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Register a new userSpatial distribution of dynamically polarized nuclear spins in electron spin domains in the $ u = 2/3$ fractional quantum Hall state studied by nuclear electric resonance
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Nuclear electric resonance (NER) is based on nuclear magnetic resonance mediated by spatial oscillations of electron spin domains excited by a radio frequency (RF) electric field, and it allows us to investigate the spatial distribution of the nuclear spin polarization around domain walls (DWs). Here, NER measurements were made of the dynamic nuclear spin polarization (DNP) at the spin phase transition of the fractional quantum Hall state at a Landau level filling factor of $ u=2/3$. From the RF pulse power and pulse duration dependence of the NER spectrum, we show that the DNP occurs only within $sim 100$ nm around DWs, and that it does not occur in DWs. We also show that DWs are pinned by the hyperfine field from polarized nuclear spins.
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We observe nuclear magnetic resonance (NMR) in the fractional quantum Hall regime at Landau level filling factor $ u=2/3$ from simultaneous measurement of longitudinal resistance and photoluminescence (PL). The dynamic nuclear spin polarization is induced by applying a huge electronic current at the spin phase transition point of $ u=2/3$. The NMR spectra obtained from changes in resistance and PL intensity are qualitatively the same; that is, the Knight shift (spin polarized region) and zero-shift (spin unpolarized region) resonances are observed in both. The observed change in PL intensity is interpreted as a consequence of the trion scattering induced by polarized nuclear spins. We conclude that both detection methods probe almost the same local phenomena.
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.
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.
The fractional quantum Hall (FQH) effect at filling factor v = 5/2 has recently come under close scrutiny, as it may possess quasi-particle excitations obeying nonabelian statistics, a property sought for topologically protected quantum operations. Yet, its microscopic origin remains unidentified, and candidate model wave functions include those with undesirable abelian statistics. Here we report direct measurements of the electron spin polarization of the v = 5/2 FQH state using resistively detected nuclear magnetic resonance (NMR). We find the system to be fully polarized, which unambiguously rules out the most-likely abelian contender and thus lends strong support for the v = 5/2 state being nonabelian. Our measurements reveal an intrinsically different nature of interaction in the first-excited Landau level underlying the physics at v = 5/2.
The tilting angular dependence of the energy gap was measured in the bilayer quantum Hall state at the Landau level filling $ u=1$ by changing the density imbalance between the two layers. The observed gap behavior shows a continuous transformation from the bilayer balanced density state to the monolayer state. Even a sample with 33 K tunneling gap shows the same activation energy anomaly reported by Murphy {it et al.}. We discuss a possible relation between our experimental results and the quantum Hall ferromagnet of spins and pseudospins.
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