Casimir Stabilization of Fluctuating Electronic Nematic Order

Vacuum cavity control of quantum materials is the engineering of quantum materials systems through electromagnetic zero-point fluctuations. We articulate a mechanism for vacuum control of correlated electronic order: Casimir control, where the zero-point energy of the electromagnetic continuum, the Casimir energy, depends on the properties of the material system. To assess the viability of this mechanism we focus on the Casimir stabilization of fluctuating nematic Fermi liquids, systems where different orientations of the electronic order are often energetically degenerate, and thermal disordering inhibits long range order. By engineering the electromagnetic environment of the electronic system, we show that variations of the Casimir energy can be used as a tool to stabilize particular orientations. As a concrete example, we consider a birefringent crystal—sourcing an anisotropic environment—and a quantum Hall stripe system, an archetypal nematic Fermi fluid. We show that for experimentally feasible setups, the differences in Casimir energies can be 10⁴ times larger than other mechanisms known to stabilize quantum Hall stripes. This finding convincingly implies that our setting may be realized with current experimental technology. Having demonstrated that the Casimir energy can stabilize fluctuating order, we discuss the implications for recent terahertz cavity experiments on quantum Hall stripes, as well as pave the road towards broader Casimir control of competing correlated electronic phases.