In 1959, Richard Feynman envisioned downscaling of information storage and machines to atomic dimensions (1). Both visions were eventually realized: by writing information via positioning single atoms on a nickel surface in 1990 (2), and by devising the first artificial, light-driven molecular machine in 1999 (3). The latter has been inspired by molecular machines in biological systems (4,5) and led to the design of countless artificial molecular machines (6–12). However, most synthetic molecular machines, although driven by quantum processes, exhibit classical kinetics (13,14), whereas operation by quantum tunneling motion is largely elusive. Scanning tunneling microscopy (STM) provides an ideal platform for investigating the dynamics of atoms and molecules on surfaces (10–12,15–22). However, few studies were aimed at achieving controlled, STM-tip position-independent, directional motion that requires breaking of inversion symmetry, which is commonly achieved by adsorbing chiral molecules on achiral surfaces (10–12,15). We reverse this concept by using the surface of noncentrosymmetric PdGa crystals as chiral stator. This relaxes the geometric constraints on the rotor molecule, and allows directed motion even for simple and symmetric molecules such as C₂H₂.

The starting point of our study is the creation of a well-defined chiral surface from a noncentrosymmetric single crystal, namely the intermetallic compound palladium–gallium with 1:1 stoichiometry (PdGa) exhibiting bulk-terminated chiral surfaces (23). The chiral structure of some of these surfaces manifests itself in pronounced enantioselective adsorption properties (24). Here we choose the threefold symmetric$\left(\overline{1}\overline{1}\overline{1}\right)$ surface of the PdGa A enantiomorph (23). Under appropriate ultrahigh vacuum preparation, it terminates by a layer containing three Pd atoms per trigonal surface unit cell$\left(a_0=6.95\AA \right)$ forming an equilateral triangle of 3.01 Å side length (SI Appendix, Fig. S1 and ref.25). The local inversion symmetry of this Pd trimer is lifted by coordination of the six second-layer Ga atoms and furthermore by three Pd atoms in the third layer (Fig. 1A andB). In the following we will denote this termination as Pd₃.

On Pd₃, acetylene molecules adsorb on top of the Pd trimers (26). When imaged by STM at 5 K, they appear as dumbbells with lobe-to-lobe separation of about 3 Å in three symmetrically equivalent 120°-rotated orientations (Fig. 1E–G) between which they switch quasiinstantaneously (Fig. 1C andD). Acetylene molecules are firmly anchored to the trimer and usually dissociate before being dragged off the trimer by STM-tip manipulation.

We have followed the rotation events by recording tunneling current time series I_T(t) at a fixed tip position (Fig. 1H), in analogy to the STM investigation of the rotation of chiral butyl–methyl–sulphide on Cu(111) (10). In the latter case, a weak (≤5%) asymmetry in the number of clockwise (CW)$n_{CW}$ and counterclockwise (CCW)$n_{CCW}$ rotations was reported and tentatively attributed to chiral STM tips, as no correlation of the directionality with the molecule’s enantiomeric form was found. The I_T(t) ofFig. 1H, recorded over$\mathrm{\Delta }t=100\hspace{0.5em}\text{s}$, exhibits cyclic jump sequences between three levels (…R_A→R_B→B_C→R_A…) with$n_{CCW}=23$ jumps in the CCW direction and$n_{CW}=0$ in CW, resulting in a frequency$f=\frac{n_{CCW}+n_{CW}}{\mathrm{\Delta }t}=0.23\hspace{0.5em}\text{Hz}$ and perfect directionality$dir=100\%\ast \frac{n_{CCW}-n_{CW}}{n_{CCW}+n_{CW}}=100\%$.Movie SV1 shows a time-lapse series of STM images evidencing the prevailing CCW rotation of the motor.

