduction band. The band-like mobilities of LUMO-b and -c also appear to be high. However, the band-like transport mechanism is probably not applicable owing to their modest hybridization within the monolayer. Their hopping mobilities are calculated to be 4.4–8.3 cm2 V−1 s−1, consistent with previous experimental and theoretical values for C60 bands with unfavorable intermolecular interactions9.

## Discussion

We have provided the experimental evidence and the theoretical understanding for an unusually dispersive NFE-like conduction band of a C60 monolayer, which we attribute to a favorable vdW templating of C60 molecules that enhance ππ interactions. In the literature on organic electronics, there are many discussions of π-π interactions, and how they might enhance charge transport, without much actual evidence that NFE band could be induced by π-π interactions. In this work, we show that it does happen for a molecule like C60 if the π-π interactions are favored by an appropriate substrate template. The first realization of the NFE conduction band in a C60 monolayer presents a new target for exploring the influence of structure on strongly correlated phenomena, e.g., insulating, metallic, superconducting and even magnetic phases5,6,43,44, in this material. The fact that the π-π vdW interactions could trigger the NFE-like electronic band formation implies that templating of intermolecular interactions by vdW forces on otherwise weakly interacting substrates45 provides a promising strategy for tailoring remarkable electronic properties in organic materials for electronics and optoelectronics2,3,4,46.

## Methods

### Sample preparation and STM/STS measurements

The BP crystals are self-grown using a chemical vapor transport (CVT) method [red phosphorus, tin iodide (SnI4), and tin powders as the starting materials] in a two-zone tube furnace in a temperature gradient of 600–540 °C. The STM and spectroscopy experiments are carried out in an ultrahigh vacuum low temperature STM system (CreaTec). Prior to STM experiments, the BP crystals are cleaved in-situ in a preparation chamber under ultrahigh vacuum at room temperature (RT). C60 molecules (99.9% purity, Aldrich) are sublimated from a resistively heated evaporator onto a freshly prepared BP surface. The room-temperature sample is then immediately transferred into the STM chamber, and cooled down to 77 and/or 4.5 K. The adsorption structure of C60 molecules within the monolayer is stable at LN2 temperature. STM topographic images are acquired in the constant-current mode. The dI/dV spectra are measured using the standard lock-in technique with a bias modulation of 15 mV at 321.333 Hz. The STM tips are chemically etched tungsten or mechanically cut Pt-Ir wires, which are further calibrated spectroscopically against the Shockley surface states of cleaned Cu(111) or Au(111) surfaces before being utilized on C60/BP.

### DFT calculations

First-principles DFT calculations are performed using the Vienna Ab initio Simulation Package47,48. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional49 along with the projector-augmented wave potentials50,51 are used for the self-consistent total energy calculations and geometry optimization. The energy cutoff for the plane-wave basis is set to 400 eV for all calculations. In the band structure calculation, a 7 × 5 × 1 K-mesh is adopted to sample the first BZ of the conventional unit cell of the slab of C60; 60 points are collected along each high symmetry line in reciprocal space. vdW interactions are considered at the vdW-DF level when optimizing the system geometry52,53. With the optB86b-vdW exchange functional, the optimized lattice constant is in good agreement with the experimental values for BP [3.3 Å (zig-zag) and 4.3 Å (arm-chair)]. The unit cell is optimized fully by letting all atoms in the cell to relax until the residual force per atom is <0.01 eV Å−1. A 15 Å vacuum layer separates the neighboring slabs of C60 monolayer in vacuum and when deposited on BP. We use a slab model composed of 3 layers of BP to simulate the BP surface.

### Charge carrier mobility calculations

Phonon-limited carrier mobility in C60 monolayer with a finite effective thickness Weff is expressed as Eq. 1:41,54,55,56,57

$$\mu _{{\mathrm{film}}} = \frac{{{\mathrm{\pi e}}\hbar ^4C_{{\mathrm{film}}}}}{{\sqrt 2 \left( {k_{\rm{B}}T} \right)^{3/2}(m ^\ast )^{5/2}(E_1^i)^2}}F.$$
(1)

Here, m* represents the effective mass along the transport direction and E1 is the deformation potential constant of the VBM (hole) or CBM (electron) along the transport direction; it is determined by $$E_1^i = \Delta V_i{{/}}(\Delta {{l/}}l_0)$$. Here ΔVi is the energy change of the ith band under proper compressive and tensile strain (by a step $$\frac{{\Delta {{l}}}}{{l_0}} = 0{\mathrm{.5\% }}$$), l0 is the corresponding lattice constant along the transport direction, and Δl is the deformation of the lattice constant. The variable Cfilm is the elastic modulus of the longitudinal strain in the propagation direction, which is derived by (EE0)/V0 = Cl/l0)2/2; E represents the total energy and V0 represents the lattice volume at the equilibrium for a 2D system. A crossover function F bridges the 2D and 3D cases, and is estimated by Eq 2:

$$F \equiv \frac{{\mathop {\sum}_n {\left\{ {\frac{{\sqrt \pi }}{2}\left[ {{\mathrm{1 - erf}}\left( {\Omega \left( n \right)} \right)} \right] + \Omega \left( n \right)e^{ - \Omega ^2\left( n \right)}} \right\}} }}{{\mathop {\sum}_n {\left[ 1 + \Omega ^2(n) \right]e^{ - \Omega ^2\left( n \right)}} }},$$
(2)

where

$$\Omega (n) \equiv \sqrt {\frac{{n^2\pi ^2\hbar ^2}}{{2m ^\ast W_{{\mathrm{eff}}}^2 k_{\mathrm{B}}T}}},$$
(3)

