# Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory

## Abstract

We present that long wavelength descriptions of a half-filled lowest Landau level (ν = 1/2) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the ν = 1/2 state pioneered by Halperin, Lee, and Read (HLR) naively appears to break PH symmetry. However, recent studies have shown that the HLR theory with weak quenched disorder can exhibit an emergent PH symmetry. We find that such inhomogeneous configurations of the ν = 1/2 fluid, when described by HLR mean-field theory, are tuned to a topological phase transition between an integer quantum Hall state and an insulator of composite fermions with a dc Hall conductivity σ$$(cf)\atop{xy}$$ = -$$\frac{1}{2}$$ $$\frac{e2}{h}$$. Finally, our observations help explain why the HLR theory exhibits PH symmetric dc response.

- Authors:

- Stanford Univ., CA (United States). Stanford Institute for Theoretical Physics
- Univ. of California, Riverside, CA (United States). Department of Physics and Astronomy
- Stanford Univ., CA (United States). Stanford Institute for Theoretical Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

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

- OSTI Identifier:
- 1475409

- Alternate Identifier(s):
- OSTI ID: 1468849

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 11; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Kumar, Prashant, Mulligan, Michael, and Raghu, S. Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory. United States: N. p., 2018.
Web. doi:10.1103/physrevb.98.115105.
```

```
Kumar, Prashant, Mulligan, Michael, & Raghu, S. Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory. United States. doi:10.1103/physrevb.98.115105.
```

```
Kumar, Prashant, Mulligan, Michael, and Raghu, S. Wed .
"Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory". United States. doi:10.1103/physrevb.98.115105. https://www.osti.gov/servlets/purl/1475409.
```

```
@article{osti_1475409,
```

title = {Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory},

author = {Kumar, Prashant and Mulligan, Michael and Raghu, S.},

abstractNote = {We present that long wavelength descriptions of a half-filled lowest Landau level (ν = 1/2) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the ν = 1/2 state pioneered by Halperin, Lee, and Read (HLR) naively appears to break PH symmetry. However, recent studies have shown that the HLR theory with weak quenched disorder can exhibit an emergent PH symmetry. We find that such inhomogeneous configurations of the ν = 1/2 fluid, when described by HLR mean-field theory, are tuned to a topological phase transition between an integer quantum Hall state and an insulator of composite fermions with a dc Hall conductivity σ$(cf)\atop{xy}$ = -$\frac{1}{2}$ $\frac{e2}{h}$. Finally, our observations help explain why the HLR theory exhibits PH symmetric dc response.},

doi = {10.1103/physrevb.98.115105},

journal = {Physical Review B},

number = 11,

volume = 98,

place = {United States},

year = {2018},

month = {9}

}

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