Analyzing the parametric dependence of the rotation frequency (Fig. 2A–C andSI Appendix, Fig. S2) shows that this molecular motor operates in two distinct regimes; the tunneling regime (TR) where its rotation frequency${\nu }_T$ is independent of temperature$T<15\hspace{0.5em}\text{K}$, bias voltage$\left|V_G\right|<30\hspace{0.5em}\text{mV}$, and current$I_T<200\hspace{0.5em}\text{pA}$, and the classical regime (CR) where the frequency strongly depends on these parameters. Even though all experimental data presented inFig. 1 have been recorded in the TR, we first discuss the CR where C₂H₂ rotations can be selectively powered by thermal or electrical excitations. We find the temperature dependence of the rotation frequency at low bias (Fig. 2A) to follow an Arrhenius characteristic (solid line inFig. 2A)$\nu \left(T\right)={\nu }_T+{\nu }_A\text{exp}\left(-\frac{\mathrm{\Delta }{E}_B}{k_{B}T}\right)$[1], with${\nu }_T=4.5\hspace{0.5em}\text{Hz}$,${\nu }_A={10}^{8.7\pm 2.0}\text{Hz}$ (attempt frequency), and$\mathrm{\Delta }{E}_B=27.5\pm 7.1\hspace{0.5em}\text{meV}$ (energy barrier for rotation). Above 30 mV the frequency increases exponentially with$V_G$, independent of polarity (Fig. 2B andC). Under the same conditions, but at constant bias voltage, the power-law dependence$\nu \propto I_T^n$ with$n\approx 1$ (Fig. 2D) identifies the electronically stimulated rotation as a single-electron process (27). As we will discuss later, the parametric dependence of the rotation frequency and directionality with$T$,$V_G$, and$I_T$ is very well reproduced by a Langevin kinetic model (solid lines inFig. 2B andC).

Before we discuss the parametric dependence of the directionality, the influence of the STM tip, required for observing the motion, must be clarified. Particularly, we have to verify that breaking of the inversion symmetry due to the tip position (and possibly tip structure) in proximity to the motor does not prevail over the influence of the chiral substrate in determining the sense of rotation. To address this issue, we have measured 6,400 constant current tip-height time series$z_T\left(t\right)$ on a grid of$80\times \hspace{0.5em}80$ equidistant points covering$1\times 1\hspace{0.5em}{\text{nm}}^2$ in the vicinity of single acetylene molecules in the TR. Analysis of all these$z_T\left(t\right)$ series reveals an intricate, regular pattern with alternating, highly directional ascending (red) and descending (blue) jump sequences (Fig. 2E). This pattern fully corroborates a tip-position-independent, unidirectional rotation of the molecule, which becomes apparent by modeling and mapping the position-dependent jump sequence assuming a cyclic unidirectional CCW rotation of the molecule by 60° steps (SI Appendix, Figs. S4–S7). After optimizing molecule configuration and tip shape in the model, an excellent agreement of the simulated jump-sequence map (Fig. 2F) with the experiment is found. Hence, we conclude that, regardless of the tip position, the jump sequences always correspond to CCW rotations. Furthermore, as witnessed fromFig. 2G, there is no pronounced dependence of${\nu }_T$ on the tip position, and all three rotational C₂H₂ configurations can be expected to be energetically equivalent, as derived from the residence time analysis inSI Appendix, Figs. S8–S10. The three rotational states only become energetically nondegenerate if the tip is brought very close to the substrate, such that it significantly alters the surface ratchet potential (SI Appendix, Fig. S3). Although we investigated hundreds of molecules with tens of different tip modifications, we never observed any systematic CW rotations in the TR or CR evidencing that solely the stator dictates the direction and directionality of the rotation. Evaluating 1,792 rotation events ($n_{CCW}=\mathrm{1,771}$ and$n_{CW}=21$) in the TR, we determine a directionality$dir\ge 96.7\%$ with$2\sigma$ confidence. By matching the simulated jump-sequence map to the experiment we identify the C₂H₂ rotation to be best described as a tumbling rotor, whose center of mass moves on a circle with radius$r=0.5\pm 0.1\hspace{0.5em}\text{Å}$ and a moment of inertia$I_{C_2{H}_2}=5.62\times {10}^{-46}{\text{kgm}}^2$ (Fig. 2H).

