There are certain crystals where the atoms are arranged like a never-ending set of Russian nesting dolls, repeating the same pattern forever as you zoom in.
April 6, 2026
Original Paper
Evolution from Landau Quantization to Discrete Scale Invariance Revealed by Quantum Oscillations in Topological Materials
arXiv · 2604.02630
The Takeaway
Researchers discovered a material where electronic properties don't just change smoothly, but repeat in perfectly scaled copies. This 'discrete scale invariance' is a rare effect usually reserved for exotic high-energy physics, but here it is happening inside a solid object.
From the abstract
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 fr