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Philipp Rahe

Publications and source records attributed to Philipp Rahe.

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From London to Morse via Binnig, Quate, and Gerber

In their landmark paper introducing the atomic force microscope [Phys. Rev. Lett. \textbf{56}, 930 (1986)], Binnig, Quate, and Gerber presciently anticipated that the technique would ultimately be capable of probing interactions running the gamut from weak van der Waals interactions to strong covalent bonding. They also highlighted that the tip-sample forces central to AFM are present, and often highly influential, in scanning tunnelling microscopy; indeed, this realisation directly inspired the invention of the force microscope. In this perspective for the \textit{Forty Years of AFM} special issue, we review selected aspects of two decades of work from our group at the University of Nottingham that span the force range highlighted by BQG and are united by a common, central theme: the probe as active participant rather than passive observer. Our selection of results also covers length- and correlation-scales from the microscopic right down to the single chemical bond limit, tracking a spectrum of interactions from van der Waals/Hamaker forces, through hydrogen bonding, to covalent bonds and, finally, atom-by-atom assembly of metal clusters via vertical tip-sample transfer. Echoing BQG's own observations on the prevalence of probe-sample forces in STM, we also discuss recent evidence that tip-induced heterogeneity underpins first-passage dynamics in molecular diffusion and highlight the challenges in acquiring non-invasive measurements of diffusion barriers for adsorbed molecules that are readily perturbed by the probe. We close with a perspective on machine learning's growing role in automating tip-driven atomic and molecular manipulation.

cond-mat.mes-hall

Static heterogeneity generates apparent universality in first-passage bursty dynamics

Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with putative universality classes $\alpha=1$ and $\alpha=\frac{3}{2}$ having been proposed. Whether the observed $\alpha = 1$ scaling reflects intrinsic scale-free dynamics or instead emerges from heterogeneous underlying rates has been debated at length. We address this question in a canonical physical system for first-passage dynamics: two-dimensional molecular diffusion detected by the tip of a scanning tunnelling microscope. The resulting inter-pulse time distributions exhibit the same apparent truncated power-law form reported for human activities such as email communication, web browsing, and library loans. Maximum-likelihood estimation and model comparison decisively favor a Kohlrausch-Williams-Watts--tempered power law, $P(t)\propto t^{-\alpha}\exp\left(-(t/t_c)^\beta\right)$, with $\alpha \sim 1$. Kinetic Monte Carlo simulations reproduce this behavior, showing that the apparent $\alpha \sim 1$ scaling is confined to a finite time window and arises from tip-induced spatial heterogeneity, not scale invariance.

cond-mat.other

On the possibility of exploring tip-molecule interactions with STM experiments

We present a theory for analyzing residence times of single molecules in a fixed detection area of a scanning tunneling microscope (STM). The approach is developed for one-dimensional molecule diffusion and can be extended to two dimensions by using the same methodology. Explicit results are derived for an harmonic attractive and repulsive tip-molecule interaction. Applications of the theory allows one to estimate the type and strength of interactions between the STM tip and the molecule. This includes the possibility of an estimation of molecule-molecule interaction when the tip is decorated by a molecule. Despite our focus on STM, this theory can analogously be applied to other experimental probes that monitor single molecules.

cond-mat.mes-hall