Gap Vanishes Research Articles

Reentrant quantum Hall effect in bilayer system at high filling factors

We report on the measurements of the quantum Hall effect states in double quantum well structures at the filling factors ν = 4 N + 1 and 4 N + 3 , where N is the Landau index number, in the presence of the in-plane magnetic field. The quantum Hall states at these filling factors vanish and reappear several times. Repeated reentrance of the transport gap occurs due to the periodic vanishing of the tunneling amplitude in the presence of the in-plane field. When the gap vanishes, the transport becomes anisotropic. The anisotropy persist at half-odd filling factors, when bilayer quantum Hall states are recovered with increase of the tilt angle.

Half-filled one-dimensional extended Hubbard model: Phase diagram and thermodynamics

We study the thermodynamics of the one-dimensional extended Hubbard model at half filling using a density-matrix renormalization group method applied to transfer matrices. We show that the various phase transitions in this system can be detected by measuring usual thermodynamic quantities such as the isothermal compressibility and the uniform magnetic susceptibility. For the isothermal compressibility, we show that universal crossing points exist, which allow us to accurately determine the line where the charge gap vanishes. By studying, in addition, several correlation functions, we confirm the existence of a phase with long-range dimer order (bond order), which has been a matter of debate for several years. According to our calculations, this phase is located in a narrow region between the spin-density and charge-density wave phases up to a tricritical point, which we estimate to be at ${U}_{t}=6.7\ifmmode\pm\else\textpm\fi{}0.2$, ${V}_{t}=3.5\ifmmode\pm\else\textpm\fi{}0.1$. Our results for the phase diagram are in good agreement with the most recent zero-temperature density-matrix renormalization group study; however, they disagree in some important aspects from the most recent Quantum-Monte-Carlo study.

FIELD-INDUCED TOMONAGA–LUTTINGER LIQUID OF A QUASI-ONE-DIMENSIONAL S = 1 ANTIFERROMAGNET

We review the results of specific-heat experiments on the S = 1 quasi-one-dimensional (quasi-1D) bond-alternating antiferromagnet Ni(C 9 H 24 N 4)( NO 2) ClO 4, alias NTENP. At low temperatures above the transition temperature of a field-induced long-range order, the magnetic specific heat (C mag ) of this compound becomes proportional to temperature (T), when a magnetic field along the spin chains exceeds the critical field H c at which the energy gap vanishes. The ratio C mag /T, which increases as the magnetic field approaches H c from above, is in good quantitative agreement with a prediction of conformal field theory combined with the field-dependent velocity of the excitations calculated by the Lanczos method. This result is the first conclusive evidence for a Tomonaga–Luttinger liquid in a gapped quasi-1D antiferromagnet.

Tl2Ba2CuO6+δ brings spectroscopic probes deep into the overdoped regime of the high-Tc cuprates

Single-particle spectroscopic probes, such as scanning tunnelling and angle-resolved photoemission spectroscopy (ARPES), have provided us with crucial insights into the complex electronic structure of the high-Tc cuprates, in particular for the under- and optimally-doped regimes where high-quality crystals suitable for surface-sensitive experiments are available. Conversely, the elementary excitations on the heavily overdoped side of the phase diagram remain largely unexplored. Important breakthroughs could come from the study of Tl2Ba2CuO6+δ (Tl2201), a structurally simple system whose doping level can be tuned from optimal to extreme overdoping by varying the oxygen content. Using a self-flux method and encapsulation, we have grown single crystals of Tl2201, which were then carefully annealed under controlled oxygen partial pressures. Their high quality and homogeneity are demonstrated by narrow rocking curves and superconducting transition widths. For higher dopings, the crystals are orthorhombic, a lattice distortion stabilized by O interstitials in the TlO layer. These crystals have enabled the first successful ARPES study of both normal and superconducting-state electronic structure in Tl2201, allowing a direct comparison with the Fermi surface from magnetoresistance and the gap from thermal conductivity experiments. This establishes Tl2201 as the first high-Tc cuprate for which a surface-sensitive single-particle spectroscopy and a comparable bulk transport technique have arrived at quantitative agreement on a major feature such as the normal state Fermi surface. The momentum dependence of the ARPES lineshape reveals, however, an unexpected phenomenology: in contrast to the case of under- and optimally-doped cuprates, quasiparticles are sharp near (π,0), the antinodal region where the gap is maximum, and broad at (π/2, π/2), the nodal region where the gap vanishes. This reversed quasiparticle anisotropy past optimal doping, and its relevance to scattering, many-body, and quantum-critical phenomena in the high-Tc cuprates, is discussed.

