Flat bands without twists: periodic holey graphene.

Holey Graphene(HG) is a widely used graphene material for the synthesis of high-purity and highly crystalline materials. The electronic properties of a periodic distribution of lattice holes are explored here, demonstrating the emergence of flat bands. It is established that such flat bands arise as a consequence of an induced sublattice site imbalance, i.e. by having more sites in one of the graphene's bipartite sublattice than in the other. This is equivalent to the breaking of a path-exchange symmetry. By further breaking the inversion symmetry, gaps and a nonzero Berry curvature are induced, leading to topological bands. In particular, the folding of the Dirac cones from the hexagonal Brillouin zone (BZ) to the holey superlattice rectangular BZ of HG, with sizes proportional to an integerntimes the graphene's lattice parameter, leads to a periodicity in the gap formation such thatn≡0(mod 3). A low-energy hamiltonian for the three central bands is also obtained revealing that the system behaves as an effectiveα-T3graphene material. Therefore, a simple protocol is presented here that allows for obtaining flat bands at will. Such bands are known to increase electron-electron correlation effects. Therefore, the present work provides an alternative system that is much easier to build than twisted systems, allowing for the production of flat bands and potentially highly correlated quantum phases.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update.

This is an update of a previous review (Naumiset al2017Rep. Prog. Phys.80096501). Experimental and theoretical advances for straining graphene and other metallic, insulating, ferroelectric, ferroelastic, ferromagnetic and multiferroic 2D materials were considered. We surveyed (i) methods to induce valley and sublattice polarisation (P) in graphene, (ii) time-dependent strain and its impact on graphene's electronic properties, (iii) the role of local and global strain on superconductivity and other highly correlated and/or topological phases of graphene, (iv) inducing polarisationPon hexagonal boron nitride monolayers via strain, (v) modifying the optoelectronic properties of transition metal dichalcogenide monolayers through strain, (vi) ferroic 2D materials with intrinsic elastic (σ), electric (P) and magnetic (M) polarisation under strain, as well as incipient 2D multiferroics and (vii) moiré bilayers exhibiting flat electronic bands and exotic quantum phase diagrams, and other bilayer or few-layer systems exhibiting ferroic orders tunable by rotations and shear strain. The update features the experimental realisations of a tunable two-dimensional Quantum Spin Hall effect in germanene, of elemental 2D ferroelectric bismuth, and 2D multiferroic NiI2. The document was structured for a discussion of effects taking place in monolayers first, followed by discussions concerning bilayers and few-layers, and it represents an up-to-date overview of exciting and newest developments on the fast-paced field of 2D materials.

Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain withs - porbitals.

The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms withs - porbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to understand the topology through a nontrivial winding number and the geometry introduced by theFubini-Study (FS)metric. This metric allows us to distinguish between pure states of systems with the same topology and thus provides a suitable tool for obtaining the fingerprint of flat bands. Moreover, it provides an appealing geometrical picture for describing flat bands as it can be associated with a local conformal transformation over circles in a complex plane. In addition, the presented model allows us to relate the topology with the formation of compact localized states and pseudo-Bogoliubov modes. Also, the properties of the squared Hamiltonian are investigated in order to provide a better understanding of the localization properties and the spectrum. The presented model is equivalent to two coupled SSH chains under a change of basis.

Description of mesoscale pattern formation in shallow convective cloud fields by using time-dependent Ginzburg-Landau and Swift-Hohenberg stochastic equations.

The time-dependent Ginzburg-Landau (or Allen-Cahn) equation and the Swift-Hohenberg equation, both added with a stochastic term, are proposed to describe cloud pattern formation and cloud regime phase transitions of shallow convective clouds organized in mesoscale systems. The starting point is the Hottovy-Stechmann linear spatiotemporal stochastic model for tropical precipitation, used to describe the dynamics of water vapor and tropical convection. By taking into account that shallow stratiform clouds are close to a self-organized criticality and that water vapor content is the order parameter, it is observed that sources must have nonlinear terms in the equation to include the dynamical feedback due to precipitation and evaporation. The nonlinear terms are derived by using the known mean field of the Ising model, as the Hottovy-Stechmann linear model presents the same probability distribution. The inclusion of this nonlinearity leads to a kind of time-dependent Ginzburg-Landau stochastic equation, originally used to describe superconductivity phases. By performing numerical simulations, pattern formation is observed. These patterns are better compared with real satellite observations than the pure linear model. This is done by comparing the spatial Fourier transform of real and numerical cloud fields. However, for highly ordered cellular convective phases, considered as a form of Rayleigh-Bénard convection in moist atmospheric air, the Ginzburg-Landau model does not allow us to reproduce such patterns. Therefore, a change in the form of the small-scale flux convergence term in the equation for moist atmospheric air is proposed. This allows us to derive a Swift-Hohenberg equation. In the case of closed cellular and roll convection, the resulting patterns are much more organized than the ones obtained from the Ginzburg-Landau equation and better reproduce satellite observations as, for example, horizontal convective fields.

