Despite topological protection and the absence of magnetic impurities, two-dimensional topological insulators display quantized conductance only in surprisingly short channels, which can be as short ...as 100 nm for atomically thin materials. We show that the combined action of short-range nonmagnetic impurities located near the edges and on site electron-electron interactions effectively creates noncollinear magnetic scatterers, and, hence, results in strong backscattering. The mechanism causes deviations from quantization even at zero temperature and for a modest strength of electron-electron interactions. Our theory provides a straightforward conceptual framework to explain experimental results, especially those in atomically thin crystals, plagued with short-range edge disorder.
The single-particle and many-body properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, particularly when the two layers are rotated ...relative to each other by a small angle (θ ≈ 1°), owing to the moiré potential induced by the twist. Here we probe the collective excitations of TBG with a spatial resolution of 20 nm, by applying mid-infrared near-field optical microscopy. We find a propagating plasmon mode in charge-neutral TBG for θ = 1.1−1.7°, which is different from the intraband plasmon in single-layer graphene. We interpret it as an interband plasmon associated with the optical transitions between minibands originating from the moiré superlattice. The details of the plasmon dispersion are directly related to the motion of electrons in the moiré superlattice and offer an insight into the physical properties of TBG, such as band nesting between the flat band and remote band, local interlayer coupling, and losses. We find a strongly reduced interlayer coupling in the regions with AA stacking, pointing at screening due to electron–electron interactions. Optical nano-imaging of TBG allows the spatial probing of interaction effects at the nanoscale and potentially elucidates the contribution of collective excitations to many-body ground states.Moiré potentials substantially alter the electronic properties of twisted bilayer graphene at a magic twist angle. A propagating plasmon mode, which can be observed with optical nano-imaging, is associated with transitions between the moiré minibands.
Present-day atomistic simulations generate long trajectories of ever more complex systems. Analyzing these data, discovering metastable states, and uncovering their nature are becoming increasingly ...challenging. In this paper, we first use the variational approach to conformation dynamics to discover the slowest dynamical modes of the simulations. This allows the different metastable states of the system to be located and organized hierarchically. The physical descriptors that characterize metastable states are discovered by means of a machine learning method. We show in the cases of two proteins, chignolin and bovine pancreatic trypsin inhibitor, how such analysis can be effortlessly performed in a matter of seconds. Another strength of our approach is that it can be applied to the analysis of both unbiased and biased simulations.
To realize the applicative potential of 2D twistronic devices, scalable synthesis and assembly techniques need to meet stringent requirements in terms of interface cleanness and twist-angle ...homogeneity. Here, we show that small-angle twisted bilayer graphene assembled from separated CVD-grown graphene single-crystals can ensure high-quality transport properties, determined by a device-scale-uniform moiré potential. Via low-temperature dual-gated magnetotransport, we demonstrate the hallmarks of a 2.4°-twisted superlattice, including tunable regimes of interlayer coupling, reduced Fermi velocity, large interlayer capacitance, and density-independent Brown-Zak oscillations. The observation of these moiré-induced electrical transport features establishes CVD-based twisted bilayer graphene as an alternative to “tear-and-stack” exfoliated flakes for fundamental studies, while serving as a proof-of-concept for future large-scale assembly.
Machine learning algorithms designed to learn dynamical systems from data can be used to forecast, control and interpret the observed dynamics. In this work we exemplify the use of one of such ...algorithms, namely Koopman operator learning, in the context of open quantum system dynamics. We will study the dynamics of a small spin chain coupled with dephasing gates and show how Koopman operator learning is an approach to efficiently learn not only the evolution of the density matrix, but also of every physical observable associated to the system. Finally, leveraging the spectral decomposition of the learned Koopman operator, we show how symmetries obeyed by the underlying dynamics can be inferred directly from data.
Policy Mirror Descent (PMD) is a powerful and theoretically sound methodology for sequential decision-making. However, it is not directly applicable to Reinforcement Learning (RL) due to the ...inaccessibility of explicit action-value functions. We address this challenge by introducing a novel approach based on learning a world model of the environment using conditional mean embeddings. We then leverage the operatorial formulation of RL to express the action-value function in terms of this quantity in closed form via matrix operations. Combining these estimators with PMD leads to POWR, a new RL algorithm for which we prove convergence rates to the global optimum. Preliminary experiments in finite and infinite state settings support the effectiveness of our method.
Interatomic potentials learned using machine learning methods have been successfully applied to atomistic simulations. However, accurate models require large training datasets, while generating ...reference calculations is computationally demanding. To bypass this difficulty, we propose a transfer learning algorithm that leverages the ability of graph neural networks (GNNs) to represent chemical environments together with kernel mean embeddings. We extract a feature map from GNNs pre-trained on the OC20 dataset and use it to learn the potential energy surface from system-specific datasets of catalytic processes. Our method is further enhanced by incorporating into the kernel the chemical species information, resulting in improved performance and interpretability. We test our approach on a series of realistic datasets of increasing complexity, showing excellent generalization and transferability performance, and improving on methods that rely on GNNs or ridge regression alone, as well as similar fine-tuning approaches.
We present and analyze an algorithm designed for addressing vector-valued
regression problems involving possibly infinite-dimensional input and output
spaces. The algorithm is a randomized adaptation ...of reduced rank regression, a
technique to optimally learn a low-rank vector-valued function (i.e. an
operator) between sampled data via regularized empirical risk minimization with
rank constraints. We propose Gaussian sketching techniques both for the primal
and dual optimization objectives, yielding Randomized Reduced Rank Regression
(R4) estimators that are efficient and accurate. For each of our R4 algorithms
we prove that the resulting regularized empirical risk is, in expectation
w.r.t. randomness of a sketch, arbitrarily close to the optimal value when
hyper-parameteres are properly tuned. Numerical expreriments illustrate the
tightness of our bounds and show advantages in two distinct scenarios: (i)
solving a vector-valued regression problem using synthetic and large-scale
neuroscience datasets, and (ii) regressing the Koopman operator of a nonlinear
stochastic dynamical system.
We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve ...any initial distribution of the state forward in time, and we investigate how estimators of these operators perform on long-term forecasting. Motivated by the observation that standard estimators may fail at this task, we introduce a learning paradigm that neatly combines classical techniques of eigenvalue deflation from operator theory and feature centering from statistics. This paradigm applies to any operator estimator based on empirical risk minimization, making them satisfy learning bounds which hold uniformly on the entire trajectory of future distributions, and abide to the conservation of mass for each of the forecasted distributions. Numerical experiments illustrates the advantages of our approach in practice.
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