Statistics of the eigenmodes and optical properties of one-dimensional disordered photonic crystals

The eigenmode spectrum and transmission properties of a certain class of one-dimensional disordered photonic crystals have been studied statistically. It is shown that the relative fluctuation of the optical width of the period of the photonic crystal is a universal parameter allowing a quantitative description of the disordered photonic crystal for various models of disorder. It is shown that the tail of the density of states is characterized by a certain penetration depth and a quantitative relation between the penetration depth, the relative band gap width, and the disorder parameter is obtained. It is found that a threshold level of disorder exists, below which the density of states in the center of the photonic band gap vanishes, and the ensemble-averaged transmission coefficient does not change significantly with increasing disorder. Also, the standard deviation of the transmission coefficient is less than its mean value. Above threshold, the ensemble averaged transmission coefficient and density of states increase with the level of disorder rapidly, and the standard deviation of the transmission coefficient exceeds its mean value. A scaling formula is presented, which relates the logarithm of the transmission to the periodic refractive index modulation and the disorder.

Tomonaga-Luttinger Liquid in a Quasi-One-DimensionalS=1Antiferromagnet Observed by Specific Heat Measurements

Specific-heat experiments on single crystals of the S = 1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9H24N4)(NO2)ClO2 (NTENP) have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C(mag)) is proportional to temperature (T) above a critical field H(c), at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C(mag)/T increases as the magnetic field approaches H(c) from above. The data are in good quantitative agreement with the prediction of the c= 1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing conclusive evidence for a Tomonaga-Luttinger liquid.

Molecular simulations of lubrication and solvation forces

We report on molecular-dynamics simulations of the drag force experienced by a smooth sphere as it approaches a smooth planar surface to test the predictions of classical hydrodynamic theory. We use a simple repulsive Lennard-Jones-like model to represent the fluid interactions, and calculate the total force on the sphere as a function of its radius, velocity, and distance from the surface. We find that the presence of static solvation forces complicates the testing of hydrodynamic theory which predicts a divergent repulsive lubrication force as the gap vanishes. The solvation force contribution is most prominent at small gaps and small velocities. For a smooth wall its presence can lead to a total force that is oscillating between positive and negative, quite different from the hydrodynamic prediction. To enable an improved test of the lubrication predictions, we propose a different approach that measures the total force for approaching as well as receding spheres. We suggest a simple general analysis that decouples the dynamic and static force contributions on the sphere. The new decoupling method is applicable to simulations and laboratory experiments alike. We illustrate its power by applying it to the molecular-dynamics data.

More about Rotons in Superfluid Helium 4

In a recent paper1 it was argued that rotons in superfluid helium 4 are the soft modes announcing a charge density wave that leads to the crystal: rotons are a normal state property. A small superfluid condensate acts to hybridize quasiparticles and soft density fluctuations - hence a level repulsion that lowers the energy: superfluidity is energetically favourable. A shallow roton implies a very small condensate density, as found in He4: what we need is a saturation mechanism. The clue is depletion due to quantum fluctuations. In (1) we assumed that such a depletion was drawn from the condensate itself: superfluidity then disappears in the liquid if the roton gap is too small. Here we explore an alternate possibility: quantum fluctuations are drawn from the normal fluid. We reach the opposite conclusion: superfluidity persists down to the spinodal limit where the roton gap vanishes, with an unusual power law dependence. We briefly mention the possible extension of that argument to a frozen charge density wave: in a toy 1d model it might shed light on the features that favour supersolids.