Más Allá de La Filogenética: Evolución Darwiniana de La Actina / Beyond Phylogenetics: Darwinian Evolution of Actin

Resumen La actina es una proteína que se polimeriza para formar citoesqueletos y cuya función es estabilizar y dirigir el movimiento de las paredes celulares. Es una de las proteínas más estables, habiendo evolucionado poco a partir de algas y levaduras, y muy poco desde los peces. Aquí analizamos la evolución de la actina usando las teorías modernas de las interacciones de conformación proteína-agua, y cómo estas han evolucionado para optimizar las funciones de la proteína. Llegamos a la conclusión de que el fracaso del análisis filogenético para identificar positivamente la evolución darwiniana de las proteínas ha sido causado por las limitaciones técnicas propias del siglo XX. Estas limitaciones pueden ser superadas mediante el escalamiento termodinámico y el promedio modular ambos llevados a niveles técnicos del siglo XXI. Los resultados para la actina son especialmente llamativos y reflejan estructuras duales estables, globulares y polimerizadas.

Abstract Actin polymerizes to form cytoskeletons which stabilize and direct motion of cellular walls. It is one of the most stable proteins, having evolved little from algae and yeast, and very little from fish. Here we analyze actin evolution using modern theories of water-protein shaping interactions, and how these have evolved to optimize protein functions. We conclude that the failure of phylogenetic analysis to identify positive Darwinian evolution has been caused by 20th century technical limitations. These are overcome using 21st century thermodynamic scaling and modular averaging. The results for actin are especially striking, and reflect dual stable structures, globular and polymerized.

Electronic and optical properties of strained graphene and other strained 2D materials: a review.

This review presents the state of the art in strain and ripple-induced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed Dirac-Schrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide- and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

Sound waves induce Volkov-like states, band structure and collimation effect in graphene.

We find exact states of graphene quasiparticles under a time-dependent deformation (sound wave), whose propagation velocity is smaller than the Fermi velocity. To solve the corresponding effective Dirac equation, we adapt the Volkov-like solutions for relativistic fermions in a medium under a plane electromagnetic wave. The corresponding electron-deformation quasiparticle spectrum is determined by the solutions of a Mathieu equation resulting in band tongues warped in the surface of the Dirac cones. This leads to a collimation effect of electron conduction due to strain waves.

Anisotropic AC conductivity of strained graphene.

The density of states and the AC conductivity of graphene under uniform strain are calculated using a new Dirac Hamiltonian that takes into account the main three ingredients that change the electronic properties of strained graphene: the real displacement of the Fermi energy, the reciprocal lattice strain and the changes in the overlap of atomic orbitals. Our simple analytical expressions for the density of states and the AC conductivity generalize previous expressions for uniaxial strain. The results suggest a way to measure the Grüneisen parameter ß that appears in any calculation of strained graphene, as well as the emergence of a sort of Hall effect due to shear strain.

Simple solvable energy-landscape model that shows a thermodynamic phase transition and a glass transition.

When a liquid melt is cooled, a glass or phase transition can be obtained depending on the cooling rate. Yet, this behavior has not been clearly captured in energy-landscape models. Here, a model is provided in which two key ingredients are considered in the landscape, metastable states and their multiplicity. Metastable states are considered as in two level system models. However, their multiplicity and topology allows a phase transition in the thermodynamic limit for slow cooling, while a transition to the glass is obtained for fast cooling. By solving the corresponding master equation, the minimal speed of cooling required to produce the glass is obtained as a function of the distribution of metastable states.

Critical wavefunctions in disordered graphene.

In order to elucidate the presence of non-localized states in doped graphene, a scaling analysis of the wavefunction moments, known as inverse participation ratios, is performed. The model used is a tight-binding Hamiltonian considering nearest and next-nearest neighbors with random substitutional impurities. Our findings indicate the presence of non-normalizable wavefunctions that follow a critical (power-law) decay, which show a behavior intermediate between those of metals and insulators. The power-law exponent distribution is robust against the inclusion of next-nearest neighbors and growing the system size.

Mean-square-displacement distribution in crystals and glasses: An analysis of the intrabasin dynamics.

In the energy landscape picture, the dynamics of glasses and crystals is usually decomposed into two separate contributions: interbasin and intrabasin dynamics. The intrabasin dynamics depends partially on the quadratic displacement distribution on a given metabasin. Here we show that such a distribution can be approximated by a Gamma function, with a mean that depends linearly on the temperature and on the inverse second moment of the density of vibrational states. The width of the distribution also depends on this last quantity, and thus the contribution of the boson peak in glasses is evident on the tail of the distribution function. It causes the distribution of the mean-square displacement to decay slower in glasses than in crystals. When a statistical analysis is performed under many energy basins, we obtain a Gaussian in which the width is regulated by the mean inverse second moment of the density of states. Simulations performed in binary glasses are in agreement with such a result.

Excess of low frequency vibrational modes and glass transition: a molecular dynamics study for soft spheres at constant pressure.

