Magnetic square lattice with vertex coupling of a preferred orientation

TL;DR

This paper investigates a square lattice graph under a magnetic field with a specific vertex coupling that breaks time reversal symmetry, revealing how magnetic effects and vertex coupling influence the spectral properties, including the Hofstadter butterfly pattern.

Contribution

It introduces a novel analysis of a square lattice with a special vertex coupling that violates time reversal symmetry, exploring its spectral behavior under magnetic flux.

Findings

High-energy spectra show dominance of magnetic field effects restoring Hofstadter's butterfly

Vertex coupling influences spectral properties and symmetry breaking

Numerical analysis reveals interplay between magnetic flux and vertex coupling

Abstract

We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum numerically for rational values of the flux per plaquette we show how the two effects compete; at the high energies it is the magnetic field which dominates restoring asymptotically the familiar Hofstadter's butterfly pattern.