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The energy gap of Bernal-stacked bilayer graphene can be tuned by applying a perpendicular electric field. The origin of this gap can be traced down to the breaking of its inversion symmetry by an onsite potential difference between the layers. This degree of tunability makes bilayer graphene a perfect playground for the study of the effects of electric fields, such as the crystalline field, which are developed when layers of other materials are deposited on top of it. Here, we introduce a novel device architecture allowing a simultaneous control over the applied displacement field and the crystalline alignment between two materials. Our experimental and numerical results confirm that the crystal field and electrostatic doping due to the interface reflect the 120$^{\circ}$ symmetry of the bilayer graphene/BN heterostructure and are highly affected by the commensurate state. These results provide an unique insight into the role of the twist angle in the development of internal crystal fields and intrinsic electrostatic doping in heterostructures. Our results highligth the importance of layer alignment, beyond the existence of a moir\'e superlattice, to understand and simulate the intrinsic properties of a van der Waal heterostructure.

Let $\mu$ be a positive measure supported on a domain $\Omega$. We consider the behavior of the balayage measure $\nu:=\mathrm{Bal}(\mu,\partial \Omega)$ near a point $z_{0}\in \partial \Omega$ at which $\Omega$ has an outward-pointing cusp. Assuming that the order and coefficient of tangency of the cusp are $d>0$ and $a>0$, respectively, and that $d\mu(z) \asymp |z-z_{0}|^{2b-2}d^{2}z$ as $z\to z_0$ for some $b > 0$, we obtain the leading order term of $\nu$ near $z_{0}$. This leading term is universal in the sense that it only depends on $d$, $a$, and $b$. We also treat the case when the domain has multiple corners and cusps at the same point. Finally, we obtain an explicit expression for the balayage of the uniform measure on the tacnodal region between two osculating circles, and we give an application of this result to two-dimensional Coulomb gases., Comment: 30 pages, 6 figures

Deep learning models for plant species identification rely on large annotated datasets. The PlantNet system enables global data collection by allowing users to upload and annotate plant observations, leading to noisy labels due to diverse user skills. Achieving consensus is crucial for training, but the vast scale of collected data makes traditional label aggregation strategies challenging. Existing methods either retain all observations, resulting in noisy training data or selectively keep those with sufficient votes, discarding valuable information. Additionally, as many species are rarely observed, user expertise can not be evaluated as an inter-user agreement: otherwise, botanical experts would have a lower weight in the AI training step than the average user. Our proposed label aggregation strategy aims to cooperatively train plant identification AI models. This strategy estimates user expertise as a trust score per user based on their ability to identify plant species from crowdsourced data. The trust score is recursively estimated from correctly identified species given the current estimated labels. This interpretable score exploits botanical experts' knowledge and the heterogeneity of users. Subsequently, our strategy removes unreliable observations but retains those with limited trusted annotations, unlike other approaches. We evaluate PlantNet's strategy on a released large subset of the PlantNet database focused on European flora, comprising over 6M observations and 800K users. We demonstrate that estimating users' skills based on the diversity of their expertise enhances labeling performance. Our findings emphasize the synergy of human annotation and data filtering in improving AI performance for a refined dataset. We explore incorporating AI-based votes alongside human input. This can further enhance human-AI interactions to detect unreliable observations.

We present a numerical scheme for the solution of the initial-value problem for the ``bad'' Boussinesq equation. The accuracy of the scheme is tested by comparison with exact soliton solutions as well as with recently obtained asymptotic formulas for the solution., Comment: 21 pages, 15 figures

The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been developed accordingly to optimize their computation cost. In particular, recursive techniques have been efficiently applied within the Green's function calculation approach. Recently, with the discovery of Moir\'e materials, several attractive superlattices have been explored using these recursive Green's function techniques. However, numerical difficulty issues were reported as most of these superlattices have relatively large supercells, and consequently a huge number of atoms to be considered. In this article, improvements to solve these issues are proposed in order to keep optimizing the recursive Green's function calculations. These improvements make the electronic structure calculations feasible and efficient in modelling large superlattice-based devices. As an illustrative example, twisted bilayer graphene superlattices are computed and presented to demonstrate the efficiency of the method., Comment: 33 pages, 10 figures

Nanomechanical measurements of minimally twisted van der Waals materials remained elusive despite their fundamental importance for device realisation. Here, we use Ultrasonic Force Microscopy (UFM) to locally quantify the variation of out-of-plane Young's modulus in minimally twisted double bilayer graphene (TDBG). We reveal a softening of the Young's modulus by 7\% and 17\% along single and double domain walls, respectively. Our experimental results are confirmed by force-field relaxation models. This study highlights the strong tunability of nanomechanical properties in engineered twisted materials, and paves the way for future applications of designer 2D nanomechanical systems.

