``Looking' at Competing Quantum Phases of the Second Landau Level

Aron Pinczuk

Antonio Levy, Ursula Wurstbauer, Y. Y. Kuznetsova +6 more

Quantum phases of electrons in the filling factor range 2≤ν≤3 are probed by the weak optical emission from the partially populated second Landau level and spin wave measurements. Observations of optical emission include a multiplet of sharp peaks that exhibit a strong filling factor dependence. Spin wave measurements by resonant inelastic light scattering probe breaking of spin rotational invariance and are used to link this optical emission with collective phases of electrons. A remarkably rapid interplay between emission peak intensities manifests phase competition in the second Landau level.

M. O. Goerbig, Pascal Lederer, C. Morais Smith

J. S. Xia, W. Pan, C. L. Vicente +7 more

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.

Xiangyu Ma, Kehuang Chen, Yuntian Gu +5 more

Fractional quantum Hall systems host strongly correlated topological phases with potential applications in topological quantum computation, yet identifying their microscopic ground states remains challenging because competing phases are often nearly degenerate and Landau-level mixing is difficult to treat. Here, we introduce a symmetry-adapted neural-network wavefunction that describes Abelian and non-Abelian states while incorporating all Landau levels. The method accurately captures composite-fermion liquids and the emergence of Wigner crystallization at low filling. When the first Landau level is partially filled, finite-size overlaps and entanglement spectra provide evidence consistent with $\bar{2}^{k}1^{k+1}$-type parton phases at $ν=4/3$ and $7/5$, while the $ν=3/2$ state exhibits anti-Pfaffian-like entanglement structure. These results demonstrate that neural-network wavefunctions offer a flexible framework for studying competing topological orders in fractional quantum Hall systems.

Heinz‐Peter Breuer, Martin Holthaus