Casimir stabilization of fluctuating electronic nematic order

The field of vacuum cavity control of quantum materials aims to engineer quantum materials through electromagnetic zero-point fluctuations. In this work we articulate and theoretically study a generic mechanism for vacuum control of electronic order: Casimir control, where a fluctuating phase is stabilized by minimizing the zero-point energy of the surrounding electromagnetic continuum. We focus on the Casimir stabilization of fluctuating nematic order, where local order develops but thermal fluctuations inhibit long-range order. As a concrete example, we stabilize fluctuating quantum Hall stripes by leveraging the anisotropic electromagnetic environment of a birefringent crystal. We show that for experimentally feasible setups, an orientation-dependent Casimir energy emerges which can be 10³ times larger than other known stabilization mechanisms, implying that our setting may be realized with currently available technology. We close by discussing connections to recent quantum Hall stripes experiments, as well as broader applications of Casimir control.