Machine learned environment-dependent corrections for a empirical tight-binding basis

Empirical tight-binding (ETB) methods have become a common choice to simulate electronic and transport properties for systems composed of thousands of atoms. However, their performance is profoundly dependent on the way the empirical parameters were fitted, and the found parametrizations often exhibit poor transferability. In order to mitigate some of the the criticalities of this method, we introduce a novel Δ-learning scheme, called MLΔTB. After being trained on a custom data set composed of ab-initio band structures, the framework is able to correlate the local atomistic environment to a correction on the on-site ETB parameters, for each atom in the system. The converged algorithm is applied to simulate the electronic properties of random GaAsSb alloys, and displays remarkable agreement both with experimental and ab-initio test data. Some noteworthy characteristics of MLΔTB include the ability to be trained on few instances, to be applied on 3D supercells of arbitrary size, to be rotationally invariant, and to predict physical properties that are not exhibited by the training set.