Beyond Attraction: A Novel Approach to Repulsive Casimir-Lifshitz Forces using heterogeneous off-stoichiometry in gapped metals

TL;DR

This work addresses the challenge of controlling Casimir-Lifshitz forces by leveraging heterogeneous off-stoichiometry in gapped metals to modulate dielectric responses, enabling attraction-to-repulsion switching for a PTFE nanosurface across liquids. It develops a three-layer planar model Ca6-xAl7O16 – liquid – PTFE, parameterizes the metal's dielectric function via an oscillator fit to DFT data, and computes the Casimir-Lifshitz free energy $F(d)$ from the Matsubara sum. It finds that retardation and a dominant zero-frequency contribution can drive sign changes at separations of a few nanometers, with metallic phases yielding repulsion at short distances in Methanol and insulating phases remaining attractive; alternative liquids can produce long-range zero-frequency–driven attraction and even trapping of PTFE nanoparticles. This approach provides a mechanism for phase-transition–based quantum levitation and suggests nanoengineering routes by tuning stoichiometry, liquids, and separation.

Abstract

We uncover a novel physical mechanism that enables a switch between attractive and repulsive Casimir forces when a Teflon surface interacts with a new form of quantum material (i.e., gapped metal) surface across different liquid media. We demonstrate the discovery of a zero-frequency Casimir effect, which, for the first time, reveals the potential for quantum switching within nanometer distances-a scale previously thought to be unattainable. Hence, our results introduce a new method to induce phase (stoichiometry)-controlled attraction-repulsion transitions and achieving quantum levitation in a liquid medium by tuning the liquid environment. This study thus not only advances our understanding of quantum forces at the nanoscale via their correlation to dielectric properties of involved materials but also opens up exciting possibilities for their manipulation in novel ways, forming the basis towards innovative advancements in nanoscale technology.

Figures (9)

• Figure 1: (Colors online) Schematic figure of the three-layer system involved here: gapped metal of infinite thickness and dielectric function $\varepsilon_1$, in contact with a liquid layer of dielectric function $\varepsilon_2$, of thickness $d$, which is in turn in contact with PTFE of dielectric function $\varepsilon_3$.
• Figure 2: (Colors online) The dielectric functions at imaginary frequencies $\xi_{m}$ for different Ca$_{6-x}$Al$_{7}$O$_{16}$ compounds (note that not all compounds are gapped metals as at high Ca vacancy concentration they become insulators), liquids (Iodobenzene, Bromobenzene, Chlorobenzene and Methanol), and PTFE surface. Zero-frequency dielectric functions of all these materials and liquids are as follows, $\varepsilon_{\mathrm{Ca_{6}Al_{7}O_{16}}}(0)$ = 300.4216, $\varepsilon_{\mathrm{Ca_{5.75}Al_{7}O_{16}}}(0)$ = 58.4389, $\varepsilon_{\mathrm{Ca_{5.5}Al_{7}O_{16}}}(0)$ = 2.815, $\varepsilon_{\mathrm{Iodobenzene}}(0)$ = 4.6, $\varepsilon_{\mathrm{Bromobenzene}}(0)$ = 5.37, $\varepsilon_{\mathrm{Chlorobenzene}}(0)$ = 5.75, $\varepsilon_{\mathrm{Methanol}}(0)$ = 32.9, $\varepsilon_{\mathrm{PTFE}}(0)$ = 2.1 .
• Figure 3: (Colors online) Product of the reflection coefficients at imaginary frequencies $\xi_{m}$ in non-retarded limit for ranges of gapped metals, Ca$_{6-x}$Al$_{7}$O$_{16}$.
• Figure 4: (Colors online) The spectral functions $\mathrm{g}(\xi_{m})$, defined in Eq. (\ref{['LifFreeEnergy']}), at different separations of liquid layer thickness in comparing the fully retarded and non-retarded limits in Ca$_{6-x}$Al$_{7}$O$_{16}$-Methanol-PTFE like systems. Solid lines indicate the retardation effect, while dashed lines represent the behavior of spectral functions in the non-retarded limit.
• Figure 5: (Colors online) Free energy vs. distance plot in Ca$_{6-x}$Al$_{7}$O$_{16}$ -- Methanol -- PTFE like system. Ca$_{6-x}$Al$_{7}$O$_{16}$ indicates different stoichiometry. Here red color dot and magenta color box denote maximum value of Casimir energy for Ca$_{6}$Al$_{7}$O$_{16}$ and Ca$_{5.75}$Al$_{7}$O$_{16}$ are occurring at 2.9 nm and 9.49 nm respectively. Here solid lines represent interaction energy in full retarded limit where dashed lines point the interaction energy in non-retarded limit.