Composite Fermions near Half-filled Landau Levels: Precise Experimental Tests of Luttinger Theorem, Particle-Hole Symmetry, and Fermi Sea Anisotropy

Composite fermions (CFs), exotic particles formed by pairing an even number of flux quanta to each electron,
provide a fascinating description of phenomena exhibited by interacting two-dimensional electrons at high
perpendicular magnetic fields and low temperatures. At and near Landau level half-fillings, CFs occupy a Fermi
sea. In this talk, I will present our experimental results aimed at probing this Fermi sea directly and quantitatively.
The probe consists of geometric resonance measurements, manifesting minima in the magneto-resistance when
the CFs’ cyclotron orbit diameter becomes commensurate with the period of a periodic potential imposed in the
plane. The data provide evidence that particle-hole symmetry and the Luttinger theorem are obeyed to very high
precision for CFs, quasi-particles which themselves are a product of interaction. There are, however, quantitative
differences from the predictions of the existing (Dirac and Halperin-Lee-Read) theories. We also report
measurements of CF Fermi sea shape, tuned by the application of uniaxial strain. The strain-induced results reveal
that the Fermi sea anisotropy for CFs (α CF ) is less than the anisotropy of their low-field hole (fermion)
counterparts (α F ), and closely follows the relation α CF = α F 1/2.

Work done in collaboration with Md. Shafayat Hossain, Insun Jo, Hao Deng, Roland Winkler, Yang Liu, Meng
K. Ma, Kevin A. Villegas Rosales, Doby Kamburov, M. A. Mueed, Medini Padmanabhan, Yoon Jang (Edwin)
Chung, Ken West, Kirk Baldwin, and Loren Pfeiffer.