Precise experimental test of the Luttinger theorem and particle-hole symmetry in composite fermions

We study a strongly interacting, flat-band system of composite fermions (CFs) in the half-filled lowest Landau level (v = ½), employing a geometric resonance technique. Our technique provides a direct measurement of the Fermi wave vector of the CF Fermi sea. The data reveal the following properties of CFs that have important implications in the physics of strong correlation [1]: (i) Luttinger theorem states that the Fermi sea and its area should be unchanged in the presence of interaction. As a function of interaction strength, our measurements reveal that indeed the area of the CF Fermi sea remains fixed to a great precision, consistent with the Luttinger theorem. (ii) We experimentally show that particle-hole symmetry is also precisely obeyed in the CF Fermi sea. (iii) We find that the density of the CFs is equal to the minority-carrier density in the lowest Landau level, i.e., electrons for ν < ½ and holes for v > ½. Surprisingly, this is very similar to p- or n-doped semiconductors. (iv) Finally, we show that our experimental results deviate from the predictions of the existing Dirac and Halperin-Lee-Read theories, the leading theories that are believed to describe the properties of CFs.

Reference: [1] M. S. Hossain, et al., Phys. Rev. Lett. 125, 046601 (2020).