Optical Signatures of Competing Quantum Phases in the Second Landau Level*

The fractional quantum Hall states and anisotropic phases of electrons in the N$=$1 Landau Level (LL) have drawn considerable experimental focus in recent years[1-3]. We report evidence that the competition and coexistence of these phases is probed directly by optical recombination from the partially populated N$=$1 LL at dilution refrigerator temperatures. Spectral bands that display striking dependence on perpendicular magnetic field in the full range 3\textgreater nu\textgreater 2 are interpreted as linked to anisotropic phases. Optical recombination thus enables the monitoring of the evolution competing phases as the N$=$1 LL filling is changed. Remarkable changes in the optical recombination reveal that coexistence of distinct quantum phases has a marked dependence on filling of the N$=$1 LL. The signatures of anisotropic phases remain strong at filling factors of the FQHE. This is consistent with recent reports on anisotropic FQHE states in the second Landau level[1-3]. References: [1] J. Xia et al, Phys. Rev. Lett. 105, 176807 (2010). [2] J.$^{\mathrm{\thinspace }}$Xia, J.P. Eisenstein, L.N. Pfeiffer, and K. West, K.W. Nature Phys$.$ 7, 845--848 (2011).$^{\mathrm{\thinspace }}$[3]$^{\mathrm{\thinspace }}$Y. Liu, et al, Phys. Rev. B 88, 035307 (2013).