Optimal traps in graphene

TL;DR

This paper develops a method to identify optimal electrostatic traps in graphene by transforming the Dirac-Weyl equation into a phase shift equation, revealing zero-energy bound states that impact scattering and resistivity.

Contribution

It introduces a novel approach using the variable phase method to find zero-energy bound states in graphene, proposing optimal traps to control chiral tunneling effects.

Findings

Zero-energy bound states occur at critical potential strengths.

Zero angular momentum states dominate scattering near the Dirac point.

Optimal traps can potentially be used to manipulate electronic properties in graphene.

Abstract

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us to utilize the Levinson Theorem to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads to us posit the use of `optimal traps' to combat the chiral tunneling found in graphene, which could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find the zero angular momentum states create a dominant peak in scattering cross-section as energy tends towards the Dirac point energy, suggesting a dominant contribution to resistivity.