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Ultrafast spectroscopy paved the way for probing transient states of matter produced through photoexcitation. Despite significant advances, the microscopic processes governing the formation of these states remain largely unknown. This study discloses the nuclear quantum dynamics of $\mathrm{SrTiO_3}$ when excited by THz laser pumping. We use a first-principles machine-learning approach accounting for all atomistic degrees of freedom to examine the time-resolved energy flow across phonon modes following the photoexcitation, revealing the mechanism underpinning the observed phonon upconversion and quantifying the lifetime of the out-of-equilibrium motion. Crucially, our simulations predict that THz pump pulses can generate persistent out-of-equilibrium stress capable of inducing polar order. We observe a correlation between the experimentally measured lifetime of the transient inversion-symmetry-broken state and the duration of the out-of-equilibrium nuclear state. This work not only explains the experimental results on $\mathrm{SrTiO_3}$ but also establishes a framework for simulating the photoexcited quantum dynamics of nuclei from first principles without any empirical input. It lays the groundwork for systematic explorations of complex materials sensitive to photoexcitation.

The rapid advancements in ultrafast laser technology have paved the way for pumping and probing the out-of-equilibrium dynamics of nuclei in crystals. However, interpreting these experiments is extremely challenging due to the complex nonlinear responses in systems where lattice excitations interact, particularly in crystals composed of light atoms or at low temperatures where the quantum nature of ions becomes significant. In this work, we address the nonequilibrium quantum ionic dynamics from first principles. Our approach is general and can be applied to simulate any crystal, in combination with a first-principles treatment of electrons or external machine-learning potentials. It is implemented by leveraging the nonequilibrium time-dependent self-consistent harmonic approximation (TD-SCHA), with a stable, energy-conserving, correlated stochastic integration scheme that achieves an accuracy of $\mathcal{O}(dt^3)$. We benchmark the method with both a simple one-dimensional model to test its accuracy and a realistic 40-atom cell of SrTiO3 under THz laser pump, paving the way for simulations of ultrafast THz-Xray pump-probe spectroscopy like those performed in synchrotron facilities.

The atomic motion in molecular crystals, such as high-pressure hydrogen or hybrid organic-inorganic perovskites, is very complex due to quantum anharmonic effects. In addition, these materials accommodate rotational degrees of freedom. All the approximate methods that describe the nuclei thermodynamics using Cartesian coordinates lead to an unphysical hybridization of roto-librations with other high-energy modes. Hence, they do not accurately account for the free energy contributions of these degrees of freedom. So, a reliable description of a molecular crystal's phase diagram is only possible with Path Integral Molecular Dynamics (PIMD) at a high computational cost. This work shows how to include roto-librational modes in the Self-Consistent Harmonic Approximation (SCHA) framework. SCHA approximates the nuclei Cartesian fluctuations to be Gaussian, thus neglecting curvilinear motion. Keeping its low computational cost, we employ the generalization of SCHA, called nonlinear SCHA (NLSCHA). Our method relies on a Gaussian \textit{ansatz} for the nuclei density matrix on a curved manifold, allowing us to map roto-librations into harmonic modes defined on a surface. By optimizing the surface's curvature variationally, we minimize the free energy, allowing the spontaneous activation of these degrees of freedom without external parameters. Notably, in the limit of vanishing curvature, we recover the standard SCHA.

Little is known about the quantum effects of friction, and first-principles studies are virtually non-existent. In multilayer graphene, the order of the stacking of the layers plays a crucial role in the electronic properties and the manifestation of superconductivity, and friction affects how layers slide to change the stacking. Here, we study the effects of friction in bilayer graphene by focusing on quantum fluctuations in the free energy barrier that layers have to overcome to slide with respect to each other. We evaluate the free energy at the barrier in bilayer graphene through the self-consistent harmonic approximation, accounting for quantum and thermal ionic fluctuations. We obtain a very large reduction of the barrier of more than 30%. Temperature effects are weaker, although high temperatures induce a significant reduction of the barrier as well. Our approach is general and paves the way for systematically accounting for nuclear quantum and thermal effects in free energy barriers of other macroscopic systems., Comment: 12 pages, 28 figures

