We perform a real-space renormalization-group analysis for the two-dimensional antiferromagnetic Heisenberg model. We first derive an effective model, described by the Hamiltonian: H=J ${\mathcal{J}}_{\mathit{j}=1\mathrm{}}^{\mathit{L}}$ S(j)⋅S(j+1)+ ${\mathcal{J}}_{\mathit{j}=1\mathrm{}}^{\mathit{L}}$(-1${)}^{\mathit{j}}$‖J(j)‖S(0)⋅S(j), where S(0) represents a single spin located in the center of the ring. We show that the renormalized coupling constants ‖J(j)‖ tend to nonzero values as one increases the block size by successive renormalization. Using analytic and numerical arguments, we establish the existence of antiferromagnetic long-range order in the effective model and hence, in the original Heisenberg model. We compare our results with those obtained from perturbation theory, spin-wave theory, and exact-diagonalization calculations.

We propose a collective-variable ansatz for a system of N extended, but finite, nonlinear excitations in magnetic systems. In contrast to earlier approaches, where the interactions between the different excitations have been treated only through an external force term, we explicitly consider a dependence of the microscopic spin field on all the coordinates and velocities of the localized objects. This leads to N coupled equations of motion with parameters (mass and gyro tensors) which explicitly depend on the mutual distances of the excitations. We apply this ansatz to vortices in two-dimensional Heisenberg ferromagnets with weak easy-plane anisotropy. For vortex pairs we find either rotational or translational motion, with an additional cyclotronlike oscillation on top of the main trajectories. Due to the interactions between the two vortices we obtain two different eigenvalues of the mass and gyro tensors with values depending on the distance between the vortices, their vorticities, and the sign of their out-of-plane structures. In contrast to the single-vortex mass, which depends logarithmically on the system size L, we find two-vortex masses, which are independent of L, but depend on their mutual distance. These predictions are in good qualitative agreement with numerical simulations of the complete spin systems. However, since these simulations are performed at zero temperature, where the vortex pairs extend throughout the whole system, we observe a strong influence of the boundaries on the absolute values of the masses.

We have observed a clear series of fine structures superposed on the angular dependence of the transverse magnetoresistance in the semimetallic spin-density-wave state of the organic conductor (TMTSF${)}_2$${\mathrm{NO}}_3$. They appear at the positions defined by the strength of the field component parallel to the least-conduction direction (B cos θ≃const). An observed asymmetry in the magnitude is due to the striking angular dependence of the oscillations amplitude. The frequency of the oscillations (${\mathit{B}}_{\mathit{S}}$=63 T) is close to the frequency of the field-induced spin-density-wave transitions found in the other Bechgaard salts. This oscillatory phenomenon is considered to result from the orbit quantization inside the closed parts of the Fermi surface which are due to the 2${\mathit{k}}_{\mathit{F}}$ anion ordering together with the imperfect spin-density-wave nesting.

The transverse magnetoresistance of the Bechgaard salt (TMTSF${)}_2$${\mathrm{NO}}_3$ has been measured up to 37 T at ambient pressure in the temperature range from 2 to 77 K. When the magnetic field is parallel to the lowest conductivity direction ${\mathit{c}}^{\mathrm{*}}$ and for temperatures higher than ∼12 K, the data can be accounted for by a power law, the exponent of which decreases as the anion ordering takes place. At lower temperatures, the magnetic field increases the spin-density-wave (SDW) transition temperature, in overall agreement with theoretical predictions for the imperfect-nesting case. Two oscillation series, both linked to the SDW state, have been observed in the 2–10 K range. Their temperature-independent frequencies, measured from 2 to 8 K, are at (63±2) and (248±5) T, respectively. These oscillations have been studied (at 4.2 K) as a function of the field direction. They were found to deviate from the two-dimensional model since, in particular, their behavior differs according to whether the field is tilted on one side of the ${\mathit{c}}^{\mathrm{*}}$ direction or on the other. The oscillation data are discussed on the basis of recent calculations of Yakovenko.

