Untangling the Nature of Exotic Hall States
A 2D electron gas subjected to a magnetic field can adopt a “fractional quantum Hall” state, in which electrons and magnetic-flux quanta come together to form composite quasiparticles. About 80 such states have been observed so far, each characterized by its filling factor—the ratio of the number of electrons to the number of magnetic-flux quanta. Of special interest are filling factors with even denominators. The charge-carrying quasiparticles in these states could be harnessed for fault-tolerant quantum computing provided they are non-Abelian—that is, they share a collective degenerate ground state. Proving non-Abelian nature is challenging, especially for so-called next-generation states whose denominators are 8 and 10. Now Misha Yutushui of the University of Cologne in Germany and David Mross of the Weizmann Institute of Science in Israel have devised a theory that encompasses those states and the ways their quasiparticles can pair up [1].
Although the first even-denominator state, 5/2, was identified in 1987, the nature of its quasiparticles remains to be firmly established. For next-generation states 3/8 and 3/10, the picture is murkier. Various lines of evidence point to two possibilities: a superfluid consisting of composite fermions, each of which is composed of electrons bound to an even number of magnetic flux quanta, and so-called Bonderson-Slingerland states. In both cases, the quasiparticles may be non-Abelian, depending on the details of their interactions.
Yutushui and Mross constructed trial wave functions for the two possibilities and used them to map phase diagrams of the 3/8 and 3/10 states. The two diagrams resembled each other qualitatively in that the superfluid of composite fermions and the Bonderson-Slingerland states occupied more or less the same regions. But the former are energetically favored at lower magnetic fields and the latter at higher ones. Besides identifying these different regimes, Yutushui and Mross proposed how they might be detected in the lab.
–Charles Day
Charles Day is a Senior Editor for Physics Magazine.
References
- M. Yutushui and D. F. Mross, “Theory of next-generation even-denominator states,” Phys. Rev. B 114, 065121 (2026).