Interlayer correlated fractional quantum Hall state in the $\nu =4/5$ bilayer system

Journal Article · 11 December 2019 · Physical Review B

DOI: https://doi.org/10.1103/physrevb.100.245122 · OSTI ID:1801537

Wang, Hao ^[1]; Seidel, Alexander ^[2]; Yang, Kun ^[3]; Zhang, Fu-Chun ^[4]

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1. Southern University of Science and Technology, Shenzhen (China); OSTI
2. Washington Univ., St. Louis, MO (United States)
3. Florida State Univ., Tallahassee, FL (United States)
4. University of Chinese Academy of Sciences, Beijing (China)

We perform exact diagonalization studies for fractional quantum Hall states at filling factor 4/5 in a bilayer system, on a torus with various aspect ratios and angles. In this work we find that in the absence of tunneling, two weakly coupled 2/5 layers undergo a phase transition into an interlayer-correlated regime, which is also Abelian with the fivefold degeneracy on the torus. In the limit of zero layer separation, this phase becomes a singlet in the pseudospin variable describing the layer degree of freedom. By studying the Chern-number matrix, we show that the K matrix describing the interlayer-correlated regime requires a matrix dimension larger than two and this regime is in particular not described by a Halperin state. A detailed analysis of possible 4 × 4 K matrices having the requisite symmetries and quantum numbers shows that there is only one equivalence class of such matrices. A model wave function representing this universality class is constructed. The role of separate particle number conservation in both layers is discussed, and it is argued that this additional symmetry allows for the further distinction of two different symmetry-protected Abelian phases in the interlayer correlated regime. Interlayer tunneling breaks this symmetry and can drive the system into a single-layer regime when strong enough. A qualitative phase diagram in the tunneling-layer separation parameter space is proposed based on our numerical results.

• Research Organization: Princeton Univ., NJ (United States)
• Sponsoring Organization: Chinese Academy of Sciences (CAS); National Basic Research Program of China; National Natural Science Foundation of China (NSFC); National Science Foundation (NSF); State of Florida; USDOE Office of Science (SC)
• Grant/Contract Number: SC0002140
• OSTI ID: 1801537
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 24 Vol. 100; ISSN 2469-9950
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English