Numerical methods for quantum transport simulation in condensed matter: a review

by Virginia Greco

A detailed review of computational techniques for studying electronic transport in complex materials or devices has been just published in Physics Reports. The paper describes, in particular, numerical implementations of the Kubo formula for the electrical conductivity in quantum systems and various applications. This work was led by ICREA Prof. Stephan Roche, head of the ICN2 Theoretical and Computational Nanoscience group.

Computational modeling is a thriving field of research, which boomed over the last two decades. Extremely useful calculation tools have been developed that allow simulating complex systems and predicting results of experiments, which is relevant to guide research and support the real measurements interpretation. In the field of condensed matter physics, the study of materials and devices relies largely on these simulation aids to investigate relevant properties, such as electron (or charge carrier) transport.

Structures of many millions or billions of atoms have to be considered, so both an accurate description of the system and efficient numerical methods are needed to perform such simulations, which also require high data processing capacity. Several approaches are used for simulating electronic transport, based on theoretical descriptions of the involved phenomena. Among them are the Kubo formula —named after the Japanese mathematical physicist who introduced it in 1957— and its various derivations (Kubo-Bastin and Kubo-Greenwood formulas).

A paper just published in Physics Reports provides a thorough review of the numerical implementations of the Kubo formula for the electrical conductivity and of the most efficient algorithms for studying electronic transport in complex forms of disordered materials. This work was led by ICREA Prof. Stephan Roche, head of the ICN2 Theoretical and Computational Nanoscience group, and involved members of Prof. Roche’s group and colleagues from Bohai University (China), Varian Medical Systems (Finland), the National Autonomous University of Mexico (UNAM) and the Technical University of Munich (Germany).

The numerical methods based on the Kubo formula are used to analyze low-dimensional materials and devices, where quantum effects —which become relevant at very small scales— cannot be disregarded. They are largely employed to simulate structures such as graphene and other 2D materials, organic semiconductors, carbon nanotubes, and topological insulators. Examples of many of these applications are provided in the review, showing the good predictive power of this approach.

The authors describe the different techniques highlighting their pros and cons, in particular in terms of accuracy and computational cost. The extension of their use to calculate other important properties of these materials, such as spin and Hall transport coefficients in a variety of transport regimes, is also covered. Given the fundamental role played nowadays by these methods in the study of quantum transport in complex systems, this review can prove a valuable source for researchers using or developing numerical simulation tools.

The authors of this review are also responsible for the recent launch of a new flagship initiative, called LSQuant, dedicated to promoting large-scale quantum transport methodologies that have demonstrated remarkable predictive power. LSQuant will initiate and promote a series of activities aimed at enlarging the user and developer community, enhancing international networking, engaging young researchers and connecting new developments to technology challenges of global concern.

Reference article:

Zheyong Fan, José H. Garcia, Aron W. Cummings, Jose Eduardo Barrios-Vargas, Michel Panhans, Ari Harju, Frank Ortmann, Stephan Roche, Linear scaling quantum transport methodologies, Physics Reports, Volume 903, 2021. DOI:10.1016/j.physrep.2020.12.001