We study blow-up solutions of the ``bad" Boussinesq equation, and prove that a wide range of asymptotic scenarios can happen. For example, for each $T>0$, $x_{0}\in \mathbb{R}$ and $\delta \in (0,1)$, we prove that there exist Schwartz class solutions $u(x,t)$ on $\mathbb{R} \times [0,T)$ such that $|u(x,t)| \leq C \frac{1+x^{2}}{(x-x_{0})^{2}}$ and $u(x_{0},t)\asymp (T-t)^{-\delta}$ as $t\to T$. We also prove that for any $q\in \mathbb{N}$, $T>0$, $x_{0}\in \mathbb{R}$, $\delta \in (0,\frac{1}{2})$, there exist Schwartz class solutions $u(x,t)$ on $\mathbb{R} \times [0,T)$ such that (i) $|\partial_{x}^{q_{1}}\partial_{t}^{q_{2}}u(x,t)|\leq C$ for each $q_{1},q_{2}\in \mathbb{N}$ such that $q_{1}+2q_{2}\leq q$, (ii) $|\partial_{x}^{q_{1}}\partial_{t}^{q_{2}}u(x,t)| \leq C \frac{1+|x|}{|x-x_{0}|}$ for each $q_{1},q_{2}\in \mathbb{N}$ such that $q_{1}+2q_{2}= q+1$, (iii) $|\partial_{x}^{q_{1}}\partial_{t}^{q_{2}}u(x_{0},t)| \asymp (T-t)^{-\delta}$ as $t\to T$ for each $q_{1},q_{2}\in \mathbb{N}$ such that $q_{1}+2q_{2}= q+1$. In particular, when $q=0$, this result establishes the existence of wave-breaking solutions, i.e. solutions that remain bounded but whose $x$-derivative blows up in finite time., Comment: 31 pages, 1 figure

Emerging two-dimensional (2D) materials bring unprecedented opportunities for electronic applications. The design of high-performance devices requires an accurate prediction of carrier mobility in 2D materials, which can be obtained using state-of-the-art $ab~initio$ calculations. However, various factors impact the computational accuracy, leading to contradictory estimations for the mobility. In this work, targeting accurate and efficient $ab~initio$ calculations, transport properties in III-V monolayers are reported using the Boltzmann transport equation, and the influences of pseudopotential, quadrupole correction, Berry connection, and spin-orbit coupling (SOC) on mobilities are systematically investigated. Our findings are as follows: (1) The inclusion of semi-core states in pseudopotentials is important to obtain accurate calculations. (2) The variations induced by dynamical quadrupole and Berry connection when treating long range fields can be respectively 40% and 10%. (3) The impact of SOC can reach up to 100% for materials with multi-peak bands. Importantly, although SOC notably modifies the electronic wavefunctions, it negligibly impacts the dynamical matrices and scattering potential variations. As a result, the combination of fully-relativistic electron calculation and scalar-relativistic phonon calculation can strike a good balance between accuracy and cost. This work compares computational methodologies, providing guidelines for accurate and efficient calculations of mobilities in 2D semiconductors., Comment: 11 pages, 15 figures

Graphene has been widely studied for various applications due to its outstanding electrical and mechanical properties. However, its potential in thermoelectric applications has been limited by a low Seebeck coefficient and high thermal conductivity. Efforts to enhance its thermoelectric properties have involved the usage of carbon-based nanoribbons, strain engineering, and heteroatom co-doping, particularly with Nitrogen and/or Boron atoms. In this work, multiscale simulation approaches combining DFT calculations and semi-empirical models are used to explore the potential improvement of the thermoelectric properties via borazine (B$_3$N$_3$)-ring doping. As bandgap engineering can be obtained with this doping, the thermoelectric properties of graphene are significantly enlarged, albeit at the cost of reduced conductance. The effects observed are not only dependent on the concentration of BN within the graphene lattice but are also notably influenced by the relative rotational alignment of the BN rings. Furthermore, the effect of the distribution and rotational disorder are considered, showing reduced electronic conductance compared to the periodic case highlighting the importance of precise control over the doping parameters of BN-ring. Lastly, the thermal lattice conductance is estimated revealing a substantial reduction of up to 40$\%$ compared to pristine graphene opening up the possibility of enhancing the thermoelectric efficiency of BNC materials. The present theoretical approach highlights how BN-ring doping can refine the thermoelectric properties of 2D graphene, offering a pathway for enhancing its suitability in practical thermoelectric applications.

