Quantized Casimir Force

TL;DR

This paper studies the Casimir effect between 2D electron systems in the quantum Hall regime, revealing quantized, tunable, and carrier-dependent forces, with potential applications in nanoscale physics.

Contribution

It demonstrates that the Casimir force becomes quantized and electrically tunable in quantum Hall systems, a novel insight into quantum fluctuation forces in 2D materials.

Findings

Casimir force is quantized in units of 3ħcα^2/(8π^2 d^4)

Force is repulsive for same carrier type, attractive for opposite

Force is suppressed in charge-neutral graphene at ν=0

Abstract

We investigate the Casimir effect between two-dimensional electron systems driven to the quantum Hall regime by a strong perpendicular magnetic field. In the large separation (d) limit where retardation effects are essential we find i) that the Casimir force is quantized in units of 3\hbar c \alpha^2/(8\pi^2 d^4), and ii) that the force is repulsive for mirrors with same type of carrier, and attractive for mirrors with opposite types of carrier. The sign of the Casimir force is therefore electrically tunable in ambipolar materials like graphene. The Casimir force is suppressed when one mirror is a charge-neutral graphene system in a filling factor \nu=0 quantum Hall state.