Using molecular dynamics at constant pressure, the relationship between the excess of low frequency vibrational modes (known as the boson peak) and the glass transition is investigated for a truncated Lennard-Jones potential. It is observed that the quadratic mean displacement is enhanced by such modes, as predicted using a harmonic Hamiltonian for metastable states. As a result, glasses loose mechanical stability at lower temperatures than the corresponding crystal, since the Lindemann criteria are observed, as is also deduced from density functional theory. Finally, we found that the average force and elastic constant are reduced in the glass due to such excess of modes. The ratio between average elastic constants can be approximated using the 2/3 rule between melting and glass transition temperatures.

Thermal relaxation and low-frequency vibrational anomalies in simple models of glasses: a study using nonlinear Hamiltonians.

Glasses exist because they are not able to relax in a laboratory time scale toward the most stable structure: a crystal. At the same time, glasses present low-frequency vibrational-mode (LFVM) anomalies. We explore in a systematic way how the number of such modes influences thermal relaxation in one-dimensional models of glasses. The model is a Fermi-Pasta-Ulam chain with nonlinear springs that join second neighbors at random, which mimics the adding of bond constraints in the rigidity theory of glasses. The corresponding number of LFVMs decreases linearly with the concentration of these springs, and thus their effect upon thermal relaxation can be studied in a systematic way. To do so, we performed numerical simulations using lattices that were thermalized and afterwards placed in contact with a zero-temperature bath. The results indicate that the time required for thermal relaxation has two contributions: one depends on the number of LFVMs and the other on the localization of modes due to disorder. By removing LFVMs, relaxation becomes less efficient since the cascade mechanism that transfers energy between modes is stopped. On the other hand, normal-mode localization also increases the time required for relaxation. We prove this last point by comparing periodic and nonperiodic chains that have the same number of LFVMs.

Use of the cage formation probability for obtaining approximate phase diagrams.

In this work, we introduce the idea of cage formation probability, defined by considering the angular space needed by a particle in order to leave a cage given an average distance to its neighbors. Considering extreme fluctuations, two phases appear as a function of the number of neighbors and their distances to a central one: Solid and fluid. This allows us to construct an approximated phase diagram based on a geometrical approach. As an example, we apply this probability concept to hard disks in two dimensions and hard spheres in three dimensions. The results are compared with numerical simulations using a Monte Carlo method.

Monte Carlo rejection as a tool for measuring the energy landscape scaling of simple fluids.

A simple modification of the Monte Carlo algorithm is proposed to explore the topography and the scaling of the energy landscape. We apply this idea to a simple hard-core fluid. The results for different packing fractions show a power law scaling of the landscape boundary, with a characteristic scale that separates the values of the scaling exponents. Finally, it is shown how the topology determines the freezing point of the system due to the increasing importance and complexity of the boundary.

Energy landscape and rigidity.

The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this effect. The model predicts a deviation from the Debye law at low temperatures. Then, the connection between the topography of the energy landscape, the topology of the phase space, and the rigidity of a glass is explored. As a result, we relate the number of constraints and floppy modes to the statistics of the landscape. We apply these ideas to a simple model for which we provide an approximate expression for the number of energy basins as a function of the rigidity. This helps to understand certain features of the glass transition, like the jump in the specific heat or the reversible window observed in chalcogenide glasses.

Attraction-driven disorder in a hard-core colloidal monolayer.

Monte Carlo simulation techniques were employed to explore the effect of short-range attraction on the orientational ordering in a two-dimensional assembly of monodisperse spherical particles. We find that if the range of square-well attraction is approximately 15% of the particle diameter, the dense attractive fluid shows the same ordering behavior as the same density fluid composed of purely repulsive hard spheres. Fluids with an attraction range larger than 15% show an enhanced tendency to crystallization, while disorder occurs for fluids with an attractive range shorter than 15% of the particle diameter. A possible link with the existence of "repulsive" and "attractive" states in dense colloidal systems is discussed.

Role of rigidity in the fluid-solid transition.

We examine the fluid-solid transition for a hard-disk system. By counting the near neighbors in the average configurations of a grand-canonical Monte Carlo simulation, this enables us to relate the thermodynamic transition with the rigidity theory, since we find that the coordination number in the fluid-solid transition is close to the coordination number predicted by a mean field rigidity theory, due to dynamical jamming of particles, where the contact region between disks is the radial ring outside a disk with a maximum allowed coordination number that is not bigger than six. Using these ideas, we were able to produce a continuous glass-like transition when nucleation of rigidity is suppressed.

A multigrid approach to the average lattices of quasicrystals.

An average structure associated with a given quasilattice is a system composed of several average lattices that in reciprocal space produces strong main reflections. The average lattice of a quasicrystal is a useful concept closely related to the geometric description of the quasicrystal to crystal transformation and has been proved to be structurally significant. Here we calculate average structures for arbitrary two- and three-dimensional quasilattices using the dual generalized method. Additionally, closed analytical expressions for the coordinates of the average structure, the quasiperiodic lattice and its diffraction pattern are given.