Continuous 3D Freezing Transition in Layered Superconductors

Radzihovsky, Leo

doi:10.1103/physrevlett.76.3416

Cited by 16 publications

(12 citation statements)

References 18 publications

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“…However, on general grounds (see below) we expect that the powerlaw I-V, displaying negative differential resistance, below this strong coupling voltage, generically crosses over to a linear I-V, corresponding to a large, narrow conductance peak, as observed in experiments. [5] We now present the highlights of calculations that lead to the tunneling results summarized above, defering most of the details [7] to a future publication. We focus on the tunneling current density J = e∆0 2πℓ 2h sin [φ − ωt − Qx] , where the angular brackets denote an expectation value in the non-equilibrium steady state at time t averaged over a thermal ensemble of initial conditions in the far past.…”

Section: Pacsmentioning

confidence: 99%

“…1. [8,7] This arises from the binding of charge to flux in the QH regime, but has short-range correlations since it is a physical field. Thus in the zero tunneling limit, for weak disorder we arrive at a 2 + 1-dimensional XY model with random vector potential (XYRVP).…”

Section: Pacsmentioning

confidence: 99%

“…[7] At large bias, eV ≫hv/ξ ≫ k B T , the current decays exponentially (I d ∼ exp(−eV ξ/hv)). Third, in the presence of an additional weak B || field the zero-bias peak of Eq.2 is split by V B =hvQ/e,…”

Section: Pacsmentioning

confidence: 99%

“…Indeed, there is very likely an intermediate regime ξ/v ≪ t ≪ τ vort over which C(r, t) ∼ t −(1+α) , with no rigorous theory for α, but strong arguments for α < 1. [7] Below the threshold disorder strength, such that ξ = ∞, the XYRVP model may be used to calculate the C(r, t). This gives a weak modification of the η exponent by quenched impurities but leaves the results otherwise unchanged.…”

Section: Pacsmentioning

confidence: 99%

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Interlayer Tunneling in Double-Layer Quantum Hall Pseudoferromagnets

Radzihovsky

2001

Phys. Rev. Lett.

167

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We show that the interlayer tunneling I-V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a "derivative" feature at VB(B || ) = 2πhvB || d/eφ0, which gives a direct measure of the dispersion of the Goldstone mode corresponding to the spontaneous symmetry breaking of the double-layer Hall state. PACS: 73.20.Dx, 14.80.Hv, 73.20.Mf Through a series of experimental and theoretical papers, it is now well-established that a bilayer of twodimensional (2d) electron gases (2DEGs), when the layers are sufficiently close, exhibits an incompressible Quantum Hall (QH) state at a total filling fraction ν = 1, [1][2][3], even when interlayer tunneling is negligible. [4]. The QH state is stabilized by the Coulomb exchange interaction, which leads to spontaneous interlayer phase coherence, with the layer phase difference φ, the "phason", as the corresponding Goldstone mode. Because the layer index may also be viewed as a pseudo-spin-1/2 degree of freedom, this state is also known as the QH FerroMagnet (QHFM), and the phasons as (pseudo-)magnons.The first direct experimental evidence for this mode was obtained recently by Spielman, et al. [5]. For bilayers with small separations d, they observed a giant and spectacularly narrow zero bias peak in the inter-layer tunneling conductance at low T , a feature that naturally emerges from our study of the QHFM. We find rich variations of the non-linear tunneling conductance G(V ) = dI/dV as a function of interlayer voltage V , tunneling strength ∆ 0 , disorder, temperature, and applied parallel magnetic field B . Two particularly appealing and testable predictions of our theory are: (1) a finite-bias feature in G(V ) at a voltage V B =hω(Q = 2πB d/φ 0 ) which tracks the collective mode dispersion relation ω(Q) as a function of B (φ 0 = hc/e) and (2) the appearance of a power-law negative differential resistance at higher bias in cleaner samples. For clarity, below we first summarize different regimes and results, and then give a brief sketch of the calculations.We focus here on voltages eV below the QH charge gap Ω, where the only available bulk excitations are phasons, described in the absence of impurities by the Lagrangianwhere v is the pseudo-magnon "sound" velocity, ρ s is the phase stiffness, [4] ℓ = hc/eB is the magnetic length, Q is the in-plane "magnetic wavevector" Q = 2πB || d/φ 0 due to applied B || = B ||ŷ , and ω = eV /h. The only other low-energy modes are edge states, which carry the in-phase, in-plane current at low temperatures. For weak tunneling, characterized by a "naive" dimensionless coupling δ 0 ≡ ∆/ρ s ≪ 1, the tunneling current density J(V ) can be computed in a controlled perturbation theory (but see below). There are thr...