Having clarified the influence of the tip, we now turn to the discussion of the parametric dependencies of the directionality (Fig. 3A–D). The temperature dependence shows a rapid drop in directionality once thermally activated rotations start to contribute significantly. The solid line inFig. 3A assumes that${\nu }_T$ exhibits 98% directionality, whereas the thermally activated jumps described by the Arrhenius equation1 are purely random. These random thermal rotation events are expected because substrate, STM tip, and hence molecule are in thermal equilibrium and, accordingly, unidirectional rotation (which reduces entropy) is forbidden by the second law of thermodynamics. At$T=5\hspace{0.5em}\text{K}$ a decrease of directionality is also observed for bias voltages$V_G$ beyond$\pm 35\hspace{0.5em}\text{meV}$ (Fig. 3B). However, unlike thermal rotations, those induced by inelastic electron tunneling (IET) only become gradually nondirectional. This is clearly observed in the regime where thermally and IET induced rotations coexist. As displayed inFig. 3C, the voltage-independent directionality of only 10% at$T=19\hspace{0.5em}\text{K}$ and$\left|V_G\right|<30\hspace{0.5em}\text{mV}$, can be increased significantly at higher$\left|V_G\right|$ due to additional directed IET rotations. This increase is only effective in a narrow voltage window, above which the directionality rapidly decreases. By contrast, the$I_T$ dependence of the directionality for a fixed voltage is weak (Fig. 3D), where the slight decrease with increasing current, i.e., frequency, is attributed to the detection of two rapidly successive CCW rotations as a single erroneous CW one (solid lines inFig. 3D). Hence we conclude that directionality stays above 95% for$\left|V_G\right|<40\hspace{0.5em}\text{mV}$ even at high current.

The observation of directional motion triggered from a noncyclic, directionless, and position-independent energy input stemming from a single IET event, prompts us to apply a variant of the biased Brownian motion concept proposed by Astumian and Hänggi for modeling the underlying mechanism (28,29). Our model of IET-induced rotation assumes a static, periodic, but asymmetric potential$U\left(\varphi \right)$ ($\varphi =\left[\mathrm{0,2}\pi \right]$, with$\frac{\pi }{3}$ periodicity), with the asymmetry of the potential,$R_{asym}$, defined inFig. 3E,Inset andSI Appendix, Fig. S11. A single IET event instantaneously excites the molecule from its ground state and its trajectory$\varphi \left(t\right)$ is obtained from Langevin dynamics$I\ddot{\varphi }=-\frac{\partial U\left(\varphi \right)}{\partial \varphi }-\lambda \dot{\varphi }$, whereI is the moment of inertia and$\lambda$ the viscous dissipation coefficient (28,29). Depending on$R_{asym}$ and$\lambda$, two dissimilar minimum kinetic energies$E_L$ and$E_R$ are required to overcome the barrier to the left (i.e., CW) and to the right (i.e., CCW), respectively. These energies are the basis for describing frequency and directionality by the kinetic model (SI Appendix).

Matching this kinetic model to our experimental data inFigs. 2C and3C allows determination of the temperature-dependent$E_L\left(T\right)$ and$E_R\left(T\right)$ which are represented by colored markers inFig. 3E. From these values we deduce$R_{asym}$ to be$1.25<R_{asym}<1.5$ assuming$\mathrm{\Delta }{E}_B=25\hspace{0.5em}\text{meV}$. The reduction of the dissipation$\lambda$ from about$1.6\times {10}^{-33}\frac{{\text{kgm}}^2}{\text{s}}$ at 5 K to around$1.1\times {10}^{-33}\frac{{\text{kgm}}^2}{\text{s}}$ at 20 K can be attributed to the less efficient coupling of the molecule to the substrate with increasing temperature.

Having successfully described the rich phenomenology of the over-the-barrier rotation processes in the CR, the unexpected, nearly perfect unidirectional rotation of C₂H₂ in the TR requires closer inspection. Tunneling, especially of hydrogen, is a well-established phenomenon in chemistry (30) and surface science (19), and plays a crucial role in numerous biological processes like enzyme-catalyzed reactions (31). The approximately exponential decrease of the tunneling rate with increasing mass, however, allows reasonably high tunneling rates of heavy atoms or molecules only for very small barrier heights and tunneling distances. Despite these restrictions, many tunneling transitions on surfaces involving heavy atoms like cobalt or small molecules have been reported (15,20,21,32).