The Self-Consistent Harmonic Approximation (SCHA) describes atoms in solids, including quantum fluctuations and anharmonic effects, in a non-perturbative way. It computes ionic free energy variationally, constraining the atomic quantum-thermal fluctuations to be Gaussian. Consequently, the entropy is analytical; there is no need for thermodynamic integration or heavy diagonalization to include finite temperature effects. In addition, as the probability distribution is fixed, SCHA solves all the equations with Monte Carlo integration without employing Metropolis sampling of the quantum phase space. Unfortunately, the Gaussian approximation breaks down for rotational modes and tunneling effects. We show how to describe these non-Gaussian fluctuations using the quantum variational principle at finite temperatures, keeping the main advantage of SCHA: direct access to free energy. Our method, nonlinear SCHA (NLSCHA), employs an invertible nonlinear transformation to map Cartesian coordinates into an auxiliary manifold parametrized by a finite set of variables. So, we adopt a Gaussian \textit{ansatz} for the density matrix in this new coordinate system. The nonlinearity of the mapping ensures that NLSCHA enlarges the SCHA variational subspace, and its invertibility conserves the information encoded in the density matrix. We evaluate the entropy in the auxiliary space, where it has a simple analytical form. As in the SCHA, the variational principle allows for optimizing free parameters to minimize free energy. Finally, we show that, for the first time, NLSCHA gives direct access to the entropy of a crystal with non-Gaussian degrees of freedom.

Understanding and simulating the thermodynamic and dynamical properties of materials affected by strong ionic anharmonicity is a central challenge in material science. Two powerful methodologies have emerged as frontrunners in this exploration: the Self-Consistent Harmonic Approximation (SCHA) with its counterpart, Self-Consistent Phonons (SCP), and the Temperature-Dependent Effective Potential (TDEP). Despite their widespread use, the limitations of these methods are often overlooked, and the absence of a formal derivation for the TDEP has led to significant missteps that hamper its predictive accuracy. Here, the theoretical foundations of both SCHA and TDEP are revised, unveiling their profound interconnection. This work introduces formal derivation for TDEP, dispelling misconceptions about how to improve its accuracy and refining best practices. The perturbative limit of these methods uncovers that both SCHA and TDEP fall short in reproducing the lowest-order perturbative free energy. While TDEP excels in providing an exact treatment of the static susceptibility, its dynamical extension violates the perturbative regime by overcounting anharmonicity. Conversely, SCHA delivers an approximate static susceptibility but maintains correct static and dynamic response functions within the perturbative limit. This work introduces a corrective strategy for TDEP's dynamical extension to address these shortcomings. All the claims provided here are benchmarked against the exact (numerical) solution on a simple one-dimensional anharmonic potential., Comment: 18 pages, 8 figures

Hydrogen hydrates present a rich phase diagram influenced by both pressure and temperature, with the so-called C$_2$ phase emerging prominently above 2.5 GPa. In this phase, hydrogen molecules are densely packed within a cubic ice-like lattice and the interaction with the surrounding water molecules profoundly affects their quantum rotational dynamics. Herein, we delve into this intricate interplay by directly solving the Schr\"{o}dinger's equation for a quantum H$_2$ rotor in the C$_2$ crystal field at finite temperature, generated through Density Functional Theory. Our calculations reveal a giant energy splitting relative to the magnetic quantum number of $\pm$3.2 meV for $l=1$. Employing inelastic neutron scattering, we experimentally measure the energy levels of H$_2$ within the C$_2$ phase at 6.0 and 3.4 GPa and low temperatures, finding remarkable agreement with our theoretical predictions. These findings underscore the pivotal role of hydrogen--water interactions in dictating the rotational behavior of the hydrogen molecules within the C$_2$ phase and indicate heightened induced-dipole interactions compared to other hydrogen hydrates., Comment: 4 Figures

We investigate the structural and thermodynamic properties of high-pressure ice by incorporating quantum anharmonicity at a non-perturbative level. Quantum fluctuations reduce the critical pressure of the phase transition between phase VIII (with asymmetric H-bonds) and phase X (with symmetric H-bonds) by 65 GPa from its classical value of 116 GPa at 0K. Moreover, quantum effects make it temperature-independent over a wide temperature range (0K-300K), in agreement with experimental estimates obtained through vibrational spectroscopy and in striking contrast to the strong temperature dependence found in the classical approximation. The equation of state shows fingerprints of the transition in accordance with experimental evidence. Additionally, we demonstrate that, within our approach, proton disorder in phase VII has a negligible impact on the occurrence of phase X. Finally, we reproduce with high accuracy the 10 GPa isotope shift due to the hydrogen-to-deuterium substitution.

