Van der Waals density functional: Self-consistent potential and the nature of the van der Waals bond

We derive the exchange-correlation potential corresponding to the nonlocal van der Waals density functional [M. Dion, H. Rydberg, E. Schroder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004)]. We use this potential for a self-consistent calculation of the ground state properties of a number of van der Waals complexes as well as crystalline silicon. For the latter, where little or no van der Waals interaction is expected, we find that the results are mostly determined by semilocal exchange and correlation as in standard generalized gradient approximations (GGA), with the fully nonlocal term giving little effect. On the other hand, our results for the van der Waals complexes show that the self-consistency has little effect at equilibrium separations. This finding validates previous calculations with the same functional that treated the fully nonlocal term as a post GGA perturbation. A comparison of our results with wave-function calculations demonstrates the usefulness of our approach. The exchange-correlation potential also allows us to calculate Hellmann-Feynman forces, hence providing the means for efficient geometry relaxations as well as unleashing the potential use of other standard techniques that depend on the self-consistent charge distribution. The nature of the van der Waals bond is discussed in terms of the self-consistent bonding charge.Comment: submitted to Phys. Rev.

Collective charge fluctuations and Casimir interactions for quasi one-dimensional metals

We investigate the Casimir interaction between two parallel metallic cylinders and between a metallic cylinder and plate. The material properties of the metallic objects are implemented by the plasma, Drude and perfect metal model dielectric functions. We calculate the Casimir interaction numerically at all separation distances and analytically at large separations. The large-distance asymptotic interaction between one plasma cylinder parallel to another plasma cylinder or plate does not depend on the material properties, but for a Drude cylinder it depends on the dc conductivity $\sigma$. At intermediate separations, for plasma cylinders the asymptotic interaction depends on the plasma wave length $\lambda_{\rm p}$ while for Drude cylinders the Casimir interaction can become independent of the material properties. We confirm the analytical results by the numerics and show that at short separations, the numerical results approach the proximity force approximation

Universality versus material dependence of fluctuation forces between metallic wires

We calculate the Casimir interaction between two parallel wires and between a wire and a metall plate. The dielectric properties of the objects are described by the plasma, Drude and perfect metal models. We find that at asymptotically large separation interactions involving plasma wires and/or plates are independent of the material properties, but depend on the dc conductivity $\sigma$ for Drude wires. Counterintuitively, at intermediate separations the interaction involving Drude wires can become independent of $\sigma$. At smaller separations, we compute the interaction numerically and observe an approach to the proximity approximation

Nature and strength of bonding in a crystal of semiconducting nanotubes: van der Waals density functional calculations and analytical results

The dispersive interaction between nanotubes is investigated through ab initio theory calculations and in an analytical approximation. A van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92, 246401 (2004)] is used to determine and compare the binding of a pair of nanotubes as well as in a nanotube crystal. To analyze the interaction and determine the importance of morphology, we furthermore compare results of our ab initio calculations with a simple analytical result that we obtain for a pair of well-separated nanotubes. In contrast to traditional density functional theory calculations, the vdW-DF study predicts an intertube vdW bonding with a strength that is consistent with recent observations for the interlayer binding in graphitics. It also produce a nanotube wall-to-wall separation which is in very good agreement with experiments. Moreover, we find that the vdW-DF result for the nanotube-crystal binding energy can be approximated by a sum of nanotube-pair interactions when these are calculated in vdW-DF. This observation suggests a framework for an efficient implementation of quantum-physical modeling of the CNT bundling in more general nanotube bundles, including nanotube yarn and rope structures.Comment: 10 pages, 4 figure

Casimir-Polder force between an atom and a dielectric plate: thermodynamics and experiment

The low-temperature behavior of the Casimir-Polder free energy and entropy for an atom near a dielectric plate are found on the basis of the Lifshitz theory. The obtained results are shown to be thermodynamically consistent if the dc conductivity of the plate material is disregarded. With inclusion of dc conductivity, both the standard Lifshitz theory (for all dielectrics) and its generalization taking into account screening effects (for a wide range of dielectrics) violate the Nernst heat theorem. The inclusion of the screening effects is also shown to be inconsistent with experimental data of Casimir force measurements. The physical reasons for this inconsistency are elucidated.Comment: 10 pages, 1 figure; improved discussion; to appear in J. Phys. A: Math. Theor. (Fast Track Communications

