Pair Coherence Length Research Articles

Spontaneous Helical Order of a Chiral p-Wave Superfluid Confined in Nanoscale Channels.

Strong interactions that favor chiral p-wave pairing, combined with strong pair breaking by confining boundaries, are shown to lead to new equilibrium states with different broken symmetries. Based on a strong-coupling extension of the Ginzburg-Landau theory that accurately accounts for the thermodynamics and phase diagram of the bulk phases of superfluid ^{3}He, we predict new phases of superfluid ^{3}He for confined geometries that spontaneously break rotational and translational symmetry in combination with parity and time-reversal symmetry. One of the newly predicted phases exhibits a unique combination of chiral and helical order that is energetically stable in cylindrical channels of radius approaching the Cooper pair coherence length, e.g., R∼100 nm. Precise numerical minimization of the free energy yields a broad region of stability of the helical phase as a function of pressure and temperature, in addition to three translationally invariant phases with distinct broken spin and orbital rotation symmetries. The helical phase is stable at both high and low pressures and favored by boundaries with strong pair breaking. We present calculations of transverse NMR frequency shifts as functions of rf pulse tipping angle, magnetic field orientation, and temperature as signatures of these broken symmetry phases.

Excitonic Insulator State of the Extended Falicov–Kimball Model in the Cluster Dynamical Impurity Approximation

We comparatively study the excitonic insulator state in the extended Falicov-Kimball model (EFKM, a spinless two-band model) on the two-dimensional square lattice using the variational cluster approximation (VCA) and the cluster dynamical impurity approximation (CDIA). In the latter, the particle-bath sites are included in the reference cluster to take into account the particle-number fluctuations in the correlation sites. We thus calculate the particle-number distribution, order parameter, ground-state phase diagram, anomalous Green's function, and pair coherence length, thereby demonstrating the usefulness of the CDIA in the discussion of the excitonic condensation in the EFKM.

Dimensional crossover of the superfluid state in the attractive Hubbard model

The superfluid state in the attractive Hubbard is studied for the stacked square lattices to simulate the two- to three-dimensional crossover effects. We use the variation cluster approximation to calculate the order parameter and pair coherence length from the weak-coupling BCS state to the strong-coupling BEC state at T = 0 K. We show that in the weak-coupling BCS region the density of states at Fermi level plays an important role in the dimensional crossover of the superfluid state but in the strong-coupling BEC region the quantum fluctuations depending on the dimensionality of the system play an essential role.

Tuning locality of pair coherence in graphene-based Andreev interferometers.

We report on gate-tuned locality of superconductivity-induced phase-coherent magnetoconductance oscillations in a graphene-based Andreev interferometer, consisting of a T-shaped graphene bar in contact with a superconducting Al loop. The conductance oscillations arose from the flux change through the superconducting Al loop, with gate-dependent Fraunhofer-type modulation of the envelope. We confirm a transitional change in the character of the pair coherence, between local and nonlocal, in the same device as the effective length-to-width ratio of the device was modulated by tuning the pair-coherence length ξT in the graphene layer.

Roles of Hund's rule coupling in excitonic density-wave states

Excitonic density-wave states realized by the quantum condensation of electron-hole pairs (or excitons) are studied in the two-band Hubbard model with Hund's rule coupling and the pair hopping term. Using the variational cluster approximation, we calculate the grand potential of the system and demonstrate that Hund's rule coupling always stabilizes the excitonic spin-density-wave state and destabilizes the excitonic charge-density-wave state and that the pair hopping term enhances these effects. The characteristics of these excitonic density-wave states are discussed using the calculated single-particle spectral function, density of states, condensation amplitude, and pair coherence length. Implications of our results in the materials' aspects are also discussed.

BCS–BEC Crossover in the Two-Dimensional Attractive Hubbard Model: Variational Cluster Approach

We use the variational cluster approximation to study the superconducting ground state in the two-dimensional attractive Hubbard model, putting particular emphasis on the significance of quantum fluctuations of the system. We first show that the order parameter is suppressed in comparison with that obtained using the mean-field theory owing to the effects of spatial fluctuations in two-dimensional systems. We then show that the calculated Bogoliubov quasiparticle spectra and condensation amplitude clearly exhibit the character of Cooper pairs in momentum space and that the pair coherence length ξ evaluated from the condensation amplitude demonstrates a smooth crossover in real space from a weakly paired BCS state (\(\xi \gg a\)) to a BEC state of tightly bound pairs (\(\xi \ll a\)), where a is the lattice constant. The calculated kinetic and potential energies in the superconducting and normal ground states indicate that the superconducting state in the weak-coupling region is driven by the gain in potential energy, while that in the strong-coupling region is driven by the gain in kinetic energy.

Effects of Pr, Tb, and Zn doping into YBa2Cu3O7 on magnetoresistivity and magnetic phase boundaries

Transverse AB-plane magnetoresistivity ρAB (C axis ∥H) of (Y1−XPrX)Ba2Cu3O7−δ and YBa2(Cu1−XZnX)3O7−δ thin films and (Y1−XTbX)Ba2Cu3O7−δ thin films and single crystals has been measured as a function of 0.0<X<XC, 2 K<T<300 K, and 0 T<H<20 T. Mean-field upper critical field HC2 and irreversibility field HI phase boundaries have been determined and are discussed in terms of proposed theories. Tb doping of YBa2Cu3O7 reflects an enhanced pinning or ‘‘stiffening’’ of the vortex system without apparent alteration to TC or the slope of the mean-field normal phase-mixed phase boundary line, dHC2/dT‖T=Tc. However, Pr and Zn doping of YBa2Cu3O7 tends to depress both TC and dHC2/dT‖T=Tc and shows a ‘‘softening’’ of the vortex system. This behavior may be understood in terms of the magnitude of the superconducting pair coherence length, which is controlled by doping, and the divergence of the vortex-glass correlation length as it relates to flux line coupling of vortices in the CuO2 planes. These systems are compared with other high TC superconducting systems which possess similar phase boundary properties.

