Research ArticleCONDENSED MATTER PHYSICS

Impact of nuclear vibrations on van der Waals and Casimir interactions at zero and finite temperature

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Science Advances  01 Nov 2019:
Vol. 5, no. 11, eaaw0456
DOI: 10.1126/sciadv.aaw0456
  • Fig. 1 RMB model of molecular response.

    A collection of atoms with electronic polarization response modeled as Gaussian basis functions fp(x) interact via long-range EM fields Genv. The individual electronic response of each atom arises from the coupling of valence electronic and phononic excitations via short-range interactions, represented schematically: For every atom p, a nuclear oscillator of mass mIp with dissipation bIp is connected to nuclear oscillators of other atoms q via anisotropic spring constants Kpq, and to an electronic oscillator of mass mep with dissipation bep and isotropic spring constant kep; only the electrons couple directly to long-range EM fields with effective charge qep.

  • Fig. 2 Impact of phonons at large separations of a fullerene from the gold plate.

    (a) Representative polarizability of an individual atomic constituent of a fullerene molecule suspended above a gold plate by a surface-surface gap z, comparing the full (including phonons) α (blue) and purely electronic αe (green) polarizabilities. (b) RMB free energy integrand Φ(iξ) as a function of imaginary frequency ξ corresponding to F (blue) and Fe (green) at a fixed z = 1 nm. (c) RMB power laws for F(0) (blue), F(300 K) (red), and Fe(0) (green). Inset: Energy ratios F(T)/Fe for the fullerene at zero (blue) or room (red) temperature.

  • Fig. 3 Nonmonotonicity and temperature deviations due to phonon-induced nonlocal response in carbyne at short distance from the gold plate.

    (a) Polarizability as a function of imaginary frequency for the middle atom (0) in a 500-atom-long carbyne wire, comparing α (blue) to αe (green). (b) Imaginary frequency integrands for F (blue) and Fe (green) at z = 1 nm via RMB (solid) or CP, without (fine dashed) or with (coarse dashed) artificial smearing. (c) RMB (solid) and CP, without (fine dashed) or with (coarse dashed) artificial smearing, interaction power laws of a 500-atom-long carbyne wire parallel to a gold plate, for F(0) (blue), F(300 K) (red), and Fe(0) (green). Inset: Free energy ratios F(300 K)/F(0) as functions of z via RMB (solid) or CP, without (fine dashed) or with (coarse dashed) artificial smearing.

  • Fig. 4 Phononic versus purely electronic response and vdW interactions in graphene.

    Magnitude of the Fourier space susceptibility ∣χ(iξ, k)∣ of a pristine (undoped) graphene sheet with rectangular unit cell 3.9 nm × 3.4 nm, obtained via either (A) RMB or (B) macroscopic, random-phase approximation (RPA) (41) models. (C) Power law of interaction free energy for a graphene sheet suspended above gold plate by a vacuum gap z, at zero (blue) or room (red) temperature, comparing RMB (solid) results to macroscopic RPA (dashed) predictions without doping. The inset shows the interaction free energy ratios F(300 K)/F(0) as a function of z.

  • Fig. 5 Graphene versus BN interaction power laws at short separations.

    RMB power laws for the vdW interactions of parallel graphene (solid) or hexagonal BN (dashed) rectangular supercell with a gold plate, without phonons (green) or with phonons at zero (blue) or room (red) temperature.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaaw0456/DC1

    Section S1. VDW interaction free energies

    Section S2. VDW interactions of one versus two carbyne wires

    Section S3. DFT phonon dispersions for carbyne and graphene

    Section S4. RPA model of doped graphene

    Section S5. VDW power laws versus dimensionality for perfect conductors

    Fig. S1. vdW free energies of low-dimensional compact molecules.

    Fig. S2. vdW free energies of two-dimensional materials.

    Fig. S3. Nonmonotonicity and temperature deviations due to phonon-induced nonlocal response in carbyne at short distance from the gold plate.

    Fig. S4. Phonon dispersions of carbyne and graphene.

    Fig. S5. Graphene interaction power laws in the continuum RPA model.

    Table S1. Power laws versus dimensionality for perfect conductors.

  • Supplementary Materials

    This PDF file includes:

    • Section S1. VDW interaction free energies
    • Section S2. VDW interactions of one versus two carbyne wires
    • Section S3. DFT phonon dispersions for carbyne and graphene
    • Section S4. RPA model of doped graphene
    • Section S5. VDW power laws versus dimensionality for perfect conductors
    • Fig. S1. vdW free energies of low-dimensional compact molecules.
    • Fig. S2. vdW free energies of two-dimensional materials.
    • Fig. S3. Nonmonotonicity and temperature deviations due to phonon-induced nonlocal response in carbyne at short distance from the gold plate.
    • Fig. S4. Phonon dispersions of carbyne and graphene.
    • Fig. S5. Graphene interaction power laws in the continuum RPA model.
    • Table S1. Power laws versus dimensionality for perfect conductors.

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