Topologically protected Casimir effect for lattice fermions

Abstract

The electromagnetic Casimir effect has a fermionic counterpart in topological insulators: Zero-point fluctuations of a massless Dirac fermion field mediate a force between magnetic scatterers. The Casimir force is insensitive to disorder that preserves the topological protection of an unpaired Dirac cone. The protection may be broken if the Dirac equation is discretized, and an exponential suppression of the Casimir effect will result if a gap opens at the Dirac point. Here we show how this lattice artefact may be avoided, by applying a recently developed local discretization of the Euclidean action that does not suffer from the fermion-doubling obstruction of local discretizations of the Hamiltonian.

9 pages, 3 figures; V2: appendix D with comparison of tangent fermions and other lattice fermions

References in corpus (5)

• The Casimir effect within scattering theory
• Casimir forces in a T operator approach
• Long-Range Interaction Between Adatoms in Graphene
• Finite difference method for transport properties of massless Dirac fermions
• Casimir Effect for Massless Fermions in One Dimension: A Force Operator Approach

Cited by in corpus (6)

• Dual chiral density wave induced oscillating Casimir effect
• Helical Luttinger liquid on a space-time lattice
• Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions
• Lifshitz formulas for finite-density Casimir effect
• Repulsive Casimir force from a Majorana zero-mode
• Casimir effect in magnetic dual chiral density waves