https://www.nature.com/articles/nature25011

The quantum Hall effect, discovered in the 1980s, is an important fundamental effect in condensed matter physics that links topological states with electronic properties in two-dimensional systems. The quantized conductance is prescribed by an integer global topological invariant and is therefore protected against perturbations. Such invariants are characterized by a so-called Chern number. Two papers in this issue experimentally confirm the prediction that the quantum Hall effect can be generalized to a four-dimensional (4D) system. Immanuel Bloch and colleagues implement the 4D quantum Hall system in a superlattice of ultracold bosonic atoms, and Mikael Rechtsman and colleagues achieve the same in a photonic waveguide array. Both groups find that their system harbours a second Chern number, as expected. The studies show an intriguing advance towards new physics provided by topological protection in higher dimensions.

**Quantum Hall annexes fourth dimension**The quantum Hall effect, discovered in the 1980s, is an important fundamental effect in condensed matter physics that links topological states with electronic properties in two-dimensional systems. The quantized conductance is prescribed by an integer global topological invariant and is therefore protected against perturbations. Such invariants are characterized by a so-called Chern number. Two papers in this issue experimentally confirm the prediction that the quantum Hall effect can be generalized to a four-dimensional (4D) system. Immanuel Bloch and colleagues implement the 4D quantum Hall system in a superlattice of ultracold bosonic atoms, and Mikael Rechtsman and colleagues achieve the same in a photonic waveguide array. Both groups find that their system harbours a second Chern number, as expected. The studies show an intriguing advance towards new physics provided by topological protection in higher dimensions.

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