Composite fermion mass in ultra-high-quality, two-dimensional electrons

2D electron systems subjected to a strong perpendicular magnetic field display rich, many-body phases like the fractional quantum Hall states (FQHSs). A description of these strongly interacting states can be mapped exactly onto the Landau levels of weakly-interacting quasi-particles each composed of an electron and two flux quanta, the so-called Composite Fermions (CFs) [1]. The FQHSs of electrons can then be thought of as the Integer quantum Hall states of CFs. The effective mass of the CF is inversely proportional to the energy gap of the FQHSs, a fundamental parameter of the many-body state. In addition, the mass is also largely robust to disorder and thus, more relevant to comparisons with theoretical calculations.  Experimentally, we extracted the mass by performing standard transport measurements on ultra-high-quality GaAs quantum wells [2] with varying well width and analyzing the temperature dependence of the Shubnikov de Haas oscillations in the FQHSs. Our data reveal that the CF mass increases with increasing well width, reflecting a decrease in the energy gap as the electron layer becomes thicker and the in-plane Coulomb energy softens. Our data also show significant quantitative discrepancies between the theoretical [3,4] and measured masses, suggesting the need for more rigorous and accurate calculations.

1. J. K. Jain, P.R.L. 63, 199 (1989).

2. Yoon Jang Chung et al., Nat. Mater. 20, 632 (2021).

3. K. Park et al., J. Phys.: Condens. Matter 11, 7283 (1999).

4. R. H. Morf et al., P.R. B 66, 075408 (2002).