Search

A system of two-species, one-dimensional fermions, with an attractive two-body interaction of the derivative-delta type, features a scale anomaly. In contrast to the well-known two-dimensional case with contact interactions, and its one-dimensional cousin with three-body interactions (studied recently by some of us and others), the present case displays dimensional transmutation featuring a power-law rather than a logarithmic behavior. We use both the Schrödinger equation and quantum field theory to study bound and scattering states, showing consistency between both approaches. We show that the expressions for the reflection (R) and the transmission (T) coefficients of the renormalized, anomalous derivative-delta potential are identical to those of the regular delta potential. The second-order virial coefficient is calculated analytically using the Beth–Uhlenbeck formula, and we make comments about the proper ϵB→0 (where ϵB is the bound-state energy) limit. We show the impact of the quantum anomaly (which appears as the binding energy of the two-body problem, or equivalently as Tan's contact) on the equation of state and on other universal relations. Our emphasis throughout is on the conceptual and structural aspects of this problem.

In contrast with the three-dimensional result, the Beth-Uhlenbeck (BU) formula in one dimension contains an extra-1/2 term. The origin of this-1/2 term is explained using a spectral density approach. To be explicit, a δ-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in one dimension. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the δ-function potential, the method and result are valid for more general potentials. Additionally, the one-dimensional Levinson theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in one dimension have a universal source: A pole at zero energy. Similar calculations using quantum field-theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (Appendix A).

We analyze, from a canonical quantum field theory (QFT) perspective, the problem of one-dimensional particles with three-body attractive interactions, which was recently shown to exhibit a scale anomaly identical to that observed in two-dimensional (2D) systems with two-body interactions. We study in detail the properties of the scattering amplitude including both bound and scattering states, using cutoff and dimensional regularization, and clarify the connection between the scale anomaly derived from thermodynamics to the nonvanishing non-relativistic trace of the energy-momentum tensor.

We show that a system of three species of one-dimensional fermions, with an attractive three-body contact interaction, features a scale anomaly directly related to the anomaly of two-dimensional fermions with two-body contact forces. We show, furthermore, that those two cases (and their multispecies generalizations) are the only nonrelativistic systems with contact interactions that display a scale anomaly. While the two-dimensional case is well known and has been under study both experimentally and theoretically for years, the one-dimensional case presented here has remained unexplored. For the latter, we calculate the impact of the anomaly on the equation of state, which appears through the generalization of Tan's contact for three-body forces, and determine the pressure at finite temperature. In addition, we show that the third-order virial coefficient is proportional to the second-order coefficient of the two-dimensional two-body case.

The magnetic and electronic properties of composites consisting of oxidized multiwall carbon nantubes (MWNTs) dispersed in elastomeric poly(ether-ester) segmented block copolymer have been studied by means of electron spin resonance (ESR) and dc magnetization measurements. A marked reduction in the MWNT diamagnetic response is identified, indicative of substantial hole doping related to the oxygen functional groups on the oxidized carbon nanotube's surface. Both ESR and the static magnetization reveal considerable enhancement of the spin susceptibility due to an excessive increase in the density of paramagnetic defects, which are sensitive to the dynamical polymer relaxation and thus to the MWNT-polymer interfacial coupling. © 2010 American Institute of Physics.

The magnetic properties of nanocrystalline titanium carbide dispersed in a carbon matrix (TiCx/C) prepared by the non-hydrolytic sol-gel process have been studied by dc magnetization measurements. The superconducting phase of titanium carbide has been observed at low temperatures with the onset of the superconducting transition temperature Tc at about 3.5 K, superimposed on a ferromagnetic component. At T > Tc the magnetic response of TiCx/C is determined by the interplay of the ferromagnetic contribution with the paramagnetic/diamagnetic signal of the metallic system and the contribution of exchange coupled paramagnetic ions. Moreover, significant differences are observed in the magnetic response for samples of the same preparation batch, indicative of the magnetic/electronic inhomogeneity of nanocrystalline titanium carbide which is important for its practical applications.

The electronic properties of single-wall carbon nanotubes (SWNTs) have been studied using dc magnetization and electron spin resonance (ESR). The dc magnetization displays a weak diamagnetic susceptibility of ≈ 10-7 emu/g. ESR measurements reveal a narrow resonance line of low intensity and metallic line shape. The spin susceptibility shows a major Pauli contribution at high temperatures (T>150 K) and an appreciable Curie component at lower temperatures. A marked drop of the spin susceptibility is observed at T

The electronic properties of boron-doped multiwall carbon nanotubes (MWNTs) have been studied using static magnetization and electron spin resonance. A relatively strong ferromagnetic signal has been identified in the dc magnetization response that shows the occurrence of ferromagnetism, coexisting with the orbital and spin magnetism of the conduction electrons. The small diamagnetic susceptibility and the weak temperature variation of the g factor, which is observed in the narrow conduction-electron spin resonance (CESR), indicate a Fermi level shift of ∼0.2eV, according to the quasi-two-dimensional graphite band model. The temperature dependence of the spin susceptibility reveals considerable enhancement compared to undoped MWNTs and the presence of thermally activated behavior, complying with an increased density of states and the formation of localized impurity states close to the Fermi level. Line-shape analysis of the CESR spectra in terms of two separate spin systems implies enhanced doping inhomogeneity. © 2005 The American Physical Society.

