Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space

TL;DR

This paper compares quantum and classical approaches to electronic transport in deformed graphene, demonstrating their agreement and introducing a geometric method to predict transport phenomena in complex nanostructures.

Contribution

It establishes a connection between quantum Green's function methods and classical trajectories in curved space for graphene, simplifying complex calculations.

Findings

Good numerical agreement between quantum and classical models

Geometric approach reduces computational complexity

Curvature and pseudo-magnetic fields enable novel transport effects

Abstract

In this work we compare two fundamentally different approaches to the electronic transport in deformed graphene: a) the condensed matter approach in which current flow paths are obtained by applying the non-equilibrium Green's function (NEGF) method to the tight-binding model with local strain, b) the general relativistic approach in which classical trajectories of relativistic point particles moving in a curved surface with a pseudo-magnetic field are calculated. The connection between the two is established in the long-wave limit via an effective Dirac Hamiltonian in curved space. Geometrical optics approximation, applied to focused current beams, allows us to directly compare the wave and the particle pictures. We obtain very good numerical agreement between the quantum and the classical approaches for a fairly wide set of parameters, improving with the increasing size of the system. The presented method offers an enormous reduction of complexity from irregular tight-binding Hamiltonians defined on large lattices to geometric language for curved continuous surfaces. It facilitates a comfortable and efficient tool for predicting electronic transport properties in graphene nanostructures with complicated geometries. Combination of the curvature and the pseudo-magnetic field paves the way to new interesting transport phenomena such as bending or focusing (lensing) of currents depending on the shape of the deformation. It can be applied in designing ultrasensitive sensors or in nanoelectronics.