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arXiv · 1312.6754

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

Andrew A. Allocca·Justin H. Wilson·Victor Galitski
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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.

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Andrew A. Allocca, Justin H. Wilson, Victor Galitski. 2013-12-24. Non-analytic behavior of the Casimir force across a Lifshitz transition in a spin-orbit coupled material. https://doi.org/10.1103/physrevb.90.075420

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