The Nancy Grace Roman Space Telescope Coronagraph Instrument is a critical technology demonstrator for NASA's Habitable Worlds Observatory. With a predicted visible-light flux ratio detection limit of 1E-8 or better, it will be capable of reaching new areas of parameter space for both gas giant exoplanets and circumstellar disks. It is in the final stages of integration and test at the Jet Propulsion Laboratory, with an anticipated delivery to payload integration in the coming year. This paper will review the instrument systems, observing modes, potential observing applications, and overall progress toward instrument integration and test., Comment: Proceedings of SPIE: Techniques and Instrumentation for Detection of Exoplanets XI, vol. 12680 (2023)

In order to characterize in detail the charge density wave (CDW) transition of 1$T$-VSe$_2$, its electronic structure and lattice dynamics are comprehensively studied by means of x-ray diffraction, angle resolved photoemission (ARPES), diffuse and inelastic x-ray scattering (IXS), and state-of-the-art first principles density functional theory calculations. Resonant elastic x-ray scattering (REXS) does not show any resonant enhancement at either V or Se K-edges, indicating that the CDW peak describes a purely structural modulation of the electronic ordering. ARPES identifies (i) a pseudogap at T$>$T$_{CDW}$, which leads to a depletion of the density of states in the $ML-M'L'$ plane at T$<$T$_{CDW}$, and (ii) anomalies in the electronic dispersion reflecting a sizable impact of phonons on it. A diffuse scattering precursor, characteristic of soft phonons, is observed at room temperature (RT) and leads to the full collapse of the low-energy phonon ($\omega_1$) with propagation vector (0.25 0 -0.3) r.l.u. We show that the frequency and linewidth of this mode are anisotropic in momentum space, reflecting the momentum dependence of the electron-phonon interaction (EPI), hence demonstrating that the origin of the CDW is, to a much larger extent, due to the momentum dependence EPI with a small contribution from nesting. The pressure dependence of the $\omega_1$ soft mode remains nearly constant up to 13 GPa at RT, with only a modest softening before the transition to the high-pressure monoclinic $C2/m$ phase. The wide set of experimental data are well captured by our state-of-the art first-principles anharmonic calculations with the inclusion of van der Waals (vdW) corrections in the exchange-correlation functional. The description of the electronics and dynamics of VSe$_2$ reported here adds important pieces of information to the understanding of the electronic modulations of TMDs.

Magnetostriction drives a rhombohedral distortion in the cubic rock salt antiferromagnet MnO at the N\'eel temperature $T_{N}=118$ K. As an unexpected consequence we show that this distortion acts to localize the site of an implanted muon due to the accompanying redistribution of electron density. This lifts the degeneracy between equivalent sites, resulting in a single observed muon precession frequency. Above $T_{N}$, the muon instead becomes delocalized around a network of equivalent sites. Our first-principles simulations based on Hubbard-corrected density-functional theory and molecular dynamics are consistent with our experimental data and help to resolve a long-standing puzzle regarding muon data on MnO, as well as having wider applicability to other magnetic oxides., Comment: 7 pages, 3 figures

Phonon anharmonicity plays a crucial role in determining the stability and vibrational properties of high-pressure hydrides. Furthermore, strong anharmonicity can render phonon quasiparticle picture obsolete questioning standard approaches for modeling superconductivity in these material systems. In this work, we show the effects of non-Lorentzian phonon lineshapes on the superconductivity of high-pressure solid hydrogen. We calculate the superconducting critical temperature T$_\mathrm{C}$ \emph{ab initio} considering the full phonon spectral function and show that it overall enhances the T$_\mathrm{C}$ estimate. The anharmonicity-induced phonon softening exhibited in spectral functions increases the estimate of the critical temperature, while the broadening of phonon lines due to phonon-phonon interaction decreases it. Our calculations also reveal that superconductivity emerges in hydrogen in the $Cmca-12$ molecular phase VI at pressures between 450 and 500 GPa and explain the disagreement between the previous theoretical results and experiments.

