Ground state, quasihole, a pair of quasihole wave functions, and instability in bilayer quantum Hall systems

Jiang, Longhua; Ye, Jinwu

doi:10.1103/physrevb.74.245311

Cited by 11 publications

(19 citation statements)

References 33 publications

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“…It is expected that this kind of disordering and pairing would lead to a charge-density wave ͑CDW͒ solution. 8 Still our general considerations open possibilities for other kinds of weak pairing that can be present in this quantum Hall system. The most likely candidate is the one with pairing function g͑z͒ϳ 1 z ‫ء‬ that results in nontrivial corrections ͑from quantum fluctuations and disordering͒ to the ground-state wave function as the distance is varied.…”

Section: Introductionmentioning

confidence: 79%

Nonperturbative approach to the quantum Hall bilayer

Milovanović

Papić

2009

Phys. Rev. B

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We develop a nonperturbative approach to the quantum Hall bilayer (QHB) at \nu=1 using trial wave functions. We predict phases of the QHB for arbitrary distance d and, our approach, in a dual picture, naturally introduces a new kind of quasiparticles - neutral fermions. Neutral fermion is a composite of two merons of the same vorticity and opposite charge. For small d (i.e. in the superfluid phase), neutral fermions appear as dipoles. At larger d dipoles dissociate into the phase of the two decoupled Fermi-liquid-like states. This scenario is relevant for the experimental situation where impurities lock charged merons. In a translation invariant (clean) system, continuous creation and annihilation of meron-antimeron pairs evolves the QHB toward a paired phase. The quantum fluctuations fix the form of the pairing function to g(z)=1/z^*. A part of the description of the paired phase is the 2D superconductor i.e. BF Chern-Simons theory. The paired phase is not very distinct from the superfluid phase.Comment: 11 pages, a longer versio

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Section: Introductionmentioning

confidence: 79%

Nonperturbative approach to the quantum Hall bilayer

Milovanović

Papić

2009

Phys. Rev. B

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“…All the calculations in LLL+HF approach assumes that the ground state wavefunction at any finite d is still the (111) wavefunction. However as shown in 39,65 , the wavefunction at any finite d is qualitatively different from the (111) wavefunction which is good only at d = 0. So the excitation spectra in the ESF side calculated by the LLL+HF based on the (111) wavefunction may not have quantitatively correct distance dependence.…”

Section: Comparison With Earlier Workmentioning

confidence: 96%

“…(2) Summary of our results on BLQH As shown in 39,65 , because of the gapless nature, at any finite d, the wavefunction is qualitatively different from the (111) wavefunction, so the wavefunction approach to BLQH is far less powerful in BLQH than in SLQH. So Field theory approaches are much more powerful in BLQH than in SLQH, especially in the pseudo-spin sector which contains the new phenomena not displayed in SLQH.…”

Section: Discussionmentioning

confidence: 99%

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Mutual Composite Fermion and Composite Boson approaches to balanced and imbalanced bi-layer quantum Hall system: An electronic analogy of the Helium 4 system

2008

Annals of Physics

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We use both Mutual Composite Fermion (MCF) and Composite Boson (CB) approach to study balanced and im-balanced Bi-Layer Quantum Hall systems (BLQH) and make critical comparisons between the two approaches. We find the CB approach is superior to the MCF approach in studying ground states with different kinds of broken symmetries. In the phase representation of the CB theory, we first study the Excitonic superfluid state (ESF). The theory puts spin and charge degree freedoms in the same footing, explicitly bring out the spin-charge connection and classify all the possible excitations in a systematic way. Then in the dual density representation of the CB theory, we study possible intermediate phases as the distance increases. We propose there are two critical distances dc1 < dc2 and three phases as the distance increases. When 0 < d < dc1, the system is in the ESF state which breaks the internal U (1) symmetry, when dc1 < d < dc2, the system is in an Pseudo-spin density wave ( PSDW ) state which breaks the translational symmetry, there is a first order transition at dc1 driven by the collapsing of magneto-roton minimum at a finite wavevector in the pseudo-spin channel. When dc2 < d < ∞, the system becomes two weakly coupled ν = 1/2 Composite Fermion Fermi Liquid ( FL) state. There is also a first order transition at d = dc2. We construct a quantum Ginzburg Landau action to describe the transition from ESF to PSDW which break the two completely different symmetries. By using the QGL action, we explicitly show that the PSDW takes a square lattice and analyze in detail the properties of the PSDW at zero and finite temperature. We also suggest that the correlated hopping of vacancies in the active and passive layers in the PSDW state leads to very large and temperature dependent drag consistent with the experimental data. Then we study the effects of imbalance on both ESF and PSDW. In the ESF side, the system supports continuously changing fractional charges as the imbalance changes. In the PSDW side, there are two quantum phase transitions from the commensurate excitonic solid to an in-commensurate excitonic solid and then to the excitonic superfluid state. We also comment on the effects of disorders and compare our results with the previous work. The very rich and interesting phases and phase transitions in the pseudo-spin channel in the BLQH is quite similar to those in 4 He system with the distance playing the role of the pressure. A BLQH system in a periodic potential is also discussed. The Quantum Hall state to Wigner crystal transition in single layer Quantum Hall system is studied.

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“…Currently, there are three typical lines of work that use: composite bosons (CB) [11,12], composite fermions (CF) [13][14][15][16][17][18][19], and both composite bosons and fermions [20][21][22]. Moreover, the importance of these theories is enhanced because not only explain the quantum Hall effect but they are also related to superconductivity [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

Manavella

Repetto

2012

Int J Theor Phys

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A higher-derivative classical nonrelativistic U(1) × U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2 + 1 dimensions is proposed. The model contains a Chern-Simons U(1) field and the electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. The model is obtained by adding suitable higher-derivative terms to the Lagrangian of a model previously proposed. One of them for the electromagnetic field and the other for the Chern-Simons field. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev-Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. In this context, only a mixed bosonic propagator can be defined. The use of the higherderivative terms eliminates the ultraviolet divergence of the primitively divergent Feynman diagrams where the bosonic propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the BecchiRouet-Stora-Tyutin algorithm is applied to the model. We will focus our attention on the issue from the point of view of the field theory.

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Ground state, quasihole, a pair of quasihole wave functions, and instability in bilayer quantum Hall systems

Cited by 11 publications

References 33 publications

Nonperturbative approach to the quantum Hall bilayer

Nonperturbative approach to the quantum Hall bilayer

Mutual Composite Fermion and Composite Boson approaches to balanced and imbalanced bi-layer quantum Hall system: An electronic analogy of the Helium 4 system

Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

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