Simulating electron wave dynamics in graphene superlattices exploiting parallel processing advantages

Abstract

This work introduces a parallel computing framework to characterize the propagation of electron waves in graphene-based nanostructures. The electron wave dynamics is modeled using both “microscopic” and effective medium formalisms and the numerical solution of the two-dimensional massless Dirac equation is determined using a Finite-Difference Time-Domain scheme. The propagation of electron waves in graphene superlattices with localized scattering centers is studied, and the role of the symmetry of the microscopic potential in the electron velocity is discussed. The computational methodologies target the parallel capabilities of heterogeneous multi-core CPU and multi-GPU environments and are built with the OpenCL parallel programming framework which provides a portable, vendor agnostic and high throughput-performance solution. The proposed heterogeneous multi-GPU implementation achieves speedup ratios up to 75x when compared to multi-thread and multi-core CPU execution, reducing simulation times from several hours to a couple of minutes. Program summaryProgram title: GslSim.Program Files doi:http://dx.doi.org/10.17632/prmfv63nj6.1Licensing provisions: GPLv3.Programming language: C, OpenCL and Matlab for results analysis.Nature of problem: Computing the time evolution of electron waves in graphene superlattices is a time consuming process due to the high number of necessary nodes to discretize the spatial and time domains.Solution method: We develop a simulator based on the C/OpenCL standards to study the time evolution of electron waves in graphene superlattices by exploiting hardware architectures such as graphics processing units (GPUs) to speedup the computation of the pseudospinor.