Efficient simulations with electronic open boundaries

TL;DR

This paper introduces a reformulated Hairy Probe method for electronic open boundaries suitable for steady state calculations with non-orthogonal basis sets, demonstrating its effectiveness on atomic chains and graphene contacts.

Contribution

The paper presents a new formulation of the Hairy Probe method tailored for non-orthogonal basis sets, enabling accurate steady state electronic transport simulations.

Findings

Conductance of atomic chains is exactly one quantum unit.

Potential in Cu chains is uniform away from probes and exponentially varies near them.

Graphene contacts show about two quantum units of conductance, with weak current through benzene due to disrupted conjugation.

Abstract

We present a reformulation of the Hairy Probe method for introducing electronic open boundaries that is appropriate for steady state calculations involving non-orthogonal atomic basis sets. As a check on the correctness of the method we investigate a perfect atomic wire of Cu atoms, and a perfect non-orthogonal chain of H atoms. For both atom chains we find that the conductance has a value of exactly one quantum unit, and that this is rather insensitive to the strength of coupling of the probes to the system, provided values of the coupling are of the same order as the mean inter-level spacing of the system without probes. For the Cu atom chain we find in addition that away from the regions with probes attached, the potential in the wire is uniform, while within them it follows a predicted exponential variation with position. We then apply the method to an initial investigation of the suitability of graphene as a contact material for molecular electronics. We perform calculations on a carbon nanoribbon to determine the correct coupling strength of the probes to the graphene, and obtain a conductance of about two quantum units corresponding to two bands crossing the Fermi surface. We then compute the current through a benzene molecule attached to two graphene contacts and find only a very weak current because of the disruption of the $\pi$-conjugation by the covalent bond between the benzene and the graphene. In all cases we find that very strong or weak probe couplings suppress the current.