Using the space-time curve representation, a bosonization scheme is constructed which includes density excitations around each point on the Fermi surface (FS) and space-time tunneling of charges which belong to different FS points. The space-time tunneling reproduces the two-dimensional Jordan-Wigner transformation. In two dimensions, since the tunneling involves two electrons, the total Jordan-Wigner phase maps boson into boson. Therefore, the tunneling corresponds to instantons in 2e bosonic systems. Using this formalism, a spinless fermion model with short-range repulsive interactions is investigated. We find two components: sound-wave excitations in the normal direction of the FS reproduce the Fermi liquid (FL); the second component corresponds to the cooperon channel, violates charge conservation, and gives rise to two-particle coherent tunneling. As a result, the FL phase is destroyed at temperature T=0, and a tunneling gap for charge 2e is formed with angular momentum l≠0. We apply our formalism to the U(1) gauge field coupled to a spinless fermion and find that at T≠0 the FL is again destroyed. We also make some remarks concerning the t-J model.

Inelastic-neutron-scattering measurements at high exchanged momentum have been performed in fluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ along a supercritical isochore in the 4.2–50 K temperature range. The data have been analyzed in the plane-wave impulse approximation to obtain the root-mean-square values of the particle momentum. Deviations from classical behavior have been interpreted as arising from the quantum nature of the particle oscillations in the framework of a cell model for the fluid.

We present high-resolution specific-heat, C, measurements on a large (4.47 mg) single crystal of κ-(BEDT-TTF${)}_2$${\mathrm{I}}_3$ from 0.25 to 20 K in zero and different magnetic fields. The electronic specific-heat coefficient in the normal state is extracted to γ=(18.9±1.5) mJ ${\mathrm{K}}^{\mathrm{-}2}$ ${\mathrm{mol}}^{\mathrm{-}1}$. For the ratio ΔC/(γ${\mathit{T}}_{\mathit{c}}$), where ΔC is the jump of C at ${\mathit{T}}_{\mathit{c}}$=3.4 K, a value of 1.6±0.2 consistent with the BCS prediction of 1.43 is found. The exact form of ΔC(T), the specific-heat difference between the superconducting and the normal state, however, deviates somewhat from the BCS dependence but might be explained by strong coupling. In magnetic fields applied perpendicular to the highly conducting b-c plane the height of the jump in C is strongly reduced and broadened with a concomitant reduction of ${\mathit{T}}_{\mathit{c}}$. In a field of B=0.5 T above ${\mathit{B}}_{\mathit{c}2}$ at low temperatures a hyperfine contribution to C is found which is larger than the value expected by nuclear hyperfine interaction alone.

Pressure effects on the tetragonal infinite-layer structure were studied in superconducting ${\mathrm{Sr}}_{0.9}$${\mathrm{La}}_{0.1}$${\mathrm{CuO}}_2$ (electron-doped) and ${\mathrm{Sr}}_{0.7}$${\mathrm{Ca}}_{0.3}$${\mathrm{CuO}}_2$ (hole-doped) samples, and in an insulating nonsuperconducting ${\mathrm{Sr}}_{0.14}$${\mathrm{Ca}}_{0.86}$${\mathrm{CuO}}_2$ sample, using time-of-flight neutron powder diffraction. Neutron-diffraction measurements, with the sample at room temperature, were performed at several hydrostatic pressures up to ≊0.6 GPa on each of the three samples, using a helium-gas pressure cell. The measured compressibilities, which are similar for the three samples, show a large anisotropy, and are in a good agreement with first-principles calculations performed for undoped ${\mathrm{Sr}}_{0.7}$${\mathrm{Ca}}_{0.3}$${\mathrm{CuO}}_2$. Atomic size effects of the A atom in A${\mathrm{CuO}}_2$ on the crystal lattice are discussed and are compared with the pressure effects. A relation is found between the in-plane compressibilities among n-layer (n=1,2,3 . . .,∞) structures of high-${\mathit{T}}_{\mathit{c}}$ superconductors.

