Emergence of Dirac Composite Fermions: Dipole Picture

TL;DR

This paper demonstrates that composite fermions in Landau levels exhibit electromagnetic responses identical to Dirac composite fermions, revealing a topological half-quantized Hall conductance and emergent Dirac behavior from a dipole perspective.

Contribution

It introduces a dipole-based picture of composite fermions that explains their Dirac-like electromagnetic response and topological properties in Landau levels.

Findings

The long-wavelength electromagnetic response matches Dirac CF theory.

Berry curvature contributes a half-quantized Hall conductance independent of filling.

Impurities do not alter the Hall conductance due to particle-hole symmetry.

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.