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Quantum computing architectures require an accurate and efficient description in terms of many-electron states. Recent implementations include quantum dot arrays, where the ground state of a multi q-bit system can be altered by voltages applied to the top gates. An extensive investigation concerning the spectra of the many-electron systems under multiple operation conditions set by external voltages typically requires a relatively large number of Hamiltonian diagonalizations, where the Coulomb interaction is considered in an exact manner. Instead of making exhaustive calculations using high throughput computing, we approach this problem by augmenting numerical diagonalizations with machine learning techniques designed to predict the many-electron eigenvalues and eigenfunctions. To this end, we employ and compare the results from linear regression methods such as multivariate least squares (MLS) as well as non-linear techniques based on kernel ridge regression (KRR), Gaussian process regression (GPR) and artificial neural networks (ANNs). The input feature vectors are assembled from readily available information comprised from a binary representation of the potential and the strength of the Coulomb interaction. Furthermore, employing a linear classifier, we establish a rule for detecting a singlet-triplet transition which may arise for certain potential configurations., Comment: 15 pages, 6 figures

In contrast to monolayer graphene, in bilayer graphene (BLG) one can induce a tunable bandgap by applying an external electric field, which makes it suitable for field effect applications. Extrinsic doping of BLGs enriches the electronic properties of the graphene-based family, as their behavior can be switched from an intrinsic small-gap semiconductor to a degenerate semiconductor. In the framework of density functional theory (DFT) calculations, we investigate the electronic and thermoelectric properties of BLGs doped with extrinsic impurities from groups III (B, Al, Ga), IV (Si, Ge) and V (N, P, As), in the context of applied external electric fields. Doping one monolayer of the BLG with p- or n-type dopants results in a degenerate semiconductor, where the Fermi energy depends on the type of the impurity, but also on the magnitude and orientation of the electric field, which modifies the effective doping concentration. Doping one layer with isoelectronic species like Si and Ge opens a gap, which may be closed upon applying an electric field, in contrast to the pristine BLG. Furthermore, dual doping by III-V elements, in a way that the BLG system is formed by one n-type and one p-type graphene monolayer, leads to intrinsic semiconductor properties with relatively large energy gaps. Si-Si and Ge-Ge substitutions render a metallic like behavior at zero field similar to the standard BLG, however with an asymmetric density of states in the vicinity of the Fermi energy. We analyze the suitability of the highly doped BLG materials for thermoelectric applications, exploiting the large asymmetries of the density of states. In addition, a sign change in the Seebeck coefficient is observed by tuning the electric field as a signature of narrow bands near the Fermi level., Comment: 10 pages, 10 figures

The electronic properties graphene nanoflakes (GNFs) with embedded hexagonal boron nitride (hBN) domains are investigated by combined {\it ab initio} density functional theory calculations and machine learning techniques. The energy gaps of the quasi-0D graphene based systems, defined as the differences between LUMO and HOMO energies, depend on the sizes of the hBN domains relative to the size of the pristine graphene nanoflake, but also on the position of the hBN domain. The range of the energy gaps for different configurations is increasing as the hBN domains get larger. We develop two artificial neural network (ANN) models able to reproduce the gap energies with high accuracies and investigate the tunability of the energy gap, by considering a set of GNFs with embedded rectangular hBN domains. In one ANN model, the input is in one-to-one correspondence with the atoms in the GNF, while in the second model the inputs account for basic structures in the GNF, allowing potential use in up-scaled structures. We perform a statistical analysis over different configurations of ANNs to optimize the network structure. The trained ANNs provide a correlation between the atomic system configuration and the magnitude of the energy gaps, which may be regarded as an efficient tool for optimizing the design of nanostructured graphene based materials for specific electronic properties., Comment: 6 pages, 5 figures

Unlike single layer graphene, in the case of $AB$-stacked bilayer graphene (BLG) one can induce a non-zero energy gap by breaking the inversion symmetry between the two layers using a perpendicular electric field. This is an essential requirement in field-effect applications, particularly since the induced gap in BLG systems can be further tuned by the magnitude of the external electric field. Doping is another way to modify the electronic properties of graphene based systems. We investigate here BLG systems doped with boron and nitrogen in the presence of external electric field, in the framework of density functional theory (DFT) calculations. Highly doped BLG systems are known to behave as degenerate semiconductors, where the Fermi energy depends on the doping concentration but, in addition, we show that the electronic properties drastically depend also on the applied electric field. By changing the magnitude and the orientation of the electric field, the gap size and position relative to the Fermi level may be tuned, essentially controlling the effect of the extrinsic doping. In this context, we discuss in how far the external electric field may suitably adjust the effective doping and, implicitly, the conduction properties of doped BLG systems., Comment: 10 pages, 13 figures

Inspired by the problem of elastic wave scattering on wrinkled interfaces, we studied the scattering of ballistic electrons on a wrinkled potential energy region. The electron transmission coefficient depends on both wrinkle amplitude and periodicity, having different behaviors for positive and negative scattering potential energies. For scattering on potential barriers, minibands appear in electron transmission, as in superlattices, whereas for scattering on periodic potential wells the transmission coefficient has a more complex form. Besides suggesting that tuning of electron transmission is possible by modifying the scattering potential via voltages on wrinkled gate electrodes, our results emphasize the analogies between ballistic electrons and elastic waves even in scattering problems on non-typical configurations.

The principle characteristics of biased greedy random walks (BGRWs) on two-dimensional lattices with real-valued quenched disorder on the lattice edges are studied. Here, the disorder allows for negative edge-weights. In previous studies, considering the negative-weight percolation (NWP) problem, this was shown to change the universality class of the existing, static percolation transition. In the presented study, four different types of BGRWs and an algorithm based on the ant colony optimization (ACO) heuristic were considered. Regarding the BGRWs, the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters: a disorder parameter rho that controls the amount of negative edge weights on the lattice and a bias strength B that governs the drift of the walkers along a certain lattice direction. Here, the pivotal observable is the probability that, after termination, a lattice walk exhibits a total negative weight, which is here considered as percolating. The behavior of this observable as function of rho for different bias strengths B is put under scrutiny. Upon tuning rho, the probability to find such a feasible lattice walk increases from zero to one. This is the key feature of the percolation transition in the NWP model. Here, we address the question how well the transition point rho_c, resulting from numerically exact and "static" simulations in terms of the NWP model can be resolved using simple dynamic algorithms that have only local information available, one of the basic questions in the physics of glassy systems., Comment: 14 pages, 7 figures