Inhomogeneous superconductivity proposed by Fulde and Ferrell (FF state) is studied in a strongly Pauli-limited type-II superconductor with a cylindrical Fermi surface. The phase diagram of the FF state, BCS state, and normal state is obtained. It is found that the FF state is remarkably enhanced owing to the two-dimensional Fermi-surface structure in comparison to the spherical symmetric case. We discuss that the Fermi-surface nesting is also advantageous to the FF state as well as nesting instabilities. Our result obtained in the cylindrical symmetric case is applicable in general to quasi-low-dimensional superconductors in which the nesting is sufficiently incomplete so that the nesting instabilities are suppressed. Relation to the exotic superconductors discovered recently is briefly discussed.

Charging effects in mesoscopic junctions suppress the tunneling of electrons. In normal-metal–superconductor systems they also suppress the proximity effect, thereby revealing the nature of the microscopic processes and of the ground state of the system. The effect can be made visible since the charging and proximity effect and hence the transport properties of the system can be modulated by gate voltages. If the superconducting electrode is isolated, electron number parity effects lead to an even-odd asymmetry in the proximity effect.

Thermal depinning has been studied for a single vortex trapped in a superconducting Nb thin film in order to determine the value of the superconducting order parameter and the superfluid density when the vortex depins and starts to move around the film. The value depends on the pinning site, but typically the location of the vortex begins to change when the order parameter is about 24% of the T=0 value and the superfluid density is about 5% of the T=0 value. For all the pinning sites probed, the vortex would exit the film when the superfluid density was under 1%. This implies that there is a window between 9.1 and 9.2 K where vortices will spontaneously leave the film in a microtesla environment even though the film is still superconducting.

The calculations of the superconducting transition temperature, including the lowest-order vertex corrections, are carried out for three models: the BCS-type instantaneous interaction, a retarded isotropic interaction described by the Eliashberg spectral function ${\mathrm{\alpha }}^2$F(Ω) and a spin-fluctuation interaction with four δ-function peaks in the corners of a square Brillouin zone. In the isotropic case the effect of higher-order self-energy diagrams is to suppress the critical temperature calculated within the mean-field approximation when the characteristic energy of the boson responsible for the pairing is not small compared to the Fermi energy. In the case of the model with sharp peaks in the momentum space the vertex correction can lead to an increase of ${\mathit{T}}_{\mathit{c}}$.

A scanning tunneling microscope has been used to form and characterize variable and reproducible superconducting weak links of known geometry. The Josephson critical voltage is observed to increase with the conductance of the weak link, which is explained using a simple theoretical model.

Collective excitations in a fluxon chain placed in a periodically modulated Josephson junction are studied analytically and numerically. In order to eliminate fluxon collisions with boundaries, we consider a Josephson ring (annular Josephson junction). Due to the interaction of the fluxons with periodically placed obstacles, we predict that linear deformation modes of the fluxon chain should bring about resonances which be be observed experimentally. The linear analysis is compared with numerical simulations, and good agreement is found in an appropriate parameter range. In the ‘‘relativistic’’ limit, the numerical simulations reveal a dynamical mode which is characterized by a strongly nonlinear interaction between the moving fluxons in the chain. A qualitative explanation of this regime is suggested by an extrapolation of the linear behavior.

Biharmonic-driven long Josephson junctions are studied within the framework of a perturbative approach for the motion of fluxons in the junctions. A thorough study of phase-locking states is carried out giving a generalization of the phase-locking conditions valid for any type of periodic external drive. These conditions give rise to a classification of phase-locked steps on the current-voltage characteristics of the junction. Enhancement of dynamical phase-locked regions and stabilization in connection with the phenomenon of chaos suppression are two interesting characteristics of biharmonic phase-locking states. Numerical simulations show that the theoretical predictions are, in general, well reproduced.

