The microscopic origin of the Quantum Hall Effect

TL;DR

This paper develops a microscopic theory explaining the Quantum Hall Effect by linking topological constraints in space to superpositions in angular space, clarifying the origin of quantum topology without relying on many-body interactions or disorder.

Contribution

It introduces a novel microscopic framework that accounts for Quantum Hall physics based on topological constraints, independent of disorder and many-body effects.

Findings

Identifies the mechanism of quantum topology through superposition of states.

Explains single-particle wavefunction regularity in 3D.

Provides a new perspective for topological quantum systems and applications.

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.