A new and extensive formalism is developed for monads and galaxies in non-standard enlargements. It is shown that monads and galaxies can be manipulated using order-preserving and order-reversing set-to-set maps, and that set properties associated with these maps can be extended not only to internal sets but to all monads and galaxies. An abstract theory of Intersections of Galaxies is introduced. These concepts are applied to basic topology as well (locally convex) topological vector spaces, their various properties and completions, allowing these to be effortlessly defined and characterized. Duality theory is studied in this framework, allowing in particular to formulate new brief and insightful proofs for the theorems of Mackey-Arens and Grothendieck completeness without any technicalities.

We report a theoretical study of dielectric properties of models of amorphous Boron Nitride, using interatomic potentials generated by machine learning. We first perform first-principles simulations on small (about $100$ atoms in the periodic cell) sample sizes to explore the emergence of mid-gap states and its correlation with structural features. Next, by using a simplified tight-binding electronic model, we analyse the dielectric functions for complex three dimensional models (containing about $10.000$ atoms) embedding varying concentrations of ${\rm sp^{1}, sp^{2}}$ and ${\rm sp^3}$ bonds between B and N atoms. Within the limits of these methodologies, the resulting value of the zero-frequency dielectric constant is shown to be influenced by the population density of such mid-gap states and their localization characteristics. We observe nontrivial correlations between the structure-induced electronic fluctuations and the resulting dielectric constant values. Our findings are however just a first step in the quest of accessing fully accurate dielectric properties of as-grown amorphous BN of relevance for interconnect technologies and beyond., Comment: 27 pages, 10 figures

Flat bands in moir\'e systems are exciting new playgrounds for the generation and study of exotic many-body physics phenomena in low-dimensional materials. Such physics is attributed to the vanishing kinetic energy and strong spatial localization of the flat-band states. Here we use numerical simulations to examine the electronic transport properties of such flat bands in magic-angle twisted bilayer graphene in the presence of disorder. We find that while a conventional downscaling of the mean free path with increasing disorder strength occurs at higher energies, in the flat bands the mean free path can actually increase with increasing disorder strength.This phenomenon is also captured by the disorder-dependent quantum metric, which is directly linked to the ground state localization.This disorder-induced delocalization suggests that weak disorder may have a strong impact on the exotic physics of magic-angle bilayer graphene and other related moir\'e systems., Comment: Main text: 7 pages, 4 figures. Sup .Mat.: 4 pages, 2 figures

We study large $n$ expansions for the partition function of a Coulomb gas $$Z_n=\frac 1 {\pi^n}\int_{\mathbb{C}^n}\prod_{1\le i

We consider Cantor real numeration system as a frame in which every non-negative real number has a positional representation. The system is defined using a bi-infinite sequence $\Beta=(\beta_n)_{n\in\Z}$ of real numbers greater than one. We introduce the set of $\Beta$-integers and code the sequence of gaps between consecutive $\Beta$-integers by a symbolic sequence in general over the alphabet $\N$. We show that this sequence is $S$-adic. We focus on alternate base systems, where the sequence $\Beta$ of bases is periodic and characterize alternate bases $\Beta$, in which $\Beta$-integers can be coded using a symbolic sequence $v_{\Beta}$ over a finite alphabet. With these so-called Parry alternate bases we associate some substitutions and show that $v_\Beta$ is a fixed point of their composition. The paper generalizes results of Fabre and Burd\'ik et al.\ obtained for the R\'enyi numerations systems, i.e., in the case when the Cantor base $\Beta$ is a constant sequence.