The number of Cooper pairs on a small superconducting island coupled to superconducting leads by a Josephson junction fluctuates due to tunneling of Cooper pairs through the junction. On the other hand, the impedance of the circuit surrounding the island tends to suppress these fluctuations and to restore charge quantization. We consider the influence of the electromagnetic environment within a two-state approximation for the charge on the island. The average charge and the slope of the steps of the Coulomb staircase are calculated for a realistic environmental impedance and finite temperatures in the range of current experimental studies. It is shown that even a low-frequency environment may lead to a considerable reduction of charge fluctuations provided the integrated total impedance is large enough.

We have studied the T=0 properties of the localized state of an excess electron in liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ using a density-functional method. The binding energy, radius, and surface tension of the electron bubble in bulk liquid${\mathrm{-}}^4$He are calculated. The modifications on the bubble properties as the electron approaches the He surface are investigated. The calculated energy barrier for thermal emission of the electron from the surface into the vacuum is found to be in agreement with the experimental value. We have calculated the escape rates for electron tunneling through the surface layer and found the results in semiquantitative agreement with the experiments.

A time-dependent equation for the interlayer phase differences is derived for Josephson-coupled layered superconductors. It generalizes the sine-Gordon equation for the phase in a standard Josephson junction to the case of multilayer systems. With the help of this equation, the dispersion of a collective mode is found at low temperatures. In highly anisotropic systems the gap in the spectrum of this mode lies below the superconducting gap and is suppressed strongly by a magnetic field parallel to the layers. The effect of this mode on the dielectric function and specific heat is calculated.

Based on extensions of quantum Monte Carlo algorithms to incorporate magnetic fields, two criteria to detect superconductivity in two-dimensional Hubbard models are investigated. In order to provide such criteria, we calculate both the internal energy E(Φ,T) as well as the ground-state energy, ${\mathit{E}}_0$(Φ), for Hubbard models on a cylinder geometry threaded by a flux Φ. The temperature derivative of the superfluid density, ∂β${\mathit{D}}_{\mathit{s}}$(β)/∂β, is obtained from the difference in internal energy of systems which differ by a phase twist π/2 in the boundary condition along one lattice direction. In the framework of a Kosterlitz-Thouless transition, ∂β${\mathit{D}}_{\mathit{x}}$(β)/∂β scales to a Dirac δ function at the transition temperature. On finite-sized lattices, ∂β${\mathit{D}}_{\mathit{s}}$(β)/∂β shows a response which increases with lattice size. Flux quantization is a T=0 method. From the functional form of ${\mathit{E}}_0$(Φ), superconducting or nonsuperconducting ground states may be identified. In both approaches, superconductivity may be detected without prior knowledge of the symmetry and nature of the pairing correlations. For single-band Hubbard models, our main quantum Monte Carlo results include numerical data which (a) confirm the existence and pin down the transition temperature of a Kosterlitz-Thouless-type transition in the attractive Hubbard model away from half-band filling and (b) show that the quarter-filled repulsive Hubbard model is not superconducting. For the three-band Hubbard model we consider two parameter sets which take into account the differences in static magnetic structure and Fermi surfaces between La-Sr-Cu-O and Y-Ba-Cu-O materials. For both parameter sets, the finite-temperature approach showed no sign of a Kosterlitz-Thouless-type transition up to inverse temperatures β=17.5, in units of the Cu-O hopping, and hole doping δ=0.25. Flux quantization results for the Y-Ba-Cu-O parameters on clusters up to 8×8 unit cells equally showed no sign of superconductivity at a hole doping δ=0.25.

We investigate the dynamics of the sine-Gordon system when the length of the spatial interval is relatively small. In our analysis ac and dc forces are applied through the boundaries and a dc force is uniformly distributed over the entire spatial interval. Phase locking of Fiske modes to the external ac boundary signal is observed and analytical perturbation results are in excellent agreement with numerical experiments.