The phase diagram of Hubbard model with alternating chemical potentials

We have investigated the ground-state phase diagram of the one-dimensional Hubbard model with alternating chemical potentials at half-filling by bosonization technique and the Gaussian wave functional method. We calculate variations of the charge density wave (CDW) and the spin density wave (SDW) gaps, ad well as their classical trajectory c,s with increasing on-site Coulomb repoulsion potential. For the fixed potential, it is found that the transition from the band insulator (BI) to the spontaneously dimerized insulator (SDI) is of the Ising type, at which charge gap vanishes, while the transition from SDI to the Mott insulator (MI) is of the KT type.

Effect of Replacing Helium with a Liquid Metal in the Fuel-Cladding Gap on Fission Gas Release

In light water reactors, a helium-filled gap between the fuel and the cladding accommodates fuel swelling and cladding creepdown. However, the low thermal conductivity of helium results in a large ΔT over the gap before closure occurs. To remedy this situation, Wright et al. proposed the use of a liquid metal (LM) bond in the fuel-cladding gap. The LM (33 wt% each of lead, tin, and bismuth) was chosen for its low melting point (~120°C), its lack of chemical reactivity with UO2 and water, and its high thermal conductivity (~100 times that of He). The thermal resistance of the LM-bonded gap is nil.Prior to closure of a helium-bonded gap, the centerline fuel temperature can be hundreds of degrees hotter than that with an LM-bonded gap at the same linear heat rating. Since the diffusion of fission gas atoms depends strongly upon temperature, it is expected that with the high thermal conductivity pellet-cladding gap, the incubation time to fission gas release should be considerably delayed. A modified Booth Sphere model, which takes into account re-solution, is adopted. The amount of fission gas atoms collected at the grain boundary is calculated using realistic time-temperature histories taken from a recent U.S. Nuclear Regulatory Commission review. The saturation value of gas at the grain boundary proposed by Dowling to fission gas release is adopted. The results show that although the temperature in the LM-bonded case is substantially lower than the He-filled case when the gap is open, the temperatures in the two cases equalize when the gap vanishes. Correspondingly, the two cases exhibit a comparable amount of fission gas at the grain boundary. Calculated differences between the times to saturation with LM and He in the gap are as high as ~1 yr and as low as 1 to 2 days.

Sulfur onTiO2(110)studied with resonant photoemission

Adsorption of sulfur on ${\mathrm{TiO}}_{2}(110)$ at room temperature (RT) and $350\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ has been studied with ultraviolet photoelectron spectroscopy. A ${\mathrm{TiO}}_{2}(110)$ $(1\ifmmode\times\else\texttimes\fi{}1)$ surface with a small amount of oxygen vacancies was prepared by sputtering and annealing in ultrahigh vacuum. Oxygen vacancies induce a defect state that pins the Fermi level just below the conduction-band minimum. Sulfur adsorption at room temperature leads to the disappearance of this vacancy-related band-gap state, indicating that the surface oxygen vacancies are filled by sulfur. Sulfur-induced valence-band features are identified at binding energies of 3.4 and 8 eV. Adsorption of S at $350\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ forms a $(4\ifmmode\times\else\texttimes\fi{}1)$ superstructure at high coverages $[\ensuremath{\approx}0.9$ monolayer (ML)] that is visible with low-energy electron diffraction. In a previously proposed model for this superstructure, sulfur replaces half of the in-plane oxygen atoms and all the bridging oxygen atoms are removed. In agreement with this model, the oxygen $2s$ peak is decreased significantly and the defect state is increased. Two additional valence features are observed: one at 2.7 eV and one at 3.9 eV. Due to those features the band gap vanishes. In resonant photoemission, these features show a similar, but weaker, resonance profile than the vacancy-related defect state. Hybridized Ti-derived states extend across the whole valence-band region. Generally, a higher resonant photon energy is found for valence-band states with lower binding energies, indicating mainly $3p\ensuremath{-}4s$ transitions in the upper valence band. Adsorption of sulfur reduces the strength of the resonances.

Interacting spin systems exhibiting spin plateaus and gaps

We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.

