# Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu}_{T}=1$ : A New Phase at Intermediate Layer Distances

## Abstract

We view the phase diagram of quantum Hall bilayer systems with total filing ${\nu}_{T}=\mathrm{1/2}$ + 1/2 of the lowest Landau level as a function of layer distances *d*. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small *d*, a composite Fermi liquid at large *d*, and an intermediate phase for 1.1 < d/l _{B} < 1.8 (l _{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Moreover, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ${\nu}_{T}=1$.

- Authors:

- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- California State Univ. Northridge (CSUN), Northridge, CA (United States)

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States); California State Univ. Northridge (CSUN), Northridge, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1505729

- Alternate Identifier(s):
- OSTI ID: 1402172

- Grant/Contract Number:
- FG02-06ER46305; SC0010526

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 119; Journal Issue: 17; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

### Citation Formats

```
Zhu, Zheng, Fu, Liang, and Sheng, D. N. Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances. United States: N. p., 2017.
Web. doi:10.1103/physrevlett.119.177601.
```

```
Zhu, Zheng, Fu, Liang, & Sheng, D. N. Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances. United States. doi:10.1103/physrevlett.119.177601.
```

```
Zhu, Zheng, Fu, Liang, and Sheng, D. N. Mon .
"Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances". United States. doi:10.1103/physrevlett.119.177601. https://www.osti.gov/servlets/purl/1505729.
```

```
@article{osti_1505729,
```

title = {Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances},

author = {Zhu, Zheng and Fu, Liang and Sheng, D. N.},

abstractNote = {We view the phase diagram of quantum Hall bilayer systems with total filing νT=1/2 + 1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1 < d/lB < 1.8 (lB is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Moreover, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling νT=1.},

doi = {10.1103/physrevlett.119.177601},

journal = {Physical Review Letters},

number = 17,

volume = 119,

place = {United States},

year = {2017},

month = {10}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*ν*= 1/2 + 1/2 quantum Hall bilayerswith varying layer distance d/l

_{B}. We identify three phases: exciton superfluid phase, the intermediate phase, and composite Fermi liquid phase. (a) The transition from exciton superfluid to intermediate phase near d

_{c1}≈ 1.1 is identified by themore »

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*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*