Surface Magnetic Catalysis

TL;DR

This paper investigates how finite size and boundary effects in a cylindrical geometry influence fermionic energy spectra and magnetic catalysis, revealing boundary amplification of magnetic enhancement of fermion pairing.

Contribution

It demonstrates that boundary conditions modify Landau levels and significantly enhance magnetic catalysis at the boundary in a finite cylindrical system.

Findings

Boundary conditions alter Landau level degeneracy.

Mode accumulation occurs at the boundary for large angular momenta.

Magnetic catalysis is strongly amplified at the boundary.

Abstract

We study fermions in a magnetic field in a finite size cylinder. With the boundary condition for the fermion flux, we show that the energy spectra and the wave-functions are modified by the finite size effect; the boundary makes the degenerate Landau levels appear only partially for states with small angular momenta, while the boundary effect becomes stronger for states with large angular momenta. We find that mode accumulation at the boundary occurs for large angular momenta and the magnetic effect is enhanced on the boundary surface. Using a simple fermionic model, we quantify the magnetic catalysis, i.e. the magnetic enhancement of the fermion pair condensation, in a finite size cylinder. We confirm that the magnetic catalysis is strongly amplified at the boundary due to the mode accumulation.