Non-analytic behavior of the Casimir force across a Lifshitz transition in a spin-orbit coupled material

Abstract

We propose the Casimir effect as a general method to observe Lifshitz transitions in electron systems. The concept is demonstrated with a planar spin-orbit coupled semiconductor in a magnetic field. We calculate the Casimir force between two such semiconductors and between the semiconductor and a metal as a function of the Zeeman splitting in the semiconductor. The Zeeman field causes a Fermi pocket in the semiconductor to form or collapse by tuning the system through a topological Lifshitz transition. We find that the Casimir force experiences a kink at the transition point and noticeably different behaviors on either side of the transition. The simplest experimental realization of the proposed effect would involve a metal-coated sphere suspended from a micro-cantilever above a thin layer of InSb (or another semiconductor with large $g$-factor). Numerical estimates are provided and indicate that the effect is well within experimental reach.

5 pages + 6 page supplement; 5 figures

References in corpus (14)

• Tests of the Gravitational Inverse-Square Law below the Dark-Energy Length Scale
• Emergence of the persistent spin helix in semiconductor quantum wells
• Control of the Casimir force by the modification of dielectric properties with light
• Tunable Casimir repulsion with three dimensional topological insulators
• Halving the Casimir force with conductive oxides
• Demonstration of the Casimir force between ferromagnetic surfaces of a Ni-coated sphere and a Ni-coated plate
• Vacuum Energy and Repulsive Casimir Forces in Quantum Star Graphs
• Zeeman-driven Lifshitz transition: A scenario for the Fermi-surface reconstruction in YbRh2Si2
• Quantized Casimir Force
• A New Apparatus for Detecting Micron-Scale Deviations from Newtonian Gravity
• Recent Developments in the Casimir Effect
• Lifshitz Transition in the Two Dimensional Hubbard Model
• Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit
• Electromagnetic semitransparent $\delta$-function plate: Casimir interaction energy between parallel infinitesimally thin plates

Cited by in corpus (2)

• Repulsive Casimir force between Weyl semimetals
• Fluctuation-induced torque on a topological insulator out of thermal equilibrium