Casimir interaction of two dielectric half spaces with Chern-Simons boundary layers

TL;DR

This paper derives the Casimir energy between dielectric half spaces with Chern-Simons boundary layers, analyzing conditions for repulsive and attractive forces, especially in systems with quantum Hall layers under magnetic fields.

Contribution

It introduces a novel diffraction problem solution for Chern-Simons layers and explores Casimir interactions in systems with boundary quantum Hall layers under magnetic fields.

Findings

Casimir force can be tuned from repulsive to attractive with boundary Chern-Simons layers.

Quantum Hall boundary layers induce Casimir repulsion at nanoscales.

Unique features of these systems are promising for force measurements and detecting long-range interactions.

Abstract

A diffraction problem for a flat Chern-Simons layer at plane boundary of a dielectric half space is solved. The Casimir energy of two dielectric half spaces with Chern-Simons layers at plane-parallel boundaries separated by a vacuum slit is derived. Crossing from the repulsive to the attractive Casimir force is analyzed for two Au and two Si half spaces with boundary Chern-Simons layers. Boundary quantum Hall layers in external magnetic field lead to Casimir repulsion at nanoscales. We discuss features that make systems with boundary quantum Hall layers unique for force measurements and search of long-range interactions beyond electromagnetism.