We study hole probabilities of two-dimensional Coulomb gases with a general potential and arbitrary temperature. The hole region $U$ is assumed to satisfy $\partial U\subset S$, where $S$ is the support of the equilibrium measure $\mu$. Let $n$ be the number of points. As $n \to \infty$, we prove that the probability that no points lie in $U$ behaves like $\exp(-Cn^{2}+o(n^{2}))$. We determine $C$ in terms of $\mu$ and the balayage measure $\nu = \mathrm{Bal}(\mu|_{U},\partial U)$. If $U$ is unbounded, then $C$ also involves the Green function of $\Omega$ with pole at $\infty$, where $\Omega$ is the unbounded component of $U$. We also provide several examples where $\nu$ and $C$ admit explicit expressions: we consider several point processes, such as the elliptic Ginibre, Mittag-Leffler, and spherical point processes, and various hole regions, such as circular sectors, ellipses, rectangles, and the complement of an ellipse. This work generalizes previous results of Adhikari and Reddy in several directions., Comment: 93 pages, 20 figures

Hexagonal boron-nitride (h-BN) provides an ideal substrate for supporting graphene devices to achieve fascinating transport properties, such as Klein tunneling, electron optics and other novel quantum transport phenomena. However, depositing graphene on h-BN creates moir\'e superlattices, whose electronic properties can be significantly manipulated by controlling the lattice alignment between layers. In this work, the effects of these moir\'e structures on the transport properties of graphene are investigated using atomistic simulations. At large misalignment angles (leading to small moir\'e cells), the transport properties (most remarkably, Klein tunneling) of pristine graphene devices are conserved. On the other hand, in the nearly aligned cases, the moir\'e interaction induces stronger effects, significantly affecting electron transport in graphene. In particular, Klein tunneling is significantly degraded. In contrast, strong Fabry-P\'erot interference (accordingly, strong quantum confinement) effects and non-linear I-V characteristics are observed. P-N interface smoothness engineering is also considered, suggesting as a potential way to improve these transport features in graphene/h-BN devices., Comment: 21 pages, 8 figures, Supplementary materials

There has been extensive activity exploring the doping of semiconducting two-dimensional (2D) transition metal dichalcogenides in order to tune their electronic and magnetic properties. The outcome of doping depends on various factors, including the intrinsic properties of the host material, the nature of the dopants used, their spatial distribution as well as their interactions with other types of defects. A thorough atomic-level analysis is essential to fully understand these mechanisms. In this work, vanadium doped WSe$_2$ monolayer grown by molecular beam epitaxy is investigated using four-dimensional scanning transmission electron microscopy (4D-STEM). Through center of mass-based reconstruction, atomic scale maps are produced, allowing the visualization of both the electric field and the electrostatic potential around individual V atoms. To provide quantitative insights, these results are successfully compared with multislice image simulations based on ab initio calculations, accounting for lens aberrations. Finally, a negative charge around the V dopants is detected as a drop in the electrostatic potential, unambiguously demonstrating that 4D-STEM can be used to detect and to accurately analyze single dopant charge states in semiconducting 2D materials., Comment: 17 pages, 4 figures and Supporting Information

The conversion efficiency from charge current to spin current via spin Hall effect is evaluated by the spin Hall ratio (SHR). Through state-of-the-art $ab~initio$ calculations involving both charge conductivity and spin Hall conductivity, we report the SHRs of the III-V monolayer family, revealing an ultrahigh ratio of 0.58 in the hole-doped GaAs monolayer. In order to find more promising 2D materials, a descriptor for high SHR is proposed and applied to a high-throughput database, which provides the fully-relativistic band structures and Wannier Hamiltonians of 216 exfoliable monolayer semiconductors and has been released to the community. Among potential candidates for high SHR, the MXene monolayer Sc$_2$CCl$_2$ is identified with the proposed descriptor and confirmed by computation, demonstrating the descriptor validity for high SHR materials discovery., Comment: 6 pages, 5 figures

This paper presents the main features of a system that aims to transform regular expressions into shorter equivalent expressions. The system is also capable of computing other operations useful for simplification, such as checking the inclusion of regular languages. The main novelty of this work is that it combines known but distinct ways of representing regular languages into a global unified data structure that makes the operations more efficient. In addition, representations of regular languages are dynamically reduced as operations are performed on them. Expressions are normalized and represented by a unique identifier (an integer). Expressions found to be equivalent (i.e. denoting the same regular language) are grouped into equivalence classes from which a shortest representative is chosen. The article briefly describes the main algorithms working on the global data structure. Some of them are direct adaptations of well-known algorithms, but most of them incorporate new ideas, which are really necessary to make the system efficient. Finally, to show its usefulness, the system is applied to some examples from the literature. Statistics on randomly generated sets of expressions are also provided., Comment: rejected at ATVA 2023

