Abstract text (incl. figure legends and references)
For most of the 20th century, the large size of electron probes restricted our view of physical science to measurements of energy and momentum, leading to many misconceptions about the electronic behavior of nanoscale structures. Thus, measurements of Al nanoparticles using angle resolved EELS showed strong surface plasmons, but very little bulk plasmons, suggesting that small structures are dominated by a surface/bulk ratio considerations.[1] When nm probes became available, experiments showed that EELS scattering depended more on the local probe/specimen geometry, than the particle size.[2] This realization contributed to an exciting period of EELS equipment development aimed at high spatial and energy resolution that continues today.[3]
At first, simple boundary value calculations, using plane waves, were used to predict energy loss spectra as a function of transferred momentum. The energy transfer was assumed to be stochastic, carrying no phase information about the specimen excited state. In 1976, Rose proposed a Mixed Dynamical Form Factor for EELS to allow imaging of the phase of a surface plasmon.[4] His convincing argument led me to a channeling experiment in 1993 that cleanly separated the bulk plasmon from inter-band scattering in diamond, based on the transverse spatial parity of the scattered electron wavefunction.[5]
After the success of sub-Ångstrom imaging using aberration correction, observation of atomic motion became ubiquitous, and yet difficult to understand.[6] It was generally thought that an attractive, dielectric response would dominate the forces between a passing keV electron and a polarizable object. Yet for very close approaches, nanoparticles were observed to move away from the passing electron beam. Using time-dependent force calculations based on experimental dielectric data, we found that the magnetic field carried by the relativistic electron appeared to mediate the repulsive behavior.[7] This conclusion is tantalizing but has not yet been confirmed by other workers.
These findings of significant dependence on space and time suggest that spatially resolved EELS might soon enter the arena of relativistic space-time physics, using the geometric space-time algebra of Hestenes.[8] In addition, this kind of treatment might synergistically couple with ongoing work in quantum gravity, through the AdS-CFT correspondence that relates electromagnetism to quantum gravity.[9] In the spirit of this reasoning, I will show an EELS experiment from Vincent and Silcox, in 1973, [10] that appears to match the topology of a Penrose Diagram for entropy information exchange through an event horizon of a black hole.
References
[1] H. Petersen, Solid State Communications 23 931-934, (1977).
[2] P.E. Batson, Solid State Communications 34 477 - 480, (1980).
[3] M.J. Lagos, I. Bicket, S. Mousavi and G. Botton, Microscopy, 71S i174-i199 (2022).
[4] H. Rose, Optik 45 139 (1976), Ultramicroscopy 15 173-192 (1984).
[5] P.E. Batson, Phys. Rev. Lett., 70 1822-1825 (1993).
[6] P.E. Batson, N. Dellby and O.L. Krivanek, Nature, 418 617 - 620 (2002).
[7] M.J. Lagos, A. Reyes-Coronado, A. Konečná, P.M. Echenique, J. Aizpurua and P.E.
Batson, Phys. Rev. B, 93 205440 (2016).
[8] D. Hestenes, Oersted Medal Lecture, American Journal of Physics 71, 104 (2003).
[9] A.V. Ramallo, https://doi.org/10.48550/arXiv.1310.4319
[10] R. Vincent, J. Silcox, Phys. Rev. Lett. 31 1487 (1973).