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Phase Diagram of the ν=5/2 Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width
- Source :
- Physical Review X, Vol 5, Iss 2, p 021004 (2015)
- Publication Year :
- 2015
- Publisher :
- American Physical Society, 2015.
-
Abstract
- Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the ν=5/2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the ν=5/2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the ν=5/2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in κ, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of κ and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for κ
Details
- Language :
- English
- ISSN :
- 21603308
- Volume :
- 5
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Physical Review X
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.361e318da50141e89073b43f1957c40e
- Document Type :
- article
- Full Text :
- https://doi.org/10.1103/PhysRevX.5.021004