Zero energy mode for an electron in graphene in a perpendicular magnetic field with constant asymptotics

TL;DR

This paper investigates zero-energy solutions for electrons in graphene under a perpendicular magnetic field with constant asymptotics, revealing pseudospin dependence and the robustness of zero-energy levels.

Contribution

It demonstrates that zero-energy solutions exist only for one pseudospin direction and are unaffected by magnetic field inhomogeneities, with infinitely many zero-energy states for one pseudospin.

Findings

Zero-energy solutions depend on the sign of the magnetic field at infinity.

Zero-energy level is robust against magnetic field inhomogeneities.

Infinite zero-energy states exist for one pseudospin projection.

Abstract

We study the influence of a perpendicular magnetic field with the asymptotics $B(r\to \infty)= B_0$ in a electrons in graphene. It is shown that the zero-energy solutions can exist only for one pseudospin direction, depending on the sign of the magnetic field in the infinite boundary. This, shows that zero-energy level is robust with respect to possible inhomogeneities of the magnetic field. In addition, we show that the number of the states with zero energy for one pseudospin projection is infinity. These results should be useful in the study of ripples which cause a scattering of Dirac particles in slowly decreasing magnetic fields where the asymptotic states is easy to define.