# Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

## Abstract

Here, we study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling ν=$$\frac{1}2$$+$$\frac{1}2$$ and $$\frac{1}4$$+$$\frac{1}4$$. The degeneracy between states with $±l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Department of Physics

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE

- OSTI Identifier:
- 1424925

- Alternate Identifier(s):
- OSTI ID: 1351933

- Grant/Contract Number:
- SC0010526

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 118; Journal Issue: 16; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Composite fermions; p-wave; two-dimensional electron gas; Eliashberg theory; random phase approximation

### Citation Formats

```
Isobe, Hiroki, and Fu, Liang.
```*Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevLett.118.166401.

```
Isobe, Hiroki, & Fu, Liang.
```*Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers*. United States. doi:10.1103/PhysRevLett.118.166401.

```
Isobe, Hiroki, and Fu, Liang. Mon .
"Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers". United States.
doi:10.1103/PhysRevLett.118.166401. https://www.osti.gov/servlets/purl/1424925.
```

```
@article{osti_1424925,
```

title = {Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers},

author = {Isobe, Hiroki and Fu, Liang},

abstractNote = {Here, we study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling ν=$\frac{1}2$+$\frac{1}2$ and $\frac{1}4$+$\frac{1}4$. The degeneracy between states with $±l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.},

doi = {10.1103/PhysRevLett.118.166401},

journal = {Physical Review Letters},

number = 16,

volume = 118,

place = {United States},

year = {Mon Apr 17 00:00:00 EDT 2017},

month = {Mon Apr 17 00:00:00 EDT 2017}

}

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