The quantum zero space charge model for semiconductors

The thermal equilibrium state of a bipolar, isothermal quantum fluid confined to a bounded domain Ω⊂ℝd, d = 1, 2 or d = 3 is the minimizer of the total energy [Escr ]ελ; [Escr ]ελ involves the squares of the scaled Planck's constant ε and the scaled minimal Debye length λ. In applications one frequently has λ2[Lt ]1. In these cases the zero-space-charge approximation is rigorously justified. As λ → 0, the particle densities converge to the minimizer of a limiting quantum zero-space-charge functional exactly in those cases where the doping profile satisfies some compatibility conditions. Under natural additional assumptions on the internal energies one gets an differential-algebraic system for the limiting (λ = 0) particle densities, namely the quantum zero-space-charge model. The analysis of the subsequent limit ε → 0 exhibits the importance of quantum gaps. The semiclassical zero-space-charge model is, for small ε, a reasonable approximation of the quantum model if and only if the quantum gap vanishes. The simultaneous limit ε = λ → 0 is analyzed.

Dynamical electron-ion coupling in the ionic conductorα−NaSn

Dynamical electron-ion coupling in an ionic solid NaSn at high temperatures is studied by ab initio molecular dynamics simulation. The cooperative ion dynamics of the migration of ${\mathrm{Na}}^{+}$ ions and the deformations of $({\mathrm{Sn}}_{4}{)}^{4\ensuremath{-}}$ tetrahedra are clarified. The band gap fluctuates between metallic and semiconducting values, and is strongly coupled with the ion dynamics. When the band gap vanishes, the character of the highest occupied eigenfunction changes from bonding to nonbonding within a tetrahedron, and it is caused by the deformations of the tetrahedra. The mechanism of the rapid rise of conductivity experimentally observed is discussed in light of our results.

Ground-State and Thermodynamic Properties of the Quantum Mixed Spin-1/2-1/2-1-1 Chain

We investigate both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian $H=\sum_{\ell=1}^{N/4} (J_1\vecs_{4\ell-3}\cdot \vecs_{4\ell-2}+J_2\vecs_{4\ell-2}\cdot\vecS_{4\ell-1}+J_3\vecS_{4\ell-1}\cdot \vecS_{4\ell}+J_2\vecS_{4\ell}\cdot\vecs_{4\ell+1})$, where two $S=1/2$ spins ($\vecs_{4\ell-3}$ and $\vecs_{4\ell-2}$) and two S=1 spins ($\vecS_{4\ell-1}$ and $\vecS_{4\ell}$) are arranged alternatively. Inseveral limiting cases of $J_1$, $J_2$, and $J_3$ we apply the Wigner-Eckart theorem and carry out a perturbation calculation to examine the behavior of the massless lines where the energy gap vanishes. Performing a quantum Monte Carlo calculation without global flips at a sufficiently low temperature for the case where $J_1=J_3=1.0$ and $J_2>0$, we find that the ground state of the present system in this case undergoes a second-order phase transition accompanying the vanishing of the energy gap at $J_2=J_{2c$ with $J_{2 c} = 0.77 \pm 0.01$. We also find that the ground states for both $J_2 < J_{2 c$ and $J_2 > J_{2c$ can be understood by means of the valence-bond-solid picture. A quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account is carried out to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, it is found that the susceptibility per unit cell for $J_2=0.77$ with $J_1=J_3=1.0$ takes a finite value at absolute zero temperature and that the specific heat per unit cell versus temperature curve for $J_2=5.0$ with $J_1=J_3=1.0$ has a double peak.