Electromagnetic force density in dissipative isotropic media

We derive an expression for the macroscopic force density that a narrow-band electromagnetic field imposes on a dissipative isotropic medium. The result is obtained by averaging the microscopic form for Lorentz force density. The derived expression allows us to calculate realistic electromagnetic forces in a wide range of materials that are described by complex-valued electric permittivity and magnetic permeability. The three-dimensional energy-momentum tensor in our expression reduces for lossless media to the so-called Helmholtz tensor that has not been contradicted in any experiment so far. The momentum density of the field does not coincide with any well-known expression, but for non-magnetic materials it matches the Abraham expression

Control of the Casimir force by the modification of dielectric properties with light

The experimental demonstration of the modification of the Casimir force between a gold coated sphere and a single-crystal Si membrane by light pulses is performed. The specially designed and fabricated Si membrane was irradiated with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of the charge-carrier density. The difference in the Casimir force in the presence and in the absence of laser radiation was measured by means of an atomic force microscope as a function of separation at different powers of the absorbed light. The total experimental error of the measured force differences at a separation of 100 nm varies from 10 to 20% in different measurements. The experimental results are compared with theoretical computations using the Lifshitz theory at both zero and laboratory temperatures. The total theoretical error determined mostly by the uncertainty in the concentration of charge carriers when the light is incident is found to be about 14% at separations less than 140 nm. The experimental data are consistent with the Lifshitz theory at laboratory temperature, if the static dielectric permittivity of high-resistivity Si in the absence of light is assumed to be finite. If the dc conductivity of high-resistivity Si in the absence of light is included into the model of dielectric response, the Lifshitz theory at nonzero temperature is shown to be experimentally inconsistent at 95% confidence. The demonstrated phenomenon of the modification of the Casimir force through a change of the charge-carrier density is topical for applications of the Lifshitz theory to real materials in fields ranging from nanotechnology and condensed matter physics to the theory of fundamental interactions.Comment: 30 pages, 10 figures, 2 table

Thermodynamical aspects of the Casimir force between real metals at nonzero temperature

We investigate the thermodynamical aspects of the Casimir effect in the case of plane parallel plates made of real metals. The thermal corrections to the Casimir force between real metals were recently computed by several authors using different approaches based on the Lifshitz formula with diverse results. Both the Drude and plasma models were used to describe a real metal. We calculate the entropy density of photons between metallic plates as a function of the surface separation and temperature. Some of these approaches are demonstrated to lead to negative values of entropy and to nonzero entropy at zero temperature depending on the parameters of the system. The conclusion is that these approaches are in contradiction with the third law of thermodynamics and must be rejected. It is shown that the plasma dielectric function in combination with the unmodified Lifshitz formula is in perfect agreement with the general principles of thermodynamics. As to the Drude dielectric function, the modification of the zero-frequency term of the Lifshitz formula is outlined that not to violate the laws of thermodynamics.Comment: 8pages, 4 figures; Phys. Rev. A, to appea

Theory of Neutron Diffraction from the Vortex Lattice in UPt3

Neutron scattering experiments have recently been performed in the superconducting state of UPt3 to determine the structure of the vortex lattice. The data show anomalous field dependence of the aspect ratio of the unit cell in the B phase. There is apparently also a change in the effective coherence length on the transition from the B to the C phases. Such observations are not consistent with conventional superconductvity. A theory of these results is constructed based on a picture of two-component superconductivity for UPt3. In this way, these unusual observations can be understood. There is a possible discrepancy between theory and experiment in the detailed field dependence of the aspect ratio.Comment: 11 pages; uses REVTEX, APS and PRABIB styles; 2 Postscript figure files include

D-Wave Superconductors near Surfaces and Interfaces: A Scattering Matrix Approach within the Quasiclassical Technique

A recently developed method [A. Shelankov and M. Ozana, Phys. Rev. B 61, 7077 (2000)] is applied to investigate d-wave superconductors in the vicinity of (rough) surfaces. While this method allows the incorporation of arbitrary interfaces into the quasiclassical technique, we discuss, as examples, diffusive surfaces and boundaries with small tilted mirrors (facets). The properties of the surface enter via the scattering matrix in the boundary condition for the quasiclassical Green's function. The diffusive surface is described by an ensemble of random scattering matrices. We find that the fluctuations of the density of states around the average are small; the zero bias conductance peak broadens with increasing disorder. The faceted surface is described in the model where the scattering matrix couples m in- and m out-trajectories (m>=2). No zero bias conductance peak is found for [100] surfaces; the relation to the model of Fogelstrom et al. [Phys. Rev. Lett. 79, 281 (1997)] is discussed.Comment: RevTeX, 19 pages, 18 figure