Gap Structure and Gapless Structure in Fractional Quantum Hall Effect
Higher-order composite fermion states are correlated with many quasiparticles. The energy calculations are very complicated. We develop the theory of Tao and Thouless to explain them. The total Hamiltonian is (𝐻𝐷+𝐻𝐼), where 𝐻𝐷 includes Landau energies and classical Coulomb energies. We find the most...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Advances in Condensed Matter Physics |
| Online Access: | http://dx.doi.org/10.1155/2012/281371 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549841850335232 |
|---|---|
| author | Shosuke Sasaki |
| author_facet | Shosuke Sasaki |
| author_sort | Shosuke Sasaki |
| collection | DOAJ |
| description | Higher-order composite fermion states are correlated with many quasiparticles. The energy calculations are very complicated. We develop the theory of Tao and Thouless to explain them. The total Hamiltonian is (𝐻𝐷+𝐻𝐼), where 𝐻𝐷 includes Landau energies and classical Coulomb energies. We find the most uniform electron configuration in Landau states which has the minimum energy of 𝐻𝐷. At 𝜈=(2𝑗−1)/(2𝑗), all the nearest electron pairs are forbidden to transfer to any empty states because of momentum conservation. Therefore, perturbation energies of the nearest electron pairs are zero in all order of perturbation. At 𝜈=𝑗/(2𝑗−1), 𝑗/(2𝑗+1), all the nearest electron (or hole) pairs can transfer to all hole (or electron) states. At 𝜈=4/11, 4/13, 5/13, 5/17, 6/17, only the specific nearest hole pairs can transfer to all electron states. For example, the nearest-hole-pair energy at 𝜈=4/11 is lower than the limiting energies from both sides (the left side 𝜈=(4𝑠+1)/(11𝑠+3) and the right side 𝜈=(4𝑠−1)/(11𝑠−3) for infinitely large 𝑠). Thus, the nearest-hole-pair energy at specific 𝜈 is different from the limiting values from both sides. The property yields energy gap for the specific 𝜈. Also gapless structure appears at other filling factors (e.g., at 𝜈=1/2). |
| format | Article |
| id | doaj-art-24d707f6fc604027acb35d2838986df8 |
| institution | Kabale University |
| issn | 1687-8108 1687-8124 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Condensed Matter Physics |
| spelling | doaj-art-24d707f6fc604027acb35d2838986df82025-02-03T06:08:20ZengWileyAdvances in Condensed Matter Physics1687-81081687-81242012-01-01201210.1155/2012/281371281371Gap Structure and Gapless Structure in Fractional Quantum Hall EffectShosuke Sasaki0KYOKUGEN (Center for Quantum Science and Technology under Extreme Conditions), Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, JapanHigher-order composite fermion states are correlated with many quasiparticles. The energy calculations are very complicated. We develop the theory of Tao and Thouless to explain them. The total Hamiltonian is (𝐻𝐷+𝐻𝐼), where 𝐻𝐷 includes Landau energies and classical Coulomb energies. We find the most uniform electron configuration in Landau states which has the minimum energy of 𝐻𝐷. At 𝜈=(2𝑗−1)/(2𝑗), all the nearest electron pairs are forbidden to transfer to any empty states because of momentum conservation. Therefore, perturbation energies of the nearest electron pairs are zero in all order of perturbation. At 𝜈=𝑗/(2𝑗−1), 𝑗/(2𝑗+1), all the nearest electron (or hole) pairs can transfer to all hole (or electron) states. At 𝜈=4/11, 4/13, 5/13, 5/17, 6/17, only the specific nearest hole pairs can transfer to all electron states. For example, the nearest-hole-pair energy at 𝜈=4/11 is lower than the limiting energies from both sides (the left side 𝜈=(4𝑠+1)/(11𝑠+3) and the right side 𝜈=(4𝑠−1)/(11𝑠−3) for infinitely large 𝑠). Thus, the nearest-hole-pair energy at specific 𝜈 is different from the limiting values from both sides. The property yields energy gap for the specific 𝜈. Also gapless structure appears at other filling factors (e.g., at 𝜈=1/2).http://dx.doi.org/10.1155/2012/281371 |
| spellingShingle | Shosuke Sasaki Gap Structure and Gapless Structure in Fractional Quantum Hall Effect Advances in Condensed Matter Physics |
| title | Gap Structure and Gapless Structure in Fractional Quantum Hall Effect |
| title_full | Gap Structure and Gapless Structure in Fractional Quantum Hall Effect |
| title_fullStr | Gap Structure and Gapless Structure in Fractional Quantum Hall Effect |
| title_full_unstemmed | Gap Structure and Gapless Structure in Fractional Quantum Hall Effect |
| title_short | Gap Structure and Gapless Structure in Fractional Quantum Hall Effect |
| title_sort | gap structure and gapless structure in fractional quantum hall effect |
| url | http://dx.doi.org/10.1155/2012/281371 |
| work_keys_str_mv | AT shosukesasaki gapstructureandgaplessstructureinfractionalquantumhalleffect |