Evidence for atomic-scale vibron-mediated electron bunching

TL;DR

This work demonstrates that atomic-scale vibron coupling can induce electron bunching in transport through a single Fe impurity in Bi_2Se_3, revealed by combined STM/STS and shot-noise measurements. The observed vibronic sidebands follow a Franck–Condon blockade with a coupling strength λ ≈ 2.6 and a surface vibron mode spacing of ħω_osc ≈ 16 meV, accompanied by super-Poissonian noise at the impurity center. A Holstein-type model links the enhanced noise to vibron excitation dynamics, while DFT and control experiments rule out alternative sources such as modulated tunnelling or interference; the findings suggest a pathway toward on-demand injection of N-paired electrons if coherence can be established. These results highlight a novel avenue for local, atomically precise control of electron correlations with potential implications for quantum materials and nanoscale electron injection technologies.

Abstract

Due to the Coulomb blockade effect, electrons rarely bunch during transport, a phenomenon observed only in a few specially engineered mesoscopic configurations. In this work, we introduce an atomically resolved shot-noise study to demonstrate the possibility of electron bunching through vibrational coupling which takes place in an atomically sized nano-electro-mechanical system. Using tunnelling spectroscopy, we observe signatures of vibron-assisted tunnelling on an Fe impurity in Bi$_2$Se$_3$. Notably, simultaneous shot-noise measurements at the centre of the vibrating impurity reveal super-Poissonian noise. In the absence of alternative sources of super-Poissonian noise, this implies vibronic-coupling-induced bunching of electrons during the tunnelling process through the impurity, as theoretically predicted decades ago. As a future outlook, if coherence between electrons can be implemented, vibron-mediated electron bunching at single atomic sites may be exploited as a local injection source of $N$-paired electrons.

Figures (4)

• Figure 1: Schematic illustration of the experiment highlighting the key aspects of the study.a A subsurface impurity (Fe) is considered in a solid-state host (Bi$_2$Se$_3$) under the STM tip. In the absence of tunnelling, the impurity remains at rest in a stationary state with only zero-point motion. For weak vibronic coupling ($\lambda \sim 0$) and/or with fast phonon relaxation, tunnelling is elastic and the vibration effectively remains unexcited. b Corresponding current–voltage ($I$–$V$) characteristics exhibit a step-like increase in current without vibrational features. c In this case, the tunnelling events are temporally uncorrelated, resulting in Poissonian shot-noise (Fano factor: $F=1$). Nonetheless, anti-bunching behaviour ($F<1$) may emerge when strong Coulomb repulsion prevents electrons from occupying the same energy state simultaneously and transport becomes sequential. d For strong electron-vibron coupling ($\lambda > 0$) and slow phonon relaxation, the injection of an electron into the impurity excites the vibrational mode. e Each time a new process involving a higher number of vibrons per tunnelling event is energetically allowed, the current increases in a step-like manner, with steps separated by the vibron energy ($\hbar\omega$). f Schematic illustration of the electron bunching process in the presence of vibronic excitations (dashed boxes). The non-zero motion of the impurity provides a positive correlation between tunnelling electrons, leading to super-Poissonian noise ($F > 1$).
• Figure 2: Microscopic and spectroscopic signature of Fe$_1$.a Large scale topography ($V_{\text{bias}}$ = -0.4 V, $\textit{I}$ = 500 pA) showing a range of different impurities. An isolated Fe$_1$ is marked by the dashed box, its position in the unit cell is shown in the inset: the impurity replaces a Bi atom in the first layer beneath the surface upon cleaving the crystal along the van der Waals (vdW) gap. b A high-resolution constant current image of the Fe$_1$ impurity. A low-pass filter is used to remove 50 Hz noise. The scale bar is 1 nm. (c) Normalised differential conductance taken at a constant current of 500 pA (constant height for $|E|<0.1$ eV) at the centre of the impurity (Fe$_1$) and in an impurity-free area (Bi$_2$Se$_3$). The spectrum at the impurity reveals the presence of a resonance within the bandgap of Bi$_2$Se$_3$
• Figure 3: Differential conductance of Fe$_1$.a Constant current image ($V_{\text{bias}}$ = -0.4 V, $\textit{I}$ = 100 pA) showing an isolated Fe$_1$. A low-pass filter is used to remove 50 Hz noise. The scale bar is 1 nm. b Normalised differential conductance, and c its derivative with respect to voltage taken along the cut indicated by the red arrow in (a), showing clear oscillations. d Characteristic differential conductance spectra and e their derivative taken on different Fe$_1$ impurities. f Histogram of the energy spacing between the maxima of the oscillations, $\hbar \omega_{\text{osc}}$. g Franck-Condon fit of the differential conductance spectra, see Supplementary Information Section 2.4 for fitting details.
• Figure 4: Visualisation of electron bunching in a vibrating Fe$_1$ and anti-bunching in 2Fe$_1$.a Normalised differential conductance, b derivative, and c current noise, respectively, taken at $\textit{I}$ = 400 pA at the centre of a Fe$_1$. d Constant current ($\textit{I}$ = 400 pA) image and e, map of the Fano factor extracted from noise measurements on a Fe$_1$. f, g Same as panels (d), (e), but for a 2Fe$_1$ dimer. The scale bar is 1 nm. The noise enhancement observed at the charging ring in (g) follows a non-linear (approximately quadratic) dependence and does not reflect tunnelling statistics or correlation effects, see Fig. S7, in Supplementary Information Section 2.6. All other noise is linear in current. The colour-scale in panels d, f are the same as in Fig. \ref{['fig:3']}a.