When Electrons Collapse to a Point express
In the crystal HfTe5, electrons behave almost like light: their mass is so small that they obey the laws of relativity. If you place such a crystal in a strong magnetic field, the electrons start to circle in tiny orbits. Their energy then changes not smoothly but in steps, like floors in a building. In a weak field, you see one pattern of these steps, and in a strong field, another, with a special rhythm.
The transition between these patterns is like a change of music: first a steady metronome, then a rhythm where each successive beat lags by the same factor. Such a rhythm is a sign that states appear in the material resembling an electron falling onto a very heavy nucleus. In ordinary atoms, this does not happen, but here an impurity with a large charge creates the conditions for 'collapse.'
But the most interesting part is that this process depends on the electron density in the crystal. By changing it, you can control how strongly the vacuum 'eats' the impurity's charge. This means that a solid acts as a tiny laboratory for testing ideas about how the vacuum behaves near superheavy nuclei. And all of this — at temperatures available in an ordinary lab.
Original abstract
as written by the authors arXiv:2604.02630
Dirac materials have been a unique solid state platform for exploring relativistic quantum phenomena including supercritical atomic collapse, which leads to emergent discrete scale symmetry and logperiodic quantum oscillations. In the relativistic regime, the fundamental effect in quantum electrodynamics, vacuum polarization, can further modulate the atomic collapselike state by screening bare charges but is rarely harnessed in condensed matter system. Here, we report a continuous progression from low field Shubnikov de Haas oscillations to high field log periodic oscillations in the Dirac material HfTe5, with both phenomena modulated by Fermi surface anisotropy. This maps the transition from single particle Landau levels to an interaction-driven, discrete scale invariant energy spectrum of quasi-bound states. Crucially, our findings suggest vacuum polarization provides a compelling mechanism for renormalizing the effective impurity charge, quantitatively explaining the carrier-density dependent scale factor. By revealing the intricate interplay between Landau quantization, many body electronic screening, and scale-symmetry breaking, our results establish Dirac solids as a controllable platform for exploring relativistic vacuum effects and emergent novel symmetry.
Log-periodic oscillations are a rare guest in solid-state physics. They arise when a system possesses discrete scale symmetry: if you change the scale by a certain factor, the pattern does not change. Such behavior occurs, for example, in turbulence and in finance.
In Stanisław Lem's novel 'Solaris,' the ocean exhibits structures that repeat themselves at different scales: this resembles the discrete scale symmetry seen in HfTe5.