SUPERCONDUCTIVITY OF SMALL PARTICLES

Superconductivity in a small metallic particle means that pairing of electrons has to be included in the treatment of size-dependent properties. Here a model is reconsidered which applies to the small-size limit of conventional superconductors with a large intrinsic range of the pair coherence length. Mainly thermal equilibrium properties are discussed, but also some remarks about related phenomena and remaining problems are made.

Superconductivity of small particles

Deviations from conventional 3D superconductivity occur when one of the spatial dimensions decreases below the large intrinsic range of the pair coherence length ξ. Here a model is reconsidered which treats the case in which all spatial dimensions are reduced below ξ. The implications of this treatment for the size dependence of thermodynamic properties are discussed and some comments about remaining problems are made.

Neutron diffraction from the vortex lattice in the heavy-fermion superconductor UPt3.

We have used neutron diffraction to observe the vortex lattice of ${\mathrm{UPt}}_{3}$. This is the first such measurement in a heavy-fermion system, a superconductor below 1 K, or in a system with such a long magnetic penetration depth (6000\ifmmode\pm\else\textpm\fi{}75 \AA{}). It also provides the first value for the pair coherence length, 111\ifmmode\pm\else\textpm\fi{}2\AA{}, to be obtained directly within the pairing state of ${\mathrm{UPt}}_{3}$. The lattice is oblique hexagonal with conventional quantization. Its anisotropy can be explained by considering a combination of gap and Fermi-surface anisotropies. The lattice does not appear to change near the transitions between the superconducting phases identified by other techniques.

Long-range proximity effect in aluminum thin films with regions of nearly identical transition temperatures.

We have investigated the resistive transition of dirty aluminum thin films whose transition temperature is spatially modulated by \ensuremath{\sim}2--4 % along the current path. At current densities as high as 600 A/${\mathrm{cm}}^{2}$, the system exhibits a single homogeneous transition for modulation lengths up to 50 \ensuremath{\mu}m, an order of magnitude longer than predicted by current theories. In the limit that the modulation length is 50 \ensuremath{\mu}m, the ${\mathit{T}}_{\mathit{c}}$ depends sensitively and monotonically on the ratio of the lengths of the etched and the unetched regions (${\mathit{d}}_{1}$/${\mathit{d}}_{2}$), but only weakly on their absolute magnitudes. This behavior is reproduced for ${\mathit{T}}_{\mathit{c}}$ modulation parallel or perpendicular to the current flow. For samples with a controlled aperiodic (Fibonacci) modulation, the ${\mathit{T}}_{\mathit{c}}$ is compatible with that of periodically modulated films. The dependence of the ${\mathit{T}}_{\mathit{c}}$ on ${\mathit{d}}_{1}$/${\mathit{d}}_{2}$ can be fitted to a simple Ginzburg-Landau theory which assumes that the effective pair coherence length is long in comparison with the modulation period. Despite the good fit, data for the full range of experimentally accessible modulation length scales are not consistent with a more detailed microscopic theory. We believe this long-range proximity effect is not the consequence of pair tunneling, but is a manifestation of the long distance over which quasiparticle phase coherence is maintained in a two-dimensional metal film.

Superconductivity in disordered thin films

Superconductivity disappears in (mesoscale) disordered thin films at a sheet resistance R□ or order 10 kΩ per square. This and other observed features of systems with both atomic and meso-scale disorder are briefly reviewed, as also theoretical models mainly based on the Josephson junction lattice. These are known to be inadequate. A new approach is described, with the sole assumption that the pair amplitude |Δ| does not vary spatially. The energy cost of wavevector (q) and frequency (ω) dependent phase fluctuations θqω is expressed exactly in terms of disordered normal state properties. It is shown that because of perfect screening, the ω2 dependent term has an extra factor |q| in two dimensions relative to the Josephson junction lattice form. The q2 or phase gradient term is calculated as a function of R□. A rapid and large drop in stiffness occurs for R□ ∼ 10 kΩ when the electron localization length and pair coherence length become comparable. At this level of disorder, the pair amplitude fluctuates spatially, so that the above approach becomes inadequate. Several indications are that a charged Bose system in a random potential would be a realistic model for disordered thin film superconductors at low temperature.

Theoretical and experimental aspects of superconducting small particles

In the world of small particle physics, superconducting phenomena form an interesting frontier land of their own. Zero-dimensional particles with diameter less than the large pair coherence length have size dependent properties which are determined mainly by order parameter fluctuations. Here we discuss and compare with experiments a simple model which treats size effects of isolated grains by means of a single parameter. In addition we will briefly touch on the properties of granular composites (superconductivity of a system of coupled particles).

Thermodynamic Properties of Small Superconducting Particles

In bulk superconducting systems the large intrinsic range of the pair coherence length implies an extremely narrow critical region. However, as is well known, the size of the critical region becomes larger as the dimensions of the system decrease below the coherence length. An interesting limiting case corresponds to particles with all dimensions less than a coherence length which form essentially zero-dimensional systems. Here we calculate the thermodynamic properties of small superconducting particles using a static approximation. Within this approximation, both the order parameter and the quasiparticle contribution are explicitely studied.