Smooth electron waveguides in graphene

TL;DR

This paper analytically solves for zero-energy modes of Dirac fermions in smooth potential wells in graphene, revealing a threshold for mode appearance and proposing an experimental setup for observation, with implications for graphene device design.

Contribution

It provides exact analytical solutions for zero-energy modes in smooth potentials in graphene and establishes a threshold condition for mode emergence, which is novel compared to non-relativistic cases.

Findings

Existence of a threshold potential strength for mode appearance.

Derived a relationship between potential strength and number of modes.

Proposed experimental setup for observing these modes.

Abstract

We present exact analytical solutions for the zero-energy modes of two-dimensional massless Dirac fermions fully confined within a smooth one-dimensional potential V(x)= - {\alpha}/cosh({\beta}x), which provides a good fit for potential profiles of existing top-gated graphene structures. We show that there is a threshold value of the characteristic potential strength {\alpha}/{\beta} for which the first mode appears, in striking contrast to the non-relativistic case. A simple relationship between the characteristic strength and the number of modes within the potential is found. An experimental setup is proposed for the observation of these modes. The proposed geometry could be utilized in future graphene-based devices with high on/off current ratios.