A knob to tune the Casimir-Lifshitz force with gapped metals

The Casimir-Lifshitz interaction, a long-range force that arises between solids and molecules due to quantum fluctuations in electromagnetic fields, has been widely studied in solid-state physics. The degree of polarization in this interaction is influenced by the dielectric properties of the materials involved, which in turn are determined by factors such as band-to-band transitions, free carrier contributions, phonon contributions, and exciton contributions. Gapped metals, a new class of materials with unique electronic structures, offer the potential to manipulate dielectric properties and, consequently, the Casimir-Lifshitz interaction. In this study, we theoretically investigate the finite temperature Casimir-Lifshitz interaction in La$_3$Te$_4$-based gapped metal systems with varying off-stoichiometry levels. We demonstrate that off-stoichiometric effects in gapped metals can be used to control the magnitude and, in some cases, even the sign of Casimir-Lifshitz interactions. We predict measurable corrections due to stoichiometry on the predicted Casimir force between a La$_3$Te$_4$ surface and a gold sphere, attached to an atomic force microscopy tip.