Theory of Atomic-Scale Vibrational Mapping and Isotope Identification with Electron Beams

Phonon transition across an isotopic interface

Isotopic mixtures result in distinct properties of materials such as thermal conductivity and nuclear process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in atomic-scale isotopic identification. Here, using electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent phonon behavior at the h-¹⁰BN/h-¹¹BN isotope heterostructure with sub-unit-cell resolution. We find the phonons' energy changes gradually across the interface, featuring a wide transition regime. Phonons near the Brillouin zone center have a transition regime of ~3.34 nm, whereas phonons at the Brillouin zone boundary have a transition regime of ~1.66 nm. We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, the variation of phonon energy between atom layers near the interface depends on both of momentum transfer and mass change. This study provides new insights into the isotopic effects in natural materials.

Entangling free electrons and optical excitations

The inelastic interaction between flying particles and optical nanocavities gives rise to entangled states in which some excitations of the latter are paired with momentum changes in the former. Specifically, free-electron entanglement with nanocavity modes opens appealing opportunities associated with the strong interaction capabilities of the electrons. However, the achievable degree of entanglement is currently limited by the lack of control over the resulting state mixtures. Here, we propose a scheme to generate pure entanglement between designated optical-cavity excitations and separable free-electron states. We shape the electron wave function profile to select the accessible cavity modes and simultaneously associate them with targeted electron scattering directions. This concept is exemplified through theoretical calculations of free-electron entanglement with degenerate and nondegenerate plasmon modes in silver nanoparticles and atomic vibrations in an inorganic molecule. The generated entanglement can be further propagated through its electron component to extend quantum interactions beyond existing protocols.

Imaging of isotope diffusion using atomic-scale vibrational spectroscopy

The spatial resolutions of even the most sensitive isotope analysis techniques based on light or ion probes are limited to a few hundred nanometres. Although vibrational spectroscopy using electron probes has achieved higher spatial resolution^1-3, the detection of isotopes at the atomic level⁴ has been challenging so far. Here we show the unambiguous isotopic imaging of ¹²C carbon atoms embedded in ¹³C graphene and the monitoring of their self-diffusion via atomic-level vibrational spectroscopy. We first grow a domain of ¹²C carbon atoms in a pre-existing crack of ¹³C graphene, which is then annealed at 600 degrees Celsius for several hours. Using scanning transmission electron microscopy-electron energy loss spectroscopy, we obtain an isotope map that confirms the segregation of ¹²C atoms that diffused rapidly. The map also indicates that the graphene layer becomes isotopically homogeneous over 100-nanometre regions after 2 hours. Our results demonstrate the high mobility of carbon atoms during growth and annealing via self-diffusion. This imaging technique can provide a fundamental methodology for nanoisotope engineering and monitoring, which will aid in the creation of isotope labels and tracing at the nanoscale.