CsSnI3 is a promising eco-friendly solution for energy harvesting technologies. It exists at room temperature in either a black perovskite polymorph or a yellow 1D double-chain, which irreversibly deteriorates in the air. In this work, we unveil the relative thermodynamic stability between the two structures with a first-principles sampling of the CsSnI3 finite-temperature phase diagram, discovering how it is driven by anomalously large quantum and anharmonic ionic fluctuations. Thanks to a comprehensive treatment of anharmonicity, the simulations deliver a remarkable agreement with known experimental data for the transition temperatures of the orthorhombic, rhombohedral, and cubic perovskite structures and the thermal expansion coefficient. We disclose how the perovskite polymorphs are the ground state above \SI{270}{\kelvin} and discover an abnormal decrease in heat capacity upon heating in the cubic black perovskite. Our results also significantly downplay the Cs+ rattling modes' contribution to mechanical instability. The remarkable agreement with experiments validates our methodology, which can be systematically applied to all metal halides., Comment: Accepted on Chemistry of Materials

The atomic motion controls important features of materials, such as thermal transport, phase transitions, and vibrational spectra. However, the simulation of ionic dynamics is exceptionally challenging when quantum fluctuations are relevant (e.g., at low temperatures or with light atoms) and the energy landscape is anharmonic. In this work, we formulate the Time-Dependent Self-Consistent Harmonic Approximation (TDSCHA) in the Wigner framework, paving the way for the efficient computation of the nuclear motion in systems with sizable quantum and thermal anharmonic fluctuations. Besides the improved numerical efficiency, the Wigner formalism unveils the classical limit of TDSCHA and provides a link with the many-body perturbation theory of Feynman diagrams. We further extend the method to account for the non-linear couplings between phonons and photons, responsible, e.g., for a nonvanishing Raman signal in high-symmetry Raman inactive crystals, firstly discussed by Rasetti and Fermi. We benchmark the method in phase III of high-pressure hydrogen ab initio. The nonlinear photon-phonon coupling reshapes the IR spectra and explains the high-frequency shoulder of the H2 vibron observed in experiments. The Wigner TDSCHA is computationally cheap and derived from first principles: it is unbiased by assumptions on the phonon-phonon and phonon-photon scattering and does not depend on empirical parameters. Therefore, the method can be adopted in unsupervised high-throughput calculations., Comment: 36 pages, 9 figures, 1 table

This paper describes a new $\nu_e$ identification method specifically designed to improve the low-energy ($< 30\,\mathrm{GeV}$) $\nu_e$ identification efficiency attained by enlarging the emulsion film scanning volume with the next generation emulsion readout system. A relative increase of 25-70% in the $\nu_e$ low-energy region is expected, leading to improvements in the OPERA sensitivity to neutrino oscillations in the framework of the 3 + 1 model. The method is applied to a subset of data where the detection efficiency increase is expected to be more relevant, and one additional $\nu_e$ candidate is found. The analysis combined with the $\nu_\tau$ appearance results improves the upper limit on $\sin^2 2\theta_{\mu e}$ to 0.016 at 90% C.L. in the MiniBooNE allowed region $\Delta m^2_{41} \sim 0.3\,\mathrm{eV}^2$., Comment: 13 pages, 6 figures

Understanding collective phenomena in quantum materials from first principles is a promising route toward engineering materials properties on demand and designing new functionalities. This work examines the quantum paraelectric state, an elusive state of matter characterized by the smooth saturation of the ferroelectric instability at low temperature due to quantum fluctuations associated with anharmonic phonon effects. The temperature-dependent evolution of the soft ferroelectric phonon mode in the quantum paraelectric KTaO$_3$ in the range 0-300 K is modelled by combining density functional theory (DFT) calculations with the stochastic self-consistent harmonic approximation assisted by an on-the-fly machine-learned force field. The calculated data show that including anharmonic terms is essential to stabilize the spurious imaginary ferroelectric phonon predicted by DFT, in agreement with experiments. Augmenting the DFT workflow with machine-learned force fields allows for efficient stochastic sampling of the configurational space using large supercells in a broad and dense temperature range, inaccessible by conventional ab initio protocols. This work proposes a robust computational workflow capable of accounting for collective behaviors involving different degrees of freedom and occurring at large time/length scales, paving the way for precise modeling and control of quantum effects in materials., Comment: 10 pages, 6 figures. To be published in Advanced Quantum Technologies. Editor: Luigi Ranalli