In this respect, the tunneling of formaldehyde (CH₂O) between two adsorption configurations on Cu(110) reported by Lin et al. is very close to the C₂H₂ rotation in terms of$\mathrm{\Delta }{E}_B$, moment of inertia, and rotation angle, and thus yields comparable frequencies${\nu }_T$ (32). In both cases${\nu }_T$ is critically tip-condition-dependent and varies between 0.01 and 0.1 Hz for CH₂O/Cu(110) and between 0.25 and 5 Hz for C₂H₂/Pd₃ surface. Thus, to evidence the strong isotopic dependence and corroborating quantum tunneling, we have paid attention that the${\nu }_T$ for C₂H₂, fully (C₂D₂), and partially deuterated acetylene (C₂DH) are determined consecutively on the same sample with the same STM tip (SI Appendix, Fig. S15).Fig. 4A shows the resulting$I_T\left(t\right)$ sequences for C₂H₂, C₂DH, and C₂D₂ which reveal${\nu }_T$ ratios (with respect to C₂H₂) of$1:0.56\left(11\right):0.24\left(5\right)$ (C₂H₂:C₂DH:C₂D₂), which we consistently observe with different tips (SI Appendix, Table ST3 and Fig. S16). This strong relative reduction of${\nu }_T$ is contrasted by the comparatively small relative change of moment of inertia 1$:1.08:1.2$ and thus indicative for quantum tunneling. Careful inspection of the$I_T\left(t\right)$ sequence of C₂DH with broken C₂ symmetry reveals that the rotation cycles through six rather than three current levels (Fig. 4B), which proves that a full acetylene rotation indeed requires six CCW 60° rotations. Comparison of the experimentally determined${\nu }_T$ ratios to the corresponding Wentzel–Kramers–Brillouin (WKB) tunneling frequency (SI Appendix) shows an excellent match for a barrier height of$\mathrm{\Delta }{E}_B=25\hspace{0.5em}\text{meV}$ (Fig. 4D).

Quantum tunneling rotations concomitant with high directionality of 97.7% allow for an estimation of the entropy change of a single tunneling rotation from the experimental CCW and CW rotation probabilities, given by$\mathrm{\Delta }S=-k_B\text{ln}(p_{pCCW}/p_{CW})\approx -k_B\text{ln}\left(100/1\right)\approx -0.4\frac{\text{meV}}{\text{K}}$. This implies that the directional rotation in the TR must be a nonequilibrium process with energy dissipation$\mathrm{\Delta }Q>2\hspace{0.5em}\text{meV}$ at 5 K and$\mathrm{\Delta }Q>6\hspace{0.5em}\text{meV}$ at 15 K per rotation. As these values of$\mathrm{\Delta }Q$ are on the order of the energy difference of two frustrated rotation modes of C₂H₂ (e.g.,$\hslash {\omega }_{10}-\hslash {\omega }_{00}=6.8\hspace{0.5em}\text{meV}$;Fig. 4C andSI Appendix, Fig. S14 and Table ST2), one might assume that the required nonequilibrium tunneling proceeds via an excitation from the ground state to a bound rotational mode as proposed by Nacci et al. (21). We estimate a maximum power dissipation of 100 meV/s per motor, assuming 10-Hz tunneling frequency as upper bound. On the other hand, the STM required for monitoring the rotation, locally dissipates at least 3 × 10⁶ meV/s even at the lowest settings of 1-pA tunneling current and 0.5-mV bias. We still observe the constant rotation frequency with persisting high directionality at such extreme settings. Therefore, the STM tip is presumably critical in driving the system out of equilibrium also in the regime of tunneling motion.

In conclusion, the highly directional tumbling rotation of C₂H₂ on the chiral PdGa{111}Pd₃ surfaces exhibits a rich phenomenology, most prominently characterized by an unprecedentedly high directionality and small motor size. Its rotor (C₂H₂) and stator (Pd₃-Ga₆-Pd₃ cluster) shown inFig. 1A comprise just 16 atoms to form a unidirectional six-state cyclic molecular motor (Fig. 4B) through all of which it cycles ceaselessly, powered exclusively by single electrons. This contrasts reported motors driven by light or chemical reactions, since for the former concerted thermal and light-driven activation is required. The latter usually requires a cycling of the chemical environment to complete one cycle. In the classical regime, we could establish a Langevin kinetic model of the motion describing frequency and directionality with temperature, STM bias voltage, and tunneling current. The model provides robust values for the rotational potential asymmetry$R_{asym}$ and the temperature dependence of the viscous dissipation coefficient$\lambda \left(T\right)$ relating the operation of this molecular machine to atomic friction. The negative entropy change associated with the high rotation directionality, also observed in the tunneling regime, challenges the understanding of this simple cyclic machine in terms of dissipative quantum tunneling dynamics (33). In the future, it might be possible to convert energy via forced excitations, e.g., optical, or by IET, into directional motion and thus investigating energy harvesting at the smallest possible length scale.