The microscopic origin of the Quantum Hall Effect

Abstract

Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic theory for the ever-expanding and still puzzling transport behavior of electrons in the Quantum Hall Effect. Here we formulate a microscopic theory able to quantitatively describe the large wealth of Quantum Hall physics starting from one basic assumption, that the topological constraint in actual space leads to a superposition of states in the associated angular space. This allows us to identify the mechanism underlying quantum topology, single-particle wavefunction regularity in 3D, while many-body physics and disorder play no fundamental role. Our findings introduce a new far-reaching perspective in analyzing topological quantum systems and applications, such as topological quantum computing.