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Section: Pacsmentioning

confidence: 99%

Section: Pacsmentioning

confidence: 99%

Section: Pacsmentioning

confidence: 99%

Section: Pacsmentioning

confidence: 99%

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Interlayer Tunneling in Double-Layer Quantum Hall Pseudoferromagnets

Radzihovsky

2001

Phys. Rev. Lett.

167

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“…It can be seen by expanding the cosine that this state has a gapless phonon mode associated with the broken translational symmetry. This category also includes more exotic crystals, such as the Abrikosov flux lattice [18] (Fig. 2e) and crystals of Laughlin quasiparticles (Fig.…”

Section: The Non Interacting Model Has the Hamiltonian Den-mentioning

confidence: 99%

Fractional Quantum Hall Effect in an Array of Quantum Wires

2002

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We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate inter-wire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the groundstate of a Hamiltonian that we explicitly construct. [7]. These have lead to a deep understanding of the excitation spectrum of QH states and of the structure of the QH hierarchy.The purpose of this paper is to develop a new formalism, which reproduces the QH hierarchy in a model consisting of a two-dimensional array of quantum wires in a perpendicular magnetic field B. The model could be relevant for semiconductor quantum wires, ropes of carbon nanotubes, and for stripes that arise in QH systems in the higher Landau systems [8]. Aside from the direct relevance of the model, our calculations provide a novel, and in many ways a simpler, approach to describe the fractional QH effect. Given its success in treating the Fractional QH effect, it is likely that our technique will prove useful for understanding other strongly correlated states.We use the bosonization technique [9], developed for one-dimensional systems, and relate the QH effect to coupled Luttinger liquids. It has been shown recently [10][11][12] that for a range of interwire charge and current interactions, there is a phase in which interwire Josephson, charge-and spin-density-wave, and single-particle couplings are irrelevant. This sliding Luttinger liquid (SLL) or smectic metal phase is the quantum analog of the sliding phase found recently in DNA-lipid complexes and stacked XY models [13,14]. The SLL resembles a Luttinger liquid, with transport properties that exhibit power-law singularities as a function of temperature. It has also been demonstrated [15] that in a magnetic field the phase space of SLL expands considerably.We will show that at commensurate magnetic fields the SLL phase can be unstable to inter-wire electron hopping processes that lead the formation of an energy gap and the QH effect. The presence of the ν = 1 QH state in such a model was first noted by Sondhi and Yang [15]. Our calculation builds on this work. We systematically classify all electron hopping operators and identify those that lead to QH states. This construction leads to QH states which are not in the Haldane-Halperin hierarchy [3]. We also show that any QH state is the groundstate of a Hamiltonian that we explicitly construct.

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2003

Journal of Low Temperature Physics

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Continuous 3D Freezing Transition in Layered Superconductors

Cited by 16 publications

References 18 publications

Interlayer Tunneling in Double-Layer Quantum Hall Pseudoferromagnets

Interlayer Tunneling in Double-Layer Quantum Hall Pseudoferromagnets

Fractional Quantum Hall Effect in an Array of Quantum Wires

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