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Register a new userInterlayer Coherence in the $ u=1$ and $ u=2$ Bilayer Quantum Hall States
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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.
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We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $lambda$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlayer entanglement more effective and robust under perturbations than in the spin-frozen situation, mainly for a large number of flux quanta $lambda$. Interlayer entanglement of an equilibrium thermal state and its dependence with temperature and bias voltage is also studied for a pseudo-Zeeman interaction.
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 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 measured the magnetoresistance of bilayer quantum Hall (QH) effects at the fractional filling factor $ u =2/3$ by changing the total electron density and the density difference between two layers. Three different QH states were separated by two types of phase transition: One is the spin transition and the other is the pseudospin transition. In addition, two different hystereses were detected, one of which is specific to bilayer systems. The phase transitions and the hystereses are described well by a composite fermion model extended to a bilayer system.
We address the problem of separating the short-distance, high-energy physics of cyclotron motion from the long- distance, low-energy physics within the Lowest Landau Level in field theoretic treatments of the Fractional Quantum Hall Effect. We illustrate our method for the case $ u =1/2$. By a sequence of field transformations we go from electrons to fermions that carry flux tubes of thickness $l_o$ (cyclotron radius) and couple to harmonic oscillators corresponding to magnetoplasmons. The fermions keep track of the low energy physics while the oscillators describe the Landau level, cyclotron currents etc. From this starting point we are able to get Jain and Rezayi-Read wavefunctions, and many subsequent modifications of the RPA analysis of Halperin, Lee and Read.
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