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Register a new userMetamorphosis of the Quantum Hall Ferromagnet at $ u = 2/5$
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We report on the dramatic evolution of the quantum Hall ferromagnet in the fractional quantum Hall regime at $ u = 2/5$ filling. A large enhancement in the characteristic timescale gives rise to a dynamical transition into a novel quantized Hall state. The observed Hall state is determined to be a zero-temperature phase distinct from the spin-polarized and spin-unpolarized $ u = 2/5$ fractional quantum Hall states. It is characterized by a strong temperature dependence and puzzling correlation between temperature and time.
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We report on results of numerical studies of the spin polarization of the half filled second Landau level, which corresponds to the fractional quantum Hall state at filling factor $ u=5/2$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. The low-energy excitation spectrum is consistent with spin-wave excitations of a fully-magnetized ferromagnet.
Several topological orders have been proposed to explain the quantum Hall plateau at $ u=5/2$. The observation of an upstream neutral mode on the sample edge [Bid et al., Nature (London) 466, 585 (2010)] supports the non-Abelian anti-Pfaffian state. On the other hand, the tunneling experiments [Radu et al., Science 320, 899 (2008); Lin et al., Phys. Rev. B 85, 165321 (2012); Baer et al., arXiv:1405.0428] favor the Halperin 331 state which exhibits no upstream modes. We find a topological order, compatible with the results of both types of experiments. That order allows both finite and zero spin polarizations. It is Abelian but its signatures in Aharonov-Bohm interferometry can be similar to those of the Pfaffian and anti-Pfaffian states.
We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.
We report quantitative measurements of the impact of alloy disorder on the $ u=5/2$ fractional quantum Hall state. Alloy disorder is controlled by the aluminum content $x$ in the Al$_x$Ga$_{1-x}$As channel of a quantum well. We find that the $ u=5/2$ state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the $ u=5/2$ state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.
Optical absorption measurements are used to probe the spin polarization in the integer and fractional quantum Hall effect regimes. The system is fully spin polarized only at filling factor $ u=1$ and at very low temperatures($sim40$ mK). A small change in filling factor ($delta uapproxpm0.01$) leads to a significant depolarization. This suggests that the itinerant quantum Hall ferromagnet at $ u=1$ is surprisingly fragile against increasing temperature, or against small changes in filling factor.
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