We study pair correlation functions for planar Coulomb systems in the pushed phase, near a ring-shaped impenetrable wall. We assume coupling constant $\Gamma=2$ and that the number $n$ of particles is large. We find that the correlation functions decay slowly along the edges of the wall, in a narrow interface stretching a distance of order $1/n$ from the hard edge. At distances much larger than $1/\sqrt{n}$, the effect of the hard wall is negligible and pair correlation functions decay very quickly, and in between sits an interpolating interface that we call the ``semi-hard edge''. More precisely, we provide asymptotics for the correlation kernel $K_{n}(z,w)$ as $n\to\infty$ in two microscopic regimes (with either $|z-w| = \mathcal{O} (1/\sqrt{n})$ or $|z-w| = \mathcal{O} (1/n)$), as well as in three macroscopic regimes (with $|z-w| \asymp 1$). For some of these regimes, the asymptotics involve oscillatory theta functions and weighted Szeg\H{o} kernels., Comment: 46 pages, 5 figures. Our results are summarized in Figure 2

Let $T$ be an $n\times n$ truncation of an $(n+\alpha)\times (n+\alpha)$ Haar distributed unitary matrix. We consider the disk counting statistics of the eigenvalues of $T$. We prove that as $n\to + \infty$ with $\alpha$ fixed, the associated moment generating function enjoys asymptotics of the form \begin{align*} \exp \big( C_{1} n + C_{2} + o(1) \big), \end{align*} where the constants $C_{1}$ and $C_{2}$ are given in terms of the incomplete Gamma function. Our proof uses the uniform asymptotics of the incomplete Beta function., Comment: 14 pages, 4 figures

We analyze the Boussinesq equation on the line with Schwartz initial data belonging to the physically relevant class of global solutions. In a recent paper, we determined ten main asymptotic sectors describing the large $(x,t)$-behavior of the solution, and for each of these sectors we provided the leading order asymptotics in the case when no solitons are present. In this paper, we give a formula valid in the asymptotic sector $x/t \in (1,M]$, where $M$ is a large positive constant, in the case when solitons are present. Combined with earlier results, this validates the soliton resolution conjecture for the Boussinesq equation everywhere in the $(x,t)$-plane except in a number of small transition zones., Comment: 43 pages, 11 figures

In a recent paper, we showed that the large $(x,t)$ behavior of a class of physically relevant solutions of Boussinesq's equation for water waves is described by ten main asymptotic sectors. In the sector adjacent to the positive $x$-axis, referred to as Sector I, we stated without proof an exact expression for the leading asymptotic term together with an error estimate. Here we provide a proof of this asymptotic formula., Comment: 29 pages, 9 figures

We consider the Boussinesq equation on the line for a broad class of Schwartz initial data relevant for water waves. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term in the case when no solitons are present. In this paper, we derive an asymptotic formula in Sector IV, characterized by $\frac{x}{t}\in (\frac{1}{\sqrt{3}},1)$, in the case when solitons are present. In particular, our results provide an exact expression for the soliton-radiation interaction to leading order and a verification of the soliton resolution conjecture for the Boussinesq equation in Sector IV., Comment: 43 pages, 9 figures. This is a standalone paper based on Section 9 of arXiv:2204.02365v1. arXiv admin note: text overlap with arXiv:2301.10669

In a recent paper, we developed an inverse scattering approach to the Boussinesq equation in the case when no solitons are present. In this paper, we extend this approach to include solutions with solitons., Comment: 37 pages, 5 figures

We consider the Boussinesq equation on the line for a broad class of Schwartz initial data for which (i) no solitons are present, (ii) the spectral functions have generic behavior near $\pm 1$, and (iii) the solution exists globally. In a recent work, we identified ten main sectors describing the asymptotic behavior of the solution, and for each of these sectors we gave an exact expression for the leading asymptotic term. In this paper, we give a proof for the formula corresponding to the sector $\frac{x}{t}\in (0,\frac{1}{\sqrt{3}})$., Comment: 34 pages, 8 figures

It is well-known that each solution of the mKdV equation gives rise, via the Miura transformation, to a solution of the KdV equation. In this work, we show that a similar Miura-type transformation exists also for the ``good'' Boussinesq equation. This transformation maps solutions of a second-order equation to solutions of the fourth-order Boussinesq equation. Just like in the case of mKdV and KdV, the correspondence exists also at the level of the underlying Riemann--Hilbert problems and this is in fact how we construct the new transformation., Comment: 31 pages, 1 figure