Nonmonotonous Distance Dependence of van der Waals Screening by a Dielectric Layer

Abstract

Van der Waals (vdW) screening or Faraday-cage-like screening of vdW interaction by monolayer crystals has recently been observed in experiments and understood from first-principles theories. Here, we investigate the vdW screening by a bulky dielectric layer using the Lifshitz theory. The ratio of vdW screening is found to depend on not only the interobject distance but also the thicknesses of the separated layers. Surprisingly, the screening ratio exhibits a nonmonotonous distance dependence, first increasing, but beyond a critical distance reducing, toward zero. The short-range trend coincides with that predicted for graphene-like trilayers by the random phase approximation, while the long-range trend poses a contrast to the increasing screening with distance by graphene predicted by the many-body dispersion approach. The positive correlation between the screening ratio and the dielectric constant revealed for atomistic layers is reproduced for the bulky dielectric layers.

Large Casimir Flipping Torque in Quantum Trap

“…As shown in Figure a, the quantum trap considered here consists of a finite-thickness Au plate immersed in ethanol and located above a finite-thickness Au substrate coated with a thin Teflon layer. According to the Casimir–Lifshitz theory, , the interaction energy between the Au plate and the substrate in the ethanol environment can be expressed as E false( d false) = k B T 8 π d 2 ∑ n = 0 ∞ ′ ∫ r n ∞ x ln false[ false( 1 − normalΔ̅ Lm normale normalf normalf ( ξ n , x ) normalΔ̅ Rm normale normalf normalf ( ξ n , x ) normale − x false) false] d x where k B and T are the Boltzmann constant and temperature, respectively. The Matsubara frequency ξ n can be 2 π k B italicTn ℏ , with n being a non-negative integer and ℏ being Planck’s constant.…”

“…As shown in Figure 2a, the quantum trap considered here consists of a finite-thickness Au plate immersed in ethanol and located above a finite-thickness Au substrate coated with a thin Teflon layer. According to the Casimir−Lifshitz theory, 47,48 the interaction energy between the Au plate and the substrate in the ethanol environment can be expressed as…”

Physical Limit of Nonlinear Brownian Oscillators in Quantum Trap

“…Ever since the study of Pythagoras’s vibrating string, the feature size of mechanical oscillator has been extended to kilometer scale as of a bridge and at the opposite extreme narrowed down to nanometer scale as of a carbon nanotube. , The restoring force, however, hardly goes beyond that of a string, namely, the chemical bond. Other types of force field, such as gravity, Coulomb interaction, and even quantum and thermal fluctuation-induced van der Waals (vdW) potential − are usually monotonous, being incapable of providing a restoring force by themselves alone. Previous mechanical oscillators based on a monotonous vdW potential require the attendance of an elastic spring; , hence, the role of vdW force therein is just to introduce a nonlinearity .…”