MÖSSBAUER SECOND-ORDER DOPPLER SHIFT AND THE RECOILLESS FRACTION OF 119Sn IN SUPERCONDUCTORS

The second-order Doppler shift (SODS) of the Mössbauer spectra in a superconductor, δ SC , is calculated for the first time. The shift depends on the fourth power of the ratio of the gap energy of the superconductor to that of the matrix element of the electron–phonon interaction. At T=T c where the gap vanishes, the shift reduces to that in the normal state. The relative values of the SODS and the isomer shifts are found in several superconductors. The isomer shift for 119 Sn in EuBa 2 Cu 2.98 Sn 0.02 O 7−δ has been found. The recoilless fraction of the 119 Sn in EuBa 2 Cu 2.98 Sn 0.02 O 7−δ is compared with a previous theory. It is found that the ordinary BCS type gap agrees with the experimental measurements of the recoilless fraction only when the gap is modified to include a lattice distortion in the superconducting state.

Testing Haldane's conjecture in the O(3) model by a meron cluster simulation

Twelve years ago, Haldane formulated his famous conjecture for 1-d antiferromagnetic quantum spin chains. In the context of the 2-d O(3) model with a \theta term, it predicts a phase transition at \theta = \pi, which has not yet been verified reliably. To simulate this we use the Wolff cluster algorithm together with an improved estimator for the topological charge distribution. Each cluster carries integer or half integer charge. Clusters with charge 1/2 are identified with merons. At \theta = \pi they are inactive, such that the mass gap vanishes. We obtain critical exponents which are consistent with predictions from the k=1 WZNW model, therefore confirming a second order phase transition.

Meron-cluster simulation of the theta vacuum in the 2D O(3) model.

The 2D O(3) model with a $\ensuremath{\theta}$ vacuum term is formulated in terms of Wolff clusters. Each cluster carries an integer or half-integer topological charge. The clusters with charge \ifmmode\pm\else\textpm\fi{}\textonehalf{} are identified as merons. At $\ensuremath{\theta}=\ensuremath{\pi}$ the merons are bound in pairs inducing a second order phase transition at which the mass gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the $k=1$ Wess-Zumino-Novikov-Witten (WZNW) model. Our results are consistent with Haldane's conjecture fro 1D antiferromagnetic quantum spin chains.

Metal-semimetal transitions in the extended Hubbard model on the fcc lattice: Implications for superconducting fullerides.

We present results from a Hartree-Fock analysis of the extended Hubbard model on the face-centered-cubic lattice. For positive U there are three metallic states at half-filling. As a result of frustration, the ordinary single-band metallic state undergoes a second-order transition (with increasing U) to a spin-density-wave semimetal at small V and to a charge-density-wave (CDW) semimetal at larger V. The semimetals give way to insulators at larger U. In an earlier paper we have shown that a similar CDW semimetal exists for U0, a state that is stabilized by V and becomes superconducting at low temperatures. In the positive U case, the CDW semimetal would require additional retarded interactions (that are always present) to become superconducting. Combining these results, a phase diagram is obtained showing that the CDW semimetal occupies a substantial region of the parameter space. Next, we extend our mean-field analysis away from half-filling in the negative-U case to study the behavior of the CDW-superconducting state across the metal-insulator transition. We find that the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$ has a minimum slightly above half-filling. In either direction ${\mathit{T}}_{\mathit{c}}$ increases rapidly as the CDW is weakened and acquires maximum values at the semimetal-metal transition where the direct CDW gap vanishes. Implications for alkali fullerides are discussed.

Localization and quantum Hall effect in a two-dimensional periodic potential

A numerical study has been made of two-dimensional electrons in the lowest Landau level in the presence of a periodic potential and a random potential. The Hall conductance, density of states and density of current-carrying states are calculated when disorder is varied. The results show that the states in a subband carrying quantized Hall conductance t (t>1 for example, and similarly t<-1) are split into two carrying unit conductance and t-1, respectively, as disorder is introduced. The states carrying unit Hall current will merge and annihilate with that carrying -1 in the neighbouring subband separated by a small gap when disorder is increased and the gap vanishes. Based on this, a diagram of current-carrying states against disorder has been proposed. There is also a calculation on the localization length, and it is found that extended states appear at singular energies under certain conditions. Furthermore, it has been shown that a plateau in the Hall conductance, rather than a rapid oscillation, can be measured as a function of magnetic field for one-third-filled Landau bands. Similar results have been obtained for tight-binding electrons in a magnetic field with random site energies.