Emerging Zero Modes for Graphene in a Periodic Potential

TL;DR

This paper explores how a periodic potential in graphene creates new zero-energy states, leading to conductance resonances and unique wavefunction phases, confirmed through numerical solutions of the Dirac equation.

Contribution

It reveals the emergence of zero-energy states in graphene under a cosine potential, linking wavefunction phases to classical periodic solutions, and confirms these states numerically.

Findings

New zero-energy states appear at specific potential strengths.

Conductance resonances are associated with these induced Dirac points.

Wavefunction phases relate to classical periodic solutions.

Abstract

We investigate the effect of a periodic potential on the electronic states and conductance of graphene. It is demonstrated that for a cosine potential $V(x)=V_0\cos(G_0x)$, new zero energy states emerge whenever $J_0(\frac {2V_0}{\hbar v_F G_0})=0$. The phase of the wavefunctions of these states is shown to be related to periodic solutions of the equation of motion of an overdamped particle in a periodic potential, subject to a periodic force. Numerical solutions of the Dirac equation confirm the existence of these states, and demonstrate the chirality of states in their vicinity. Conductance resonances are shown to accompany the emergence of these induced Dirac points.