The Ω(n) (Eq. 3) represents an error function and the summation over integer n is due to quantum confinement along the z-direction. Effective thickness of the film, Weff, is expressed by Eq. 4:

$$\frac{1}{{W_{{\mathrm{eff}}}}} = {\smallint }_{{\mathrm{ - }}\infty }^{{\mathrm{ + }}\infty } P_i{{(z)}}P_f{(z)\mathrm{d}z} = \mathop {\sum }\limits_n \frac{{\rho _i^n{{(z)}}}}{{{\mathrm{N}}\Delta {{z}}}} \cdot \frac{{\rho _i^n{{(z)}}}}{{{\mathrm{N}}\Delta {{z}}}}\Delta {{z}},$$
(4)

Here, P(x) is the electron probability density along the z direction. We divided the space along the z direction into n parts by Δz. Variable ρn(z) is the sum of the number of electrons nth region along the z direction. Here, N is the total number of valence electrons in the film, i and f represent equilibrium and deformed films, respectively. All lattice structural properties and electronic structures in the calculation of carrier mobilities are obtained using the optB86b-vdW functional. The temperature used for the mobility calculations is 300 K.

To evaluate the mobility due to the electron/hole hopping between the adjacent molecules, we apply a treatment expounded by Deng and Goddard58, which is based on the Marcus-Hush theory59,60. The charge transfer rate, Wij, between the i-th and j-th pair of molecules is evaluated as Eq. 5:

$$W_{{\mathrm{ij}}} = \frac{{V_{{\mathrm{ij}}}^2}}{\hbar }\left(\frac{\pi }{{\lambda k_{\rm{B}}T}}\right)^{{\mathrm{1/2}}}{\mathrm{exp}}^{ - \frac{\lambda }{{4k_{\rm{B}}T}}},$$
(5)

where Vij is the coupling matrix element and λ is the reorganization energy. By assuming that the charge transfers between pairs of molecules are independent of each other, we can obtain the diffusion constant as Eq. 6:

$${\mathrm{D = }}\left\langle {\frac{1}{{2d}}\mathop {\sum }\limits_j r_{{\mathrm{ij}}}^2W_{{\mathrm{ij}}}P_{{\mathrm{ij}}}} \right\rangle _{i = {\mathrm{1,2}}};P_{{\mathrm{ij}}}{\mathrm{ = }}\frac{{W_{{\mathrm{ij}}}}}{{\mathop {\sum }\nolimits^ W_{{\mathrm{ij}}}}},$$
(6)

where for 〈…〉i = 1,2 we take the mean value over two independent molecules in a unit cell, and j runs over six neighboring molecules to the i-th molecule. rij is the distance between adjacent molecules and d= 2 is the system dimension. The Einstein’s relation gives the mobility in the form of Eq. 7:

$$\mu \, {\mathrm{ = }}\frac{e}{{k_BT}}{\mathrm{D}}.$$
(7)

We take the reorganization energy of single C60 molecule to be λ = 0.06eV61,62.

## Data Availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

This work is financially supported by the National Key R&D Program of China (Grant Nos. 2017YFA0303500, 2017YFA0303504); the Strategic Priority Research Program of Chinese Academy of Science (Grant No. XDB30000000); the National Natural Science Foundation of China (Grant Nos. 11574364, 11622437 and 61674171), the Fundamental Research Funds for the Central Universities of China and the Research Funds of Renmin University of China (Grant No. 16XNLQ01). Calculations are performed at the Supercomputer Center of Wuhan University and Environmental Molecular Sciences Laboratory at the PNNL, and Physics Lab of High-Performance Computing of Renmin University of China. The contributions from M.F. and H.P. thank partial support from DOE-BES Division of Chemical Sciences, Geosciences, and Biosciences Grant No. DE-SC0002313, and Petek thanks the Luo Jia Visiting Chair Professorship.

## Author information

L.C. synthesized BP crystals. X.C., D.H., Q.L., Z.C. and Y.L. performed STM experiments. H.G., L.Z. and J.Q. performed theoretical calculations. M.F. conceived and provided advice on the experiment and analysis. W. J. conceived and provided advice on theoretical calculation. M.F., C.L., W.J. and H.P. participated in the data discussion. M.F., W.J. and H.P. wrote the paper with contributions from all the authors.

Correspondence to Wei Ji or Hrvoje Petek or Min Feng.

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### Competing interests

The authors declare no competing interests.

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