This five-day online school will focus on the field of theoretical condensed matter electronic transport exploiting the non-equilibrium Green’s function approach. In particular, recent advances in transport theory [1] will be presented in the form of lectures and hands-on sessions on hot topics in the field. The teachers will present novel methods used for materials research modelling. The participants will learn the advanced features of SIESTA [2], such as the calculations of non-equilibrium properties using the TranSIESTA/TBtrans approach and the python framework SISL [3]. For example, the school lectures will cover a recent scheme introducing truly single-junction transport calculations [4] and the new implementations to include in the transport calculations different corrections to the Hamiltonian accounting for electron-phonon coupling [5], spin orbit coupling and electronic correlation. Moreover, the users will learn how to extract a tight-binding Hamiltonian from a DFT Hamiltonian allowing them to deal with very large systems [6,7].

The lectures will take place via Zoom with an invited list of speakers who will present their work in a variety of fields in which the covered tools have been used. Each topic will be followed by a hands-on session allowing participants first-hand experience with the tools and analysis.

While this is an open workshop (for everybody!), we ask participants to sign-up due to content distribution prior to the workshop itself.

The workshop will also host 2 evenings with online poster sessions, and all participants are expected to present their research in one of the two sessions.

The deadline for the abstract submission is April 1^th.

Provisional program

Day 1: Introduction to NEGF theory and hands-on with TBtrans, TranSiesta and SISL

Day 2: DFT-TB parametrization and surrounding real space self-energies, evening poster session

Day 3: Topological insulators and inelastic transport mechanisms, evening poster session

Day 4: Electrochemistry and electron correlation in graphene nano structures

Day 5: Solution to participant projects and ad-hoc follow up questions

Up to one month before the school, participants are invited to submit project suggestions (for the last day of the school) via this GitHub repository (please do so ASAP!) submit project suggestion here.

We invite everybody to join the online school (link will follow) and all material will be made available at https://github.com/zerothi/ts-tbt-sisl-tutorial

Detailed School Topics:

Advanced usage of SIESTA, TranSIESTA/TBtrans and sisl

Participants will learn how to use the advanced features implemented in the aforementioned code and python framework. In particular students will be taught how to perform efficient DFT+NEGF calculations, pre-processing, post-processing analysis and data visualization.

Electrochemistry

First principles simulations are now crucial in many areas of materials science. However, this has not yet reached the field of electrochemistry, where the complexity of the electrochemical environment and the presence of the external electrode potential are difficulties that have precluded direct application of the usual first-principles methods like DFT. We will explain how some of these problems, like the presence of the electrostatic potential, can be tackled using TranSIESTA.

Topological Insulators

Topological insulators (TI) are a phase of matter characterized by a bulk energy gap and conducting surface (or edge) states symmetry-protected against small perturbations. Quantum transport simulations are crucial to compute and validate the topological properties of materials. We will show how SIESTA can be used to predict the essential features of topological materials, leveraging on the recent Spin-Orbit Coupling implementation and SISL.

Inelastic transport

The modelling of inelastic effects due to the electron-phonon coupling in nano-scale devices is of great technological importance as it impacts both the transport properties and Joule heating. It is especially challenging to include the effects in large-scale atomistic first principles device simulations. We will discuss how this can be addressed using various approximations and introduce the Inelastica package (https://github.com/tfrederiksen/inelastica/) based on TranSIESTA.

Correlated systems and the meanfield Hubbard model

Coulomb repulsion between electrons can lead to unpaired electron states and interesting spin structures. For graphene-like nanostructures the meanfield Hubbard model provides a simple and, yet, often sufficient method to understand how electronic interactions lead to magnetism. We will describe an implementation of this model based on SISL.

Single contacts by removal of periodic images

Understanding transport properties under non-equilibrium is of vital importance to the development of next-generation electronics. A basic principle of conducting such simulations is by using Bloch’s theorem which has the disadvantage of adding a periodic image of the junction. We will present how users can overcome this limitation and simulate truly single junctions.

Modelling of extremely large-systems with DFT precision

Recent increase in compute power is rapidly decreasing the gap between experimental and theoretical works. This allows theoreticians to study one-to-one samples matching an exact experiment. However, there is still some way to go in terms of scalability and precision. Here we present a method to extract the important part of a Hamiltonian in an energy window allowing simulations of transport properties of even larger systems by retaining the band-structure without using any wannierization techniques.

Lecturers

Gaetano Calogero, Institute for Microelectronics and Microsystems, Catania (CNR)

Thomas Frederiksen (DIPC - Donostia International Physics Center)

P. Khomyakov (Synopsis)

Pablo Ordejon (Institut Català de Nanociéncia i Nanotecnologia - ICN2)

Nick Papior (Technical University of Denmark)

Sofia Sanz, Donostia International Physics Center (DiPC)

Zeila Zanolli (Utrecht University)

Tutors

Jonas Bertelsen (Technical University of Denmark, Lyngby)

Ernane de Freitas Martins, Institut Català de Nanociència i Nanotecnologia/Royal Melbourne Institute of Technology (ICN2/RMIT)

Pol Febrer, Institut Català de Nanociència i Nanotecnologia (ICN2)

Aleksander Lorentzen (Technical University of Denmark, Lyngby)

Nils Wittemeier, Institut Català de Nanociència i Nanotecnologia (ICN2)