Bloch oscillations in two-dimensional crystals: Inverse problem

Abstract

Within an artificial neural network (ANN) approach, we classify simulated signals corresponding to the semi-classical description of Bloch oscillations on a two-dimensional square lattice. After the ANN is properly trained, we consider the inverse problem of Bloch oscillations (BO) in which a new signal is classified according to the lattice spacing and external electric field strength oriented along a particular direction of the lattice with an accuracy of 96%. This approach can be improved depending on the time spent in training the network and the computational power available. This work is one of the first efforts for analyzing the BO with ANN in two-dimensional crystals.

Study of simulated Bloch oscillations in strained graphene using neural networks

“…It is worth to mention that as the errors in the predictions decrease, also the efficiency in the classification decreases, as we will illustrated in the next section. This numerical approach, where simulations are generated and classifications are studied considering different values for the parameters and the number of classes,was previously used in [28,29,30] where are studied Bloch oscillations in simpler physical systems.…”

“…All these observations make it relevant to study this phenomenon beyond solids. In this connection the inverse problem of BO has already been addressed by our group for the linear chain [28], the 2D square lattice [29] and pristine graphene [30] through an Artificial Neural Networks (ANN) approach. In this article we extend and generalize these findings to the case of graphene under uniaxial strain.…”

Bloch oscillations in graphene from an artificial neural network study

“…Therefore, the result is a time series for both electron velocities (v x and v y ). The signals time lapse depends on the frequency of them, since for higher frequencies, a larger sampling is required to describe the BO signals appropriately, in terms of precision and available computational resources, as we have already analyzed in [27]. With this in mind, both time series (v x and v y ), have been discretized into 100 values each, that work as the input data for the ANN.…”

“…On each scenario, the ANN has been trained with a supervised learning algorithm, which means that we need to specify the corresponding targets, i.e, the electric field employed to create the signals. Similarly to the work done in [27], the ANN works as a classifier. This 4 means that the outputs of the ANN are associated with classes, defining different ranges of the electric field used to generate the BO signal.…”

“…Therefore, there is an obvious relevance in the study of such systems that goes beyond solids. The inverse problem of BO has already been addressed by our group for crystal structures in one and two dimensions, categorizing simulated signals of BO via an Artificial Neural Networks (ANN) approach [26,27]. These works give confidence enough to implement ANNs in more complex systems such as the one reviewed here, namely a Dirac-Weyl material.…”