Both topological insulators and Weyl semimetals, two of the most prominent discoveries in condensed matter physics in recent years, can be derived from 4-D quantum Hall models.
In 2013, Oded Zilberberg and collaborators realized that key signatures of the 4-D quantum Hall effect should also be visible in special time-dependent systems in two dimensions, so-called topological charge pumps, which constitute a dynamical version of the higher-dimensional model.
By carefully monitoring and analyzing at which positions in the superlattice the atoms are located during this process, the scientists could furthermore demonstrate that this motion is quantized, thereby revealing the quantum nature of the Hall effect in 4-D. The results have now been published in the journal Nature together with complementary work by an American research team, which used photonic structures to study the intricate boundary phenomena that accompany this motion as a result of the 4-D quantum Hall effect.
Together, these papers provide the first experimental glimpse into the physics of higher-dimensional quantum Hall systems, which offer a number of fascinating future prospects.
These include fundamental questions for our understanding of the universe like the interplay of quantum correlations and dimensionality, the generation of cosmic magnetic fields and quantum gravity, for which 4-D quantum Hall systems have been proposed as toy models.
Exploring 4-D quantum Hall physics with a 2-D topological charge pump, Nature.
Photonic topological boundary pumping as a probe of 4D quantum Hall physics, Nature.