Anyon superconductivity

In this chapter we will consider the problemof predicting the behavior of an assembly of particlesobeying fractional statistics. We have already considered the problem of the quantum mechanics of systems of anyons. However, we did not consider what new phenomena may arise if the system has a macroscopic number of anyons present. At the time of writing, the physical reality of this problem is still unclear. However, this is such a fascinating problem that we will discuss it despite the lack of firm experimental support for the model.

There are two different physical situations in which the problem of anyons at finite density is important. Halperin, (1984) observed that the quasiparticles of the Laughlin state for the FQHE obeyed fractional statistics (i.e. they are anyons). In Chapter 13 we will discuss Halperin’s theory. Furthermore, Halperin and Haldane suggested that, for filling fractions of a Landau level different from the 1/m Laughlin sequence, the ground state of a 2D electron gas in a strong magnetic field could be understood as a Laughlin state of anyons. Shortly afterwards, Arovas, Schrieffer, Wilczek, and Zee (Arovas et al., 1985) studied the high-temperature behavior of a gas of anyons and calculated the second virial coefficient.