Theory of Interlayer Tunneling in Bilayer Quantum Hall Ferromagnets

Stern, Ady; Girvin, S. M.; MacDonald, Allan H.; Ma, Ning

doi:10.1103/physrevlett.86.1829

Cited by 111 publications

(178 citation statements)

References 24 publications

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“…Thus, much as in a superconducting Josephson junction, we expect an enormous zero bias anomaly in the tunnel current. 7,13,14,15 This prediction, first made by Wen and Zee 7 on the basis of the broken symmetry ground state proposed by Fertig 6 was recently dramatically confirmed in a remarkable set of experiments by Spielman et al 20,21 The data shown in Fig. (1) represent the differential conductance (and in the lower panel the conductance) as a function of bias voltage in a sample with extremely weak tunneling (∆ SAS ∼ 85µK).…”

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confidence: 78%

“…Various proposals involving a finite phase coherence time have been made to explain the finite height and width of the differential conductance peak. 13,14,15,17 but this is a question which is still poorly understood and is a subject of current study. In order to understand the finite dissipation, it is necessary mbtfinal2: submitted to World Scientific on May 28, 2018 to understand the excitations above the phase coherent ground state.…”

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confidence: 99%

“…Strong correlations between the electrons in different layers lead a great deal of completely new physics involving spontaneous interlayer phase coherence. 6,7,3,8,9,10,11,12,13,14,15,16,17,18,19 As we will discuss below, this is the first example of a QHE system with a finite-temperature phase transition. This transition is in fact a Kosterlitz-Thouless transition into a broken symmetry state which is closely analogous to that of a 2D superfluid.…”

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confidence: 99%

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Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Girvin

2002

Recent Progress in Many-Body Theories

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I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.The various quantum Hall effects are among the most remarkable many-body phenomena discovered in the second half of the twentieth century. 1, 2, 3, 4 The fractional effect has yielded fractional charge, spin and statistics, as well as unprecedented order parameters. 5 There are beautiful connections with a variety of different topological and conformal field theories of interest in nuclear and high energy physics.The quantum Hall effect (QHE) takes place in a two-dimensional electron gas formed in a quantum well in a semiconductor host material and subjected to a very high magnetic field. In essence it is a result of a commensuration between the number of electrons, N , and the number of flux quanta, N Φ , in the applied magnetic field. The electrons condense into distinct and highly non-trivial ground states ('vacua') formed at each rational fractional value of the filling factor ν ≡ N/N Φ .The essential feature of (most) of these exotic states is the existence of an excitation gap. The electron fluid is incompressible and flows rigidly past obstacles (impurities in the sample) with no dissipation. A weak external electric field will cause the fluid to move, but the excitation gap prevents the fluid from absorbing any energy from the electric field. Hence the current flow must be exactly at right angles to the field and the conductivity tensor takes the remarkable universal formIronically, this ideal behavior occurs because of imperfections and disorder in the samples which localize topological defects (vortices) whose motion would otherwise dissipate energy. In a two-dimensional superconductor, such vortices undergo a confinement phase transition at the Kosterlitz-Thouless temperature and dissipation ceases. In most cases in the QHE, an analog of the Anderson-Higgs mechanism causes the vortices to be deconfined 5 so that dissipation is strictly zero only at zero temperature. In practice, values of σ xx /σ xy as small as 10 −13 are not difficult to obtain at dilution refrigerator tempertures. Recent technological progress in molecular beam epitaxy techniques has led to the ability to produce pairs of closely spaced two-dimensional electron gases. Strong correlations between the electrons in different layers lead a great deal of completely new physics involving spontaneous interlayer phase coherence. 6,

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confidence: 99%

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confidence: 99%

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Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Girvin

2002

Recent Progress in Many-Body Theories

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“…Also, transport in counterflow experiments should be completely dissipationless under a critical temperature for phase coherence but in experiments dissipationless counterflow is only seen in the zero-temperature limit. 7 The effect of quenched disorder is believed to be crucial to reconcile these discrepancies, [8][9][10] although a quantitative understanding is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems

et al. 2010

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A bilayer system of two-dimensional electron gases in a perpendicular magnetic field exhibits rich phenomena. At total filling factor tot = 1, as one increases the layer separation, the bilayer system goes from an interlayer-coherent exciton condensed state to an incoherent phase of, most likely, two decoupled compositefermion Fermi liquids. Many questions still remain as to the nature of the transition between these two phases. Recent experiments have demonstrated that spin plays an important role in this transition. Assuming that there is a direct first-order transition between the spin-polarized interlayer-coherent quantum Hall state and spin partially polarized composite Fermi-liquid state, we calculate the phase boundary ͑d / l͒ c as a function of parallel magnetic field, NMR/heat pulse, temperature, and density imbalance, and compare with experimental results. Remarkably good agreement is found between theory and various experiments.

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“…When B > B * || , there is a finite temperature KT transition which restores the translation symmetry by means of dislocations in the domain wall structure in the incommensurate phase. Starting from the EPQFM approach, several groups investigated I − V curves in the presence of small tunneling 13 . In addition to the work mentioned above, there are also many other works done on BLQH.…”

Section: Introductionmentioning

confidence: 99%

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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Theory of Interlayer Tunneling in Bilayer Quantum Hall Ferromagnets

Cited by 111 publications

References 24 publications

Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems

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

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