Recently the use of mobile technologies in Ecological Momentary Assessments (EMA) and Interventions (EMI) has made it easier to collect data suitable for intra-individual variability studies in the medical field. Nevertheless, especially when self-reports are used during the data collection process, there are difficulties in balancing data quality and the burden placed on the subjects. In this paper, we address this problem for a specific EMA setting which aims to submit a demanding task to subjects at high/low values of a self-reported variable. We adopt a dynamic approach inspired by control chart methods and design optimization techniques to obtain an EMA triggering mechanism for data collection which takes into account both the individual variability of the self-reported variable and of the adherence rate. We test the algorithm in both a simulation setting and with real, large-scale data from a tinnitus longitudinal study. A Wilcoxon-Mann-Whitney Rank Sum Test shows that the algorithm tends to have both a higher F1 score and utility than a random schedule and a rule-based algorithm with static thresholds, which are the current state-of-the-art approaches. In conclusion, the algorithm is proven effective in balancing data quality and the burden placed on the participants, especially, as the analysis performed suggest, in studies where data collection is impacted by adherence., Comment: 12 pages, 4 figures

The interplay between electron correlation and nuclear quantum effects makes our understanding of elemental hydrogen a formidable challenge. Here, we present the phase diagram of hydrogen and deuterium at low temperatures and high-pressure ($P > 300$ GPa by accounting for highly accurate electronic and nuclear enthalpies. We evaluated internal electronic energies by diffusion quantum Monte Carlo, while nuclear quantum motion and anharmonicity have been included by the stochastic self-consistent harmonic approximation. Our results show that the long-sought atomic metallic hydrogen, predicted to host room-temperature superconductivity, forms at $577\pm 10$ GPa ($640\pm 14$ GPa in deuterium). Indeed, anharmonicity pushes the stability of this phase towards pressures much larger than previous theoretical estimates or attained experimental values. Before atomization, molecular hydrogen transforms from a conductive phase III to another metallic structure that is still molecular (phase VI) at $422\pm 40$ GPa ($442\pm30$ GPa in deuterium). We predict clear-cut signatures in optical spectroscopy and DC conductivity that can be used experimentally to distinguish between the two structural transitions. According to our findings, the experimental evidence of metallic hydrogen has so far been limited to molecular phases.

Magnesium hydride (MgH$_2$) has been widely studied for effective hydrogen storage. However, its bulk desorption temperature (553 K) is deemed too high for practical applications. Besides doping, a strategy to decrease such reaction energy for releasing hydrogen is the use of MgH$_2$-based nanoparticles (NPs). Here, we investigate first the thermodynamic properties of Mg$_n$H$_{2n}$ NPs ($n<10$) from first-principles, in particular by assessing the anharmonic effects on the enthalpy, entropy and thermal expansion by means of the Stochastic Self Consistent Harmonic Approximation (SSCHA). The latter method goes beyond previous approaches, typically based on molecular mechanics and the quasi-harmonic approximation, allowing the ab initio calculation of the fully-anharmonic free energy. We find an almost linear dependence on temperature of the interatomic bond lengths - with a relative variation of few percent over 300K -, alongside with a bond distance decrease of the Mg-H bonds. In order to increase the size of NPs toward experiments of hydrogen desorption from MgH$_2$ we devise a computationally effective Machine Learning model trained to accurately determine the forces and total energies (i.e. the potential energy surfaces), integrating the latter with the SSCHA model to fully include the anharmonic effects. We find a significative decrease of the H-desorption temperature for sub-nanometric clusters Mg$_n$H$_{2n}$ with $n \leq 10$, with a non-negligible, although little effect due to anharmonicities (up to 10%)., Comment: 29 pages, t figures, 6 tables

Water ice is a unique material presenting intriguing physical properties, like negative thermal expansion and anomalous volume isotope effect (VIE). They arise from the interplay between weak hydrogen bonds and nuclear quantum fluctuations, making theoretical calculations challenging. Here, we employ the stochastic self-consistent harmonic approximation (SSCHA) to investigate how thermal and quantum fluctuations affect the physical properties of ice XI ab initio. Regarding the anomalous VIE, our work reveals that quantum effects on hydrogen are so strong to be in a nonlinear regime: when progressively increasing the mass of hydrogen from protium to infinity (classical limit), the volume firstly expands and then contracts, with a maximum slightly above the mass of tritium. We observe an anharmonic renormalization of about 10% in the bending and stretching phonon frequencies probed in IR and Raman experiments. For the first time, we report an accurate comparison of the low energy phonon dispersion with the experimental data, possible only thanks to high-level accuracy in the electronic correlation and nuclear quantum and thermal fluctuations, paving the way for the study of thermal transport in ice from first principles and the simulation of ice under pressure.