The magnetic properties of two series of trivalent rare earth (R 3+) molecular complexes with hydrazone ligands (R=Ce, Pr, Dy, Ho, Er), adopting different crystal structures, have been investigated by static susceptibility measurements. At high temperatures, the magnetic response is dominated by the paramagnetic contribution of R3+ ions determined by the crystal-field interaction. At low temperatures (T

The diamagnetic susceptibility of multiwall carbon nanotubes is studied as function of magnetic field and temperature. Both the low-field and the low-temperature susceptibility reveal a definite paramagnetic upturn in qualitative agreement with the Aharonov-Bohm effect. Analysis of the high-field magnetic susceptibility in terms of the orbital diamagnetism of quasi-two-dimensional graphite implies hole-doping and supports further the intrinsically divergent paramagnetic contribution of small metallic nanotubes. © 2003 Elsevier B.V. All rights reserved.

The magnetic properties of three mononuclear copper complexes where the metal ion is coordinated by Schiff base ligands have been investigated by magnetic susceptibility and electron paramagnetic resonance (EPR) studies. Significant extended magnetic coupling has been observed comprising competing antiferromagnetic and ferromagnetic components, which are explained in terms of the interactions between copper ions mediated through the organic ligands. Distant substitutions in the ligand structure are suggested to affect critically the magnetic coupling leading to frustration effects on the cooperative transition that may develop under favorable structural conditions. The temperature dependence of intensity of the EPR line was studied in the temperature range 130-280K and fitted to the Curie-Weiss-type law. The consistency of magnetic and EPR results is discussed for the three investigated complexes. © 2003 Elsevier B.V. All rights reserved.

The magnetic properties of the polymerized phase of RbC60 have been investigated by static magnetization measurements. The magnetic susceptibility comprises a temperature dependent part that decreases rapidly below 50 K, where the metal-insulator transition and the subsequent antiferromagnetic ordering are expected according to electron spin resonance results. The temperature variation of this contribution resembles that of quasi-one-dimensional gapped systems and shows substantial field dependence suggesting a disordered antiferromagnetic phase.

Influence of water molecule coordination on the magnetic properties of polyamine copper dinitrate complexes was studied. It was found that the magnetic coupling between Cu2+ ions strongly depends on the presence of water molecules in the crystal structure. Electron paramagnetic resonance (EPR) measurements showed considerable temperature dependence of the Lande′ splitting factors and resonance linewidths for both complexes at low temperatures.

The magnetic properties of the rare earth molecular compounds with hydrazone ligands containing Nd3+ Gd3+ and Yb3+ have been investigated by electron paramagnetic resonance (EPR) and magnetization measurements. For the Gd-compound, partially resolved fine structure due to Gd and exchange narrowing effects at low temperatures are observed in the EPR spectra, suggesting, consistent with the EPR and dc magnetic susceptibility, weak antiferromagnetic exchange interactions. Paramagnetic behavior sustained down to low temperatures is derived for Yb3+ ions, whereas substantial ferromagnetic exchange coupling is inferred for the lighter Nd3+ ions, indicating significant variations of the exchange integrals along the lanthanide series.

When attempting to prepare Rb2NaC60, one obtains a phase-separated material, consisting of the energetically more stable superconducting Rb3C60 and nonsuperconducting NaxC60. This sample exhibits a very sharp superconducting transition temperature at 26.3 K. The decrease in Tc with respect to that of pure-phase Rb3C60 is explained as the result of the decrease in density of states in Josephson-like junctions formed between the two phases. This composition displays a large volume fraction of superconductivity, and all measurements of superconducting parameters are extremely well defined, implying high phase purity of the Rb3C60. The zero temperature values of the upper and lower critical magnetic fields are Hc2(0) = 165 kOe and Hc1(0) = 62 Oe, calculated from measurements of the field dependence of the magnetization as a function of temperature. The coherence length and penetration depth are 44 angstrom and 3400 angstrom, significantly higher than earlier literature estimates.

Two binuclear copper(II) complexes with macrocyclic Schiff bases Cu2LI(CH3COO)2·5H2O (complex I) and Cu2LII(CH3COO)2·2H2O (complex II) were synthesized and then characterized by IR, UV, and thermogravimetric analysis (TGA) measurements. TGA was used to investigate the desolvation of lattice water molecules. IR spectra demonstrated the formation of the cyclic compound and together with chemical elemental analysis were used to propose the structure of the complexes. The UV spectra of both complexes are typical for binuclear copper(II) complexes with Robson-type ligands. Variable-temperature magnetic susceptibility measurements corroborated by EPR and low-temperature isothermal magnetization data confirmed the formation of copper dimers with antiferromagnetic exchange coupling constants of -400 and -1250 cm-1 for complexes I and II, respectively, residing outside the usual range for the phenoxide bridged Cu(II) complexes. This implies the possibility that additional superexchange paths through the macrocyclic ligand may affect the intradimer exchange interaction as well as the phenoxide oxygen bridges.

The directly isolated precipitate of RbxC60 from liquid ammonia contains solvent molecules, NH3. Thermal treatment is necessary to remove ammonia solvent molecules from the lattice as well as to homogenize the Rb distribution within the synthetic product, to produce a face-centered cubic (fcc) unit cell. This latter unit cell is the form of Rb3C60 which shows superconductivity. The superconducting transition temperature, Tc, is found to be lower in Rb3C60 samples prepared from liquid ammonia than from those prepared by a conventional vapor transport technique. The depression of Tc can be explained in terms of a large degree of orientational disorder of C60 ions, along with effects of a trace amount of residual NH3, as suggested from solid-state NMR results.

Alkylamines (n-propylamine and n-butylamine) can be employed at room temperature as solvents for the preparation of alkali-metal-intercalated C60. In this work, the preparation of Rb3C60 was studied in detail. The reaction produces a single phase as characterized by X-ray diffraction structural analysis. The product shows a superconducting transition at Tc ∼ 28 K after thermal elimination of the amine. A stepwise mechanism of intercalation is proposed in which a fullerene-amine adduct forms first, followed by charge transfer between the adduct and Rb metal, followed by thermal decomposition of the adduct to yield Rb3C60.