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Register a new userSimultaneous Excitation of Spins and Pseudospins in the Bilayer $ u=1$ Quantum Hall State
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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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We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor $ u =1$, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance $R_{xx}$ appears at the transition point between the commensurate and incommensurate phases. The $R_{xx}$ at the peak is highly anisotropic for the angle between the in-plain magnetic field $B_parallel $ and the current, and indicates a formation of the soliton lattice aligned parallel to $B_parallel $. Temperature dependence of the $R_{xx}$ peak reveals that the dissipation is caused by thermal fluctuations of pseudospin solitons. We construct a phase diagram of the bilayer $ u =1$ system as a function of $B_parallel$ and the total electron density. We also study effects of density imbalance between the two layers.
We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ u=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ u =1$ and discovered at $ u =2$. In particular, three different $ u =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
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$. Our studies are performed using both exact diagonalization and Density Matrix Renormalization Group (DMRG) on the sphere. We find that for the Coulomb interaction the exact finite-system ground state is fully polarized, for shifts corresponding to both the Moore-Read Pfaffian state and its particle-hole conjugate (anti-Pfaffian). This result is found to be robust against small variations of the interaction. The low-energy excitation spectrum is consistent with spin-wave excitations of a fully-magnetized ferromagnet.
The Hall-plateau width and the activation energy were measured in the bilayer quantum Hall state at filling factor u=2, 1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells. Their behavior are remarkably different from one to another. The u=1 state is found stable over all measured range of the density difference, while the u=2/3$ state is stable only around the balanced point. The u=2 state, on the other hand, shows a phase transition between these two types of the states as the electron density is changed.
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.
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