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Anomalous fractional quantum Hall effect and multi-valued Hamiltonians
Xi Wu1, M A Zubkov1
1Physics Department, Ariel University, Ariel 40700, Israel.
Summary
We explore the anomalous fractional quantum Hall effect without magnetic fields. Our findings show excitations can be modeled as non-interacting particles, yielding fractional Hall conductivity values.
Area of Science:
- Condensed Matter Physics
- Quantum Hall Effect
Background:
- The fractional quantum Hall effect typically requires strong external magnetic fields.
- Understanding exotic states of matter is crucial for advancing quantum technologies.
Purpose of the Study:
- To investigate the possibility of an anomalous fractional quantum Hall effect in the absence of external magnetic fields.
- To develop a theoretical framework for describing such a phenomenon.
Main Methods:
- Modeling system excitations using non-interacting particles with specific Hamiltonians.
- Defining Hamiltonians on the Brillouin zone with a branch cut.
- Expressing Hall conductivity via the one-particle Green function.
Main Results:
- Demonstrated that the proposed Hamiltonians lead to fractional values of Hall conductivity multiplied by the von Klitzing constant.
- Showcased a theoretical model for magnetic-field-free fractional quantum Hall states.
Conclusions:
- The proposed theoretical construction provides a potential explanation for anomalous fractional quantum Hall effects.
- Further research may explore the connection between this model and ground state degeneracy.
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