The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approximation method. This technique rigorously describes the full thermodyamics of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivatives with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles density-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to determine the phase diagram of any crystal at finite temperature. It enables the calculation of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theoretical framework of the stochastic self-consistent harmonic approximation and its dynamical extension, making particular emphasis on the physical interpretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calculation to illustrate the potential of the code.

Most material properties of great physical interest are directly related to nuclear dynamics, e.g. the ionic thermal conductivity, Raman/IR vibrational spectra, inelastic X-ray, and Neutron scattering. A theory able to compute from first principles these properties, accounting for the anharmonicity and quantum fluctuations in the nuclear energy landscape that can be implemented in systems with hundreds of atoms is missing. Here, we derive an approximate theory for the quantum time evolution of lattice vibrations at finite temperature. This theory introduces the time dynamics in the Self-Consistent Harmonic Approximation (SCHA) and shares with the static case the same computational cost. It is nonempirical, as pure states evolve according to the Dirac least action principle and the dynamics of the thermal ensemble conserves both energy and entropy. The static SCHA is recovered as a stationary solution of the dynamical equations. We apply perturbation theory around the static SCHA solution and derive an algorithm to compute efficiently quantum dynamical response functions. Thanks to this new algorithm, we have access to the response function of any general external time-dependent perturbation, enabling the simulation of phonon spectra without following any perturbative expansion of the nuclear potential or empirical methods. We benchmark the algorithm on the IR and Raman spectroscopy of high-pressure hydrogen phase III, with a simulation cell of 96 atoms. Our work also explores the nonlinear regime of the dynamical nuclear motion, providing a paradigm to simulate the interaction with intense or multiple probes, as in pump-probe spectroscopy, or chemical reactions involving light atoms, as the proton transfer in biomolecules

Among transition metal dichalcogenides (TMDs), VSe$_2$ is considered to develop a purely 3-dimensional (3D) charge-density wave (CDW) at T$_{CDW}$=110 K. Here, by means of high resolution inelastic x-ray scattering (IXS), we show that the CDW transition is driven by the collapse of an acoustic mode at the critical wavevector \textit{q}$_{CDW}$= (2.25 0 0.7) r.l.u. and critical temperature T$_{CDW}$=110 K. The softening of this mode starts to be pronounced for temperatures below 2$\times$ T$_{CDW}$ and expands over a rather wide region of the Brillouin zone, suggesting a large contribution of the electron-phonon interaction to the CDW formation. This interpretation is supported by our first principles calculations that determine a large momentum-dependence of the electron-phonon interaction, peaking at the CDW wavevector, in the presence of nesting. Fully anharmonic {\it ab initio} calculations confirm the softening of one acoustic branch at \textit{q}$_{CDW}$ as responsible for the CDW formation and show that van der Waals interactions are crucial to melt the CDW. Our work also highlights the important role of out-of-plane interactions to describe 3D CDWs in TMDs.

Most metallic transition metal dichalcogenides undergo charge density wave (CDW) instabilities with similar or identical ordering vectors in bulk and in single layer, albeit with different critical temperatures. Metallic 1T-TiTe$_2$ is a remarkable exception as it shows no evidence of charge density wave formation in bulk, but it displays a stable $2\times2$ reconstruction in single-layer form. The mechanism for this 3D-2D crossover of the transition is still unclear, although strain from the substrate and the exchange interaction have been pointed out as possible formation mechanisms. Here, by performing non-perturbative anharmonic calculations with gradient corrected and hybrid functionals, we explain the thickness behaviour of the transition in 1T-TiTe$_2$. We demonstrate that the occurrence of the CDW in single-layer TiTe$_2$ occurs from the interplay of non-perturbative anharmonicity and an exchange enhancement of the electron-phonon interaction, larger in the single layer than in the bulk. Finally, we study the electronic and structural properties of the single-layer CDW phase and provide a complete description of its electronic structure, phonon dispersion as well as infrared and Raman active phonon modes., Comment: 11 pages, 10 pictures

