Weiss oscillations and particle-hole symmetry at the half-filled Landau level

Abstract

Particle-hole symmetry in the lowest Landau level of the two-dimensional electron gas requires the electrical Hall conductivity to equal $\pm e^2/2h$ at half-filling. We study the consequences of weakly broken particle-hole symmetry for magnetoresistance oscillations about half-filling in the presence of an applied periodic one-dimensional electrostatic potential using the Dirac composite fermion theory proposed by Son. At fixed electron density, the oscillation minima are asymmetrically biased towards higher magnetic fields, while at fixed magnetic field, the oscillations occur symmetrically as the electron density is varied about half-filling. We find an approximate "sum rule" obeyed for all pairs of oscillation minima that can be tested in experiment. The locations of the magnetoresistance oscillation minima for the composite fermion theory of Halperin, Lee, and Read (HLR) and its particle-hole conjugate agree exactly. Within the current experimental resolution, the locations of the oscillation minima produced by the Dirac composite fermion coincide with those of HLR. These results may indicate that all three composite fermion theories describe the same long wavelength physics.

22 pages, 3 figures; v2 corrected discussion of composite fermion theory comparison (thanks to C. Wang, N. Cooper, B. Halperin, and A. Stern for discussions)

References in corpus (5)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Quantum transport of Dirac electrons in graphene in the presence of a spatially modulated magnetic field
• Emergent particle-hole symmetry in the half-filled Landau level
• Particle-hole symmetry and electromagnetic response of a half-filled Landau level
• Weiss oscillations in graphene with a modulated height profile

Cited by in corpus (17)

• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Particle-hole symmetry and composite fermions in fractional quantum Hall states
• Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Geometric Resonance of Four-Flux Composite Fermions
• Why is the HLR theory particle-hole symmetric?
• Composite fermion Hall conductivity and the half-filled Landau level
• Fluctuations and magnetoresistance oscillations near the half-filled Landau level
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime
• Thermopower and Nernst measurements in a half-filled lowest Landau level
• Asymmetry of the Geometrical Resonances of Composite Fermions
• Weiss Oscillations in the Galilean-Invariant Dirac Composite Fermion Theory for Even-Denominator Filling Fractions of the Lowest Landau Level
• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$