Density-Functional Theory of the Fractional Quantum Hall Effect

Journal Article · 10 May 2017 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.118.196802 · OSTI ID:1489116

Zhao, Jianyun ^[1]; Thakurathi, Manisha ^[2]; Jain, Manish ^[2]; Sen, Diptiman ^[2]; Jain, J. K. ^[3]

---

1. Pennsylvania State Univ., University Park, PA (United States); Penn State University
2. Indian Institute of Science, Bengaluru (India)
3. Pennsylvania State Univ., University Park, PA (United States)

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.

• Research Organization: The Pennsylvania State Univ., University Park, PA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: SC0005042
• OSTI ID: 1489116
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 19 Vol. 118; ISSN 0031-9007; ISSN PRLTAO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English