The Chern number physically represents topological invariants in quantum Hall systems

the verdict

SUPPORTED

the evidence backs this

Recorded sources

4 sources for · 0 against

Counts group repeated records of the same source within each side. They do not measure evidence strength or source independence.

The Chern number serves as the foundational topological invariant that characterizes the quantized response in integer quantum Hall systems.

The analysis

Multiple retrieved papers explicitly state that the integer quantum Hall effect and its quantized responses are characterized by topological invariants known as Chern numbers. There are no papers refuting this well-established physical principle.

Evidence for · 4

Exploring 4D quantum Hall physics with a 2D topological charge pump

Recorded source metadata

M. Lohse, C. Schweizer, H. Price, O. Zilberberg, I. Bloch. Exploring 4D quantum Hall physics with a 2D topological charge pump. 2017. https://doi.org/10.1038/nature25000

Paper [0] discusses how the two-dimensional integer quantum Hall effect is characterized by the first Chern number, which manifests as a quantized Hall response.

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More for · 3

Photonic topological boundary pumping as a probe of 4D quantum Hall physics

Recorded source metadata

O. Zilberberg, Sheng Huang, J. Guglielmon, Mohan Wang, Kevin P. Chen, Yaacov E. Kraus, M. Rechtsman. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. 2017. https://doi.org/10.1038/nature25011

Paper [1] explains that the quantum Hall effect arises from non-trivial band topology where an integer topological invariant, the first Chern number, leads to quantized Hall conductance.

Source citation format

Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number

Recorded source metadata

K. Sone, M. Ezawa, Yuto Ashida, N. Yoshioka, T. Sagawa. Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number. 2023. https://doi.org/10.1038/s41567-024-02451-x

Paper [2] notes that linear topological systems such as the quantum Hall effect are characterized using invariants like the Chern number.

Source citation format

Edge states and integer quantum Hall effect in topological insulator thin films

Recorded source metadata

Song-Bo Zhang, Hai-Zhou Lu, Shun-Qing Shen. Edge states and integer quantum Hall effect in topological insulator thin films. 2015. https://doi.org/10.1038/srep13277

Paper [3] examines the integer quantum Hall effect as a topological state of quantum matter in two dimensions.

Source citation format

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first checked01 Aug 2026

judged → SUPPORTED · 9201 Aug 2026

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