Review article

Physics and astronomy

Half quantized Hall effect

Coshare Science 02, 01
| Published 18 March 2024
| DOI:
https://doi.org/10.61109/cs.202402.128

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S.Q. Shen, Half quantized Hall effect, *Coshare Science* **02**, 01 (2024).

Abstract

Here we report a half-quantized Hall effect in a metal or semimetal. The Hall conductance is half quantized and the longitudinal conductance is nonzero. Consequently, the Hall resistivity is not quantized. The half quantization occurs when the parity symmetry or time reversal symmetry emerges near the Fermi surface or Fermi level while the symmetry is broken in the whole system. A recent experiment reports the observation of the half-quantized Hall conductance in a magnetically-doped topological insulator. We discover that a single gapless Dirac cone exists in the band structure and has half-quantized conductance when the Fermi level intercepts the gapless surface states in which the parity symmetry is invariant. As there are no localized chiral edge states in the gapless and metallic system, we find that the chiral edge current is carried by the gapless surface states. The current density peaks at the edge and decays in a power law rather than the exponential decay as in the conventional quantum anomalous Hall effect. The half quantized Hall conductance is a signature of parity anomaly in a single gapless Dirac cone on a lattice. We term the nontrivial quantum phase as “parity anomalous semimetal”. The work opens the door to exploring novel topological states of matter with fractional topological invariants.

Keywords

Half quantized Hall effect

parity anomaly

gapless Dirac cone

half-quantized Hall conductance

topological metallic phase

Introduction

Results and discussion

Conclusions

Declarations

The author declares no competing interests.

Acknowledgements

This work was supported by the National Key R&D Program of China under Grant No. 2019YFA0308603, the Research Grants Council, University Grants Committee, Hong Kong under Grant No. C7012-21G and No. 17301823; the and Quantum Science Center of Guangdong-Hong Kong Macau Greater Bay, China.

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