Why is the HLR theory particle-hole symmetric?

Abstract

Long wavelength descriptions of a half-filled lowest Landau level ($\nu =1/2$) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the $\nu =1/2$ 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 $\nu =1/2$ 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 ${\sigma }_{xy}^{(\mathrm{cf})}=-\frac{1}{2}\frac{e^2}{h}$. Our observations help explain why the HLR theory exhibits PH symmetric dc response.

arXiv comment14 pages, 4 figures; v3: Fixed a reference and funding information

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Cited by in corpus (11)

• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Dirac Composite Fermions and Emergent Reflection Symmetry about Even Denominator Filling Fractions
• Quantum Hall hierarchy from coupled wires
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Composite fermion Hall conductivity and the half-filled Landau level
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Self-duality of the integer quantum Hall to insulator transition: composite fermion description
• Emergent reflection symmetry from non-relativistic composite fermions
• Composite Fermion Nonlinear Sigma Models