Despite many of the applications of graphene rely on its uneven stiffness and high thermal conductivity, the mechanical properties of graphene, and in general of all 2D materials, are still elusive. The harmonic theory predicts a quadratic dispersion for the flexural acoustic vibrational mode, which leads the unphysical result that long wavelength in-plane acoustic modes decay before vibrating one period, preventing the propagation of sound. The robustness of the quadratic dispersion has been questioned by arguing that the anharmonic phonon-phonon interaction linearizes it. However, this implies a divergent bending rigidity in the long wavelength limit not reproduced experimentally. Here we show that rotational symmetry protects the quadratic flexural dispersion against phonon-phonon interactions and that, consequently, the bending stiffness is non-divergent irrespective of the temperature. Our non-perturbative anharmonic calculations also determine that sound propagation coexists with a quadratic dispersion. We also show that the temperature dependence of the height fluctuations of the membrane, known as ripples, is fully determined by thermal or quantum fluctuations, but without the anharmonic suppression of their amplitude previously assumed. The universality of our conclusions reconcile experimental evidence and theory not just in graphene, but all 2D materials.

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H NbSe$_2$. While scanning tunnelling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a non-perturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.

An event topology with two secondary vertices compatible with the decay of short-lived particles was found in the analysis of neutrino interactions in the Opera target. The observed topology is compatible with tau neutrino charged current (CC) interactions with charm production and neutrino neutral current (NC) interactions with $c\overline{c}$ pair production. However, other processes can mimic this topology. A dedicated analysis was implemented to identify the underlying process. A Monte Carlo simulation was developed and complementary procedures were introduced in the kinematic reconstruction. A multivariate analysis technique was used to achieve an optimal separation of signal from background. Most likely, this event is a $\nu_{\tau}$ CC interaction with charm production, the tau and charm particle decaying into 1 prong and 2 prongs, respectively. The significance of this observation is evaluated., Comment: 10 pages, 7 figures; Editors: Marco Roda, Chiara Sirignano and Gabriele Sirri

Production of metallic hydrogen is one of the top three open quests of physics. Recent low-temperature experiments report different metallization pressures, varying from 360GPa to 490GPa. In this work, we simulate structural properties, vibrational Raman, IR and optical spectra of hydrogen phase III accounting for proton quantum effects. We demonstrate that nuclear quantum fluctuations downshift the vibron frequencies by 25%, introduce a broad line-shape in the Raman spectra, and reduce the optical gap by 3eV. We show that hydrogen metallization occurs at 380GPa in phase III due to band overlap, in good agreement with transport data. By simulating the optical properties, we predict this state to be a peculiar black metal, transparent in the IR. The transparent window closes at 450GPa, but the reflectivity remains low, discarding phase III as the shiny metal observed at 490GPa. We predict the conductivity onset to increase by 70GPa and the transparent window to increase by 1.3eV when replacing hydrogen by deuterium at 0K, underlining that metallization is driven by quantum fluctuations and is thus isotope dependent. We show how hydrogen acquires metallic features (conductivity and brightness) at different pressures, explaining the apparent contradictions in existing experimental scenarios.

Most of the DNA that composes a complex organism is non-coding and defined as junk. Even the coding part is composed of genes that affect the phenotype differently. Therefore, a random mutation has an effect on the specimen fitness that strongly depends on the DNA region where it occurs. Such heterogeneous composition should be linked to the evolutionary process. However, the way is still unknown. Here, we study a minimal model for the evolution of an ecosystem where two antagonist species struggle for survival on a lattice. Each specimen possesses a toy genome, encoding for its phenotype. The gene pool of populations changes in time due to the effect of random mutations on genes (entropic force) and of interactions with the environment and between individuals (natural selection). We prove that the relevance of each gene in the manifestation of the phenotype is a key feature for evolution. In the presence of a uniform gene relevance, a mutational meltdown is observed. Natural selection acts quenching the ecosystem in a non-equilibriumstate that slowly drifts, decreasing the fitness and leading to the extinction of the species. Conversely, if a specimen is provided with a heterogeneous gene relevance, natural selection wins against entropic forces, and the species evolves increasing its fitness. We finally show that heterogeneity together with spatial correlations is responsible for spontaneous sympatric speciation., Comment: 8 pages, 4 figures