Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases

At a very low temperature of 9mK, electrons in the 2nd Landau level of an extremely high mobility two-dimensional electron system exhibit a very complex electronic behavior. With 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 $ u=2+2/5$ state separated from the even-denominator $ u=2+1/2$ state by an insulating phase and a $ u=2+2/7$ and $ u=2+1/5$ state surrounded by such phases. A developing plateau at $ u=2+3/8$ points to the existence of other even-denominator states.