At a very low-temperature of 9 mK, electrons in the second Landau level of an extremely high-mobility two-dimensional electron system exhibit a very complex electronic behavior. With a varying filling factor, quantum liquids of different origins compete with several insulating phases leading to an irregular pattern in the transport parameters. We observe a fully developed $\nu =2+2/5$ state separated from the even-denominator $\nu =2+1/2$ state by an insulating phase and a $\nu =2+2/7$ and $\nu =2+1/5$ state surrounded by such phases. A developing plateau at $\nu =2+3/8$ points to the existence of other even-denominator states.

• Received 23 June 2004

DOI:https://doi.org/10.1103/PhysRevLett.93.176809