Abstract
Composite fermions (CFs) are the particles underlying the novel phenomena observed in partially filled Landau levels. Both microscopic wave functions and semi-classical dynamics suggest that a CF is a dipole consisting of an electron and a double $2h/e$ quantum vortex, and its motion is subject to a Berry curvature that is uniformly distributed in the momentum space. Based on the picture, we study the electromagnetic response of composite fermions. We find that the response in the long-wavelength limit has a form identical to that of the Dirac CF theory. To obtain the result, we show that the Berry curvature contributes a half-quantized Hall conductance which, notably, is independent of the filling factor of a Landau level and not altered by the presence of impurities. The latter is because CFs undergo no side-jumps when scattered by quenched impurities in a Landau-level with the particle-hole symmetry. The remainder of the response is from an effective system that has the same Fermi wavevector, effective density, Berry phase, and therefore long-wavelength response to electromagnetic fields as a Dirac CF system. By interpreting the half-quantized Hall conductance as a contribution from a redefined vacuum, we can explicitly show the emergence of a Dirac CF effective description from the dipole picture. We further determine corrections due to electric quadrupoles and magnetic moments of CFs and show deviations from the Dirac CF theory when moving away from the long wavelength limit.
Highlights
The fractional quantum Hall (FQH) effect, a phenomenon discovered nearly four decades ago [1], remains unique as the only topological effect driven by electron correlations and observed in laboratories
I.e., the absence of a half-quantized Composite fermions (CFs) Hall conductance expected for a halffilled LL with the particle-hole symmetry [14], is remedied only recently by Wang et al, who show that spatial fluctuations of the effective magnetic field can induce CF scattering with side jumps and gives rise to a half-quantized CF Hall conductance [15]
In the long-wavelength limit, the response has a form identical to Eq (3) of the Dirac CF
Summary
The fractional quantum Hall (FQH) effect, a phenomenon discovered nearly four decades ago [1], remains unique as the only topological effect driven by electron correlations and observed in laboratories. To remove the unwelcome presence of the bare band mass of electrons without introducing inconsistencies, one has to assume phenomenologically that a mass renormalization is accompanied by a corresponding renormalization to the effective interaction between CFs [12,13] Another obvious flaw, i.e., the absence of a half-quantized CF Hall conductance expected for a halffilled LL with the particle-hole symmetry [14], is remedied only recently by Wang et al, who show that spatial fluctuations of the effective magnetic field can induce CF scattering with side jumps and gives rise to a half-quantized CF Hall conductance [15]. Fermi circle √acquires a π -Berry phase; (2) the Fermi wave vector kF = eB/his set only by the magnetic field and independent of the electron density These properties underly various effects predicted for the Dirac CF theory [17,18,30].
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