Molecular motor crossing the frontier of classical to quantum tunneling motion

Abstract

The reliability by which molecular motor proteins convert undirected energy input into directed motion or transport has inspired the design of innumerable artificial molecular motors. We have realized and investigated an artificial molecular motor applying scanning tunneling microscopy (STM), which consists of a single acetylene (C₂H₂) rotor anchored to a chiral atomic cluster provided by a PdGa(111) surface that acts as a stator. By breaking spatial inversion symmetry, the stator defines the unique sense of rotation. While thermally activated motion is nondirected, inelastic electron tunneling triggers rotations, where the degree of directionality depends on the magnitude of the STM bias voltage. Below 17 K and 30-mV bias voltage, a constant rotation frequency is observed which bears the fundamental characteristics of quantum tunneling. The concomitantly high directionality, exceeding 97%, implicates the combination of quantum and nonequilibrium processes in this regime, being the hallmark of macroscopic quantum tunneling. The acetylene on PdGa(111) motor therefore pushes molecular machines to their extreme limits, not just in terms of size, but also regarding structural precision, degree of directionality, and cross-over from classical motion to quantum tunneling. This ultrasmall motor thus opens the possibility to investigate in operando effects and origins of energy dissipation during tunneling events, and, ultimately, energy harvesting at the atomic scales.

Keywords: molecular motor; scanning tunneling microscopy; surface science.

Fig. 1.

Acetylene rotation on the PdGa:A$\left(\overline{1}\overline{1}\overline{1}\right)$Pd₃ surface. (A) Sketch of the acetylene (C₂H₂) on Pd₃ motor. (B) Atomic structure of the PdGa:A$\left(\overline{1}\overline{1}\overline{1}\right)$Pd₃ surfaces with the PdGa cluster acting as stator highlighted in saturated colors. The C₂H₂ rotor is depicted in one (R_a) of its three equivalent adsorption configurations R_a, R_b, R_c. In A and B, the top-layered Pd trimers $\left(z=0\right)$ are depicted in bright blue, the second-layer Ga trimers $\left(z=-0.85\hspace{0.5em}\text{Å}\right)$ in red, and the third-layered single Pd atoms $\left(z=-1.61\hspace{0.5em}\text{Å}\right)$ in dark blue. (C–G) Constant current STM images of C₂H₂ adsorbed on the Pd₃ surface ($T=5\hspace{0.5em}\text{K}$; $V_G=10\hspace{0.5em}\text{mV}$; $I_T=50\hspace{0.5em}\text{pA}$). In C two rotating molecules are pointed out, whereas in D, recorded 60 s after C, no molecular rotation is observed. (E–G) STM images of the same acetylene molecule in its three rotational configurations. In E the underlying PdGa stator structure is superposed. (H) Tunneling current time series $I_T\left(t\right)$ ($\mathrm{\Delta }t=100\hspace{0.5em}\text{s}$; $V_G=25\hspace{0.5em}\text{mV}$; 1-ms time resolution) measured at the relative position to the C₂H₂ indicated by the red marker in G.

Fig. 2.

Parametric dependence of the rotation frequency and jump sequence. (A) Rotation frequency dependence on temperature ($V_G=10\hspace{0.5em}\text{mV}$; $I_T=100\hspace{0.5em}\text{pA}$), B on bias voltage for both polarities ($T=5\hspace{0.5em}\text{K}$; $I_T=100\hspace{0.5em}\text{pA}$), C on bias voltage at various temperatures between 5 and 19 K; $I_T=100\hspace{0.5em}\text{pA}$), and D on tunneling current for different bias voltages between 33 and 45 mV at $T=5\hspace{0.5em}\text{K}$. In A–D, the markers represent experimental data, while the solid lines are derived from the kinetic model (SI Appendix). (E) Constant current jump-sequence map ($js=3\ast \frac{n_{up}-n_{down}}{n_{up}+n_{down}}=sign\left(js\right)\ast \left|dir\right|$; n_up/down: number of jumps increasing/decreasing the tip height) generated from an 80 × 80 grid (1 × 1 nm²) of individual tip-height time series $z_T\left(t\right)$, each recorded for 4 s (4,000 points; $V_G=10\hspace{0.5em}\text{mV}$; $I_T=100\hspace{0.5em}\text{pA}$). (F) Simulated jump-sequence map for a 100% CCW rotation based on the motion pattern shown in H. (G) Frequency map of the C₂H₂ rotation extracted from the same experimental $z_T\left(t\right)$ grid of E. (H) Our best estimation of the tumbling acetylene rotation on Pd₃ for a full 360° rotation in six 60° steps indicated by tracking the motion of one H atom (1→2→3→1′→2′→3′ with n and n′ denoting indistinguishable C₂H₂ configurations) with the green circle indicating the motion of acetylene’s center of mass.

Fig. 3.

Parametric dependence of the nanomotor’s directionality. (A) Dependence of the directionality on temperature ($V_G=10\hspace{0.5em}\text{mV}$; $I_T=100\hspace{0.5em}\text{pA}$), (B) bias voltage for both polarities ($I_T=100\hspace{0.5em}\text{pA}$; $T=5\hspace{0.5em}\text{K}$), (C) bias voltage at various temperatures between 5 and 19 K ($I_T=100\hspace{0.5em}\text{pA}$), and (D) rotation frequency controlled via varying $I_T$ for several $V_G$. In A–D the markers represent experimental data, while the solid lines in A–C are derived from the kinetic model (SI Appendix). The solid lines in D show simulated dependencies of constant directionality (given in brackets) with frequency considering finite time resolution of the experiment (SI Appendix). (E) Schematic representation of the Langevin rotation dynamics derived for ratchet potentials with $\mathrm{\Delta }{E}_B=25\hspace{0.5em}\text{meV}$. (Left) The range of transferred kinetic energy $E_{kin}$ for directed motion, i.e., $E_L<E_{kin}<E_R$, in dependence on energy dissipation is colored for several $R_{asym}$, as defined in the inset. The experimentally determined $E_L$ and $E_R$ are represented by two markers of the same color for several temperatures. (Right) The trajectories of the C₂H₂ 60° rotation in a ratchet potential with $R_{asym}=2.0$, $\lambda =2\times {10}^{-33}\frac{{\text{kgm}}^2}{\text{s}}$ and $\mathrm{\Delta }{E}_B=25\hspace{0.5em}\text{meV}$ are displayed as a function of $E_{kin}$. From top to bottom: For $E_L<E_R<E_{kin}$ there is no unidirected motion, $E_L<E_{kin}<E_R$ results in directed motion by overcoming the steeper potential barrier, and $E_{kin}<E_L<E_R$ induces no rotation.

Fig. 4.

Quantum tunneling rotation of acetylene. (A) $I_T\left(t\right)$ curves for C₂H₂, C₂DH, and C₂D₂, with a special focus on the six different current levels in an $I_T\left(t\right)$ curve of C₂DH in B. In C the ratchet potential is shown in turquoise, based on which the C₂H₂ quantum states, energy levels, and tunneling frequencies are determined. The color (black to yellow) represents the probability density of the quantum states. The dependence of ${\nu }_T$ in the WKB approximation with the moment of inertia, normalized to the ${\nu }_T$ at 5.62 × 10⁻⁴⁶ kgm² (C₂H₂) is displayed as solid lines in D for several $\mathrm{\Delta }{E}_B$ (SI Appendix). The black markers represent the experimental ${\nu }_T$ for C₂H₂, C₂DH, and C₂D₂, each normalized to the one of C₂H₂.