Composite fermion Hall conductivity and the half-filled Landau level

Abstract

We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We find that deviations from particle-hole symmetric response can appear in the ac Hall conductivity at frequencies sufficiently large compared to the inverse system size. Our results agree with a recent semi-classical analysis by Wang et al., Phys. Rev. X 7, 031029 (2017) and complement the arguments based on the fully quantum-mechanical model by Kumar et al., Phys. Rev. B 98, 11505 (2018). These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.

Emergent reflection symmetry from nonrelativistic composite fermions

“…The second equality above follows directly from analyzing the equations of motion of a and a in Eq. (18). Now, let us vary the chemical potential slightly away from ν = 1/2q.…”

“…This way, much of the phenomenology of the quantum Hall effect can be captured qualitatively by composite fermion descriptions. 8 One remaining challenge, which has been the focus of a great deal of recent work, [9][10][11][12][13][14][15][16][17][18][19] amounts to determining how the constraint of particle-hole symmetry can be incorporated in composite fermion based theories. 20 In this note, we consider the observation of particlehole symmetric fractional quantum Hall states within various composite fermion descriptions.…”

Dirac composite fermions and emergent reflection symmetry about even-denominator filling fractions

“…This fermion-vortex duality has also led to progress in other areas of condensed matter physics [22][23][24][25]. Despite its success in incorporating PH symmetry, it still remains to understand how Son's theory might emerge from microscopics and the extent to which it can be experimentally distinguished from the HLR theory, although very interesting arguments have been put forward suggesting that Son's theory may emerge from the HLR theory upon incorporating the effect of quenched disorder [26][27][28] or as a percolation transition between the HLR theory and its PH conjugate [29]. Encouragingly, evidence for the Dirac composite fermion theory has been found in numerical studies [30,31].…”

Fluctuations and magnetoresistance oscillations near the half-filled Landau level

“…This theory is part of a larger web of (2 + 1)-dimensional quantum field theory dualities [15]. On the other hand, it has recently been shown that HLR mean-field theory can produce PH symmetric electrical response, if quenched disorder is properly included in the form of a precisely correlated random chemical potential and magnetic flux [16][17][18]. (Mean-field theory means that fluctuations of an emergent gauge field coupling to the composite fermion are ignored.)…”

“…Recent works [16][17][18] have shown that PH symmetry at ν = 1/2 and reflection symmetry about ν = 1/2 rely on precisely correlated electric and magnetic perturbations. (This correlation is implemented by the Chern-Simons gauge field in the HLR theory.)…”