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 ±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.

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

“…(Mean-field theory means that fluctuations of an emergent gauge field coupling to the composite fermion are ignored.) Furthermore, both composite fermion theories yield identical predictions for a number of observables in mean-field theory [14,16,[19][20][21], e.g., thermopower at half-filling and magnetoroton spectra away from half-filling. These results suggest that the HLR and Dirac composite fermion theories may belong to the same universality class.…”

“…However, the magnitude of the scalar potential is suppressed relative to the vector potential by a factor of B /d ≈ 1/50 [13]. Cheung et al [20] found that upon including the effects of the scalar potential in HLR mean-field theory, there is a slight correction to the expected locations of the oscillation minima both above and below ν = 1/2. The nature of the corrections are such that HLR mean-field theories of composite electrons or composite holes that take either k F = √ 4πn e or k F = 4π( B 2π − n e ) produce identical results.…”

“…Our strategy is to include their effects by determining the fluctuation corrections to the meanfield Hamiltonian. We obtain this corrected Hamiltonian through an approximate large N The blue curve corresponds to Dirac composite fermion mean-field theory [20]. The orange curve includes the effects of a Dirac composite fermion mass m ∝ |B − 4πn e | 1/3 B 1/6 induced by gauge fluctuations.…”

“…The resulting Dirac composite fermion propagator specifies the input parameters, namely, the chemical potential and mass, of the corrected mean-field Hamiltonian. We then follow the analysis by Cheung et al [20] to determine the corrected Weiss oscillation curves. Our results are summarized in Fig.…”

Geometric resonance of four-flux composite fermions

“…Figure 1(c) zooms in around ν = 1/4. From the period of the modulation, a = 240 nm, we determine the expected positions for the primary i = 1 GR resistance minima according to [3,10,15,16,21,22,26,27]. The difference between the expected B i=1 for the two assumptions is very small and cannot be resolved in our experiments.…”