# Density-Functional Theory of the Fractional Quantum Hall Effect

## Abstract

Here, a conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn- Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.

- Authors:

- Pennsylvania State Univ., University Park, PA (United States)
- Indian Institute of Science, Bengaluru (India)

- Publication Date:

- Research Org.:
- Pennsylvania State Univ., University Park, PA (United States)

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

- OSTI Identifier:
- 1489116

- Alternate Identifier(s):
- OSTI ID: 1356453

- Grant/Contract Number:
- SC0005042

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 118; Journal Issue: 19; 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; fractional quantum Hall effect; density functional theory; composite fermions

### Citation Formats

```
Zhao, Jianyun, Thakurathi, Manisha, Jain, Manish, Sen, Diptiman, and Jain, J. K. Density-Functional Theory of the Fractional Quantum Hall Effect. United States: N. p., 2017.
Web. doi:10.1103/PhysRevLett.118.196802.
```

```
Zhao, Jianyun, Thakurathi, Manisha, Jain, Manish, Sen, Diptiman, & Jain, J. K. Density-Functional Theory of the Fractional Quantum Hall Effect. United States. doi:10.1103/PhysRevLett.118.196802.
```

```
Zhao, Jianyun, Thakurathi, Manisha, Jain, Manish, Sen, Diptiman, and Jain, J. K. Wed .
"Density-Functional Theory of the Fractional Quantum Hall Effect". United States. doi:10.1103/PhysRevLett.118.196802. https://www.osti.gov/servlets/purl/1489116.
```

```
@article{osti_1489116,
```

title = {Density-Functional Theory of the Fractional Quantum Hall Effect},

author = {Zhao, Jianyun and Thakurathi, Manisha and Jain, Manish and Sen, Diptiman and Jain, J. K.},

abstractNote = {Here, a conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn- Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.},

doi = {10.1103/PhysRevLett.118.196802},

journal = {Physical Review Letters},

number = 19,

volume = 118,

place = {United States},

year = {2017},

month = {5}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

*E*

_{xc}(

*ν*) (Eq. 5) and potential

*V*

_{xc}(

*ν*) =

*E*

_{xc}+

*ν*∂

*E*

_{xc}/∂

*ν*as a function of the filling factor

*ν*for several temperatures.

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Figures / Tables found in this record:

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