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Alessio Zaccone

Publications and source records attributed to Alessio Zaccone.

At least 91 records · Page 5Linked to original sources
arXiv2023

Extended analytical BCS theory of superconductivity in thin films

We present an analytically solvable theory of BCS-type superconductivity in good metals which are confined along one of the three spatial directions, such as thin films. Closed-form expressions for the dependence of the superconducting critical temperature $T_c$ as a function of the confinement size $L$ are obtained, in quantitative agreement with experimental data with no adjustable parameters. Upon increasing the confinement, a crossover from a spherical Fermi surface, which contains two growing hollow spheres corresponding to states forbidden by confinement, to a strongly deformed Fermi surface, is predicted. This crossover represents a new topological transition, driven by confinement, between two Fermi surfaces belonging to two different homotopy classes. This topological transition provides a mechanistic explanation of the commonly observed non-monotonic dependence of $T_c$ upon film thickness with a maximum which, according to our theory, coincides with the topological transition.

cond-mat.supr-con↗
arXiv2023

Vibrational density of states and specific heat in glasses from random matrix theory

The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s' at least, it is a well established experimental fact that the specific heat of glasses is instead just linear in $T$ at $T \sim 1K$, and presents a pronounced peak when normalized by $T^{3}$, known as the boson peak. Here we present a new approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus.

cond-mat.dis-nn↗
arXiv2022

Microscopic theory for the pair correlation function of liquidlike colloidal suspensions under shear flow

We present a theoretical framework to investigate the microscopic structure of concentrated hard-sphere colloidal suspensions under strong shear flows by fully taking into account the boundary-layer structure of convective diffusion. We solve the pair Smoluchowski equation with shear separately in the compressing and extensional sectors of the solid angle, by means of matched asymptotics. A proper, albeit approximate, treatment of the hydrodynamic interactions in the different sectors allows us to construct a potential of mean force containing the effect of the flow field on pair correlations. We insert the obtained pair potential in the Percus-Yevick relation and use the latter as a closure to solve the Ornstein-Zernike integral equation. For a wide range of either the packing fraction $η$ and the Péclet ($\textrm{Pe}$) number, we compute the pair correlation function and extract scaling laws for its value at contact. For all the considered value of $\textrm{Pe},$ we observe a very good agreement between theoretical findings and numerical results from literature, up to rather large values of $η.$ The theory predicts a consistent enhancement of the structure factor $ S(k)$ at $k \to 0,$ upon increasing the $\textrm{Pe}$ number. We argue this behaviour may signal the onset of a phase transition from the isotropic phase to a non-uniform one, induced by the external shear flow.

cond-mat.soft↗
arXiv2022

Combined Description of Pressure-Volume-Temperature and Dielectric Relaxation of Several Polymeric and Low-Molecular-Weight Organic Glass-Formers using 'SL-TS2' Mean-Field Approach

We apply our recently-developed mean-field 'SL-TS2' (two-state Sanchez-Lacombe) model to simultaneously describe dielectric alpha-relaxation time and pressure-volume-temperature (PVT) data in four polymers (polystyrene, poly(methylmethacrylate), poly(vinyl acetate) and poly(cyclohexane methyl acrylate)) and four organic molecular glass formers (ortho-terphenyl, glycerol, PCB-62, and PDE). Previously, it has been shown that for all eight materials, the Casalini-Roland thermodynamical scaling, /tau_{/alpha} = f(TV_{sp}^{/gamma}) (where T is temperature and V_{sp} is specific volume), (Casalini, R.; Roland, C. M. Phys. Rev. Lett. 2014, 113 (8), 85701), is satisfied. It has also been previously shown that the same scaling emerges naturally (for sufficiently low pressures) within the 'SL-TS2' framework (Ginzburg, V. V. Soft Matter 2021, 17, 9094). Here, we fit the ambient pressure curves for the relaxation time and the specific volume as functions of temperature for the eight materials and observe a good agreement between theory and experiment. We then use the Casalini-Roland scaling to convert those results into 'master curves', thus enabling predictions of relaxation times and specific volumes at elevated pressures. The proposed approach can be used to describe other glass-forming materials, both low-molecular-weight and polymeric.

cond-mat.soft↗
arXiv2022

Predicting plasticity of amorphous solids from instantaneous normal modes

We present a mathematical description of amorphous solid deformation and plasticity by extending the concept of instantaneous normal modes (INMs) to deformed systems, which allows us to retain the effect of strain on the vibrational density of states (VDOS). Starting from the nonaffine lattice dynamics (NALD) description of elasticity and viscoelasticity of glasses, we formulate the linear response theory up to large deformations by considering the strain-dependent tangent modulus at finite values of shear strain. The (nonaffine) tangent shear modulus is computed from the vibrational density of states (VDOS) of affinely strained configurations at varying strain values. The affine strain, found analytically on the static (undeformed) snapshot of the glass, leads to configurations that are rich of soft low-energy modes as well as unstable modes (negative eigenvalues) that are otherwise completely "washed out" and lost, if one lets the system relax after strain. This procedure is fully consistent with the structure of NALD. The INM spectrum of deformed states allows for the analytical prediction of the stress-strain curve of a model glass, including the prediction of the yield point. Good parameter-free quantitative agreement is shown between the prediction and simulations of athermal quasi-static shear of a coarse-grained polymer glass.

cond-mat.soft↗
arXiv2022

Solution to the two-body Smoluchowski equation with shear flow for charge-stabilized colloids at low to moderate Péclet numbers

We developed an analytical theoretical method to determine the microscopical structure of weakly to moderately sheared colloidal suspensions in dilute conditions. The microstructure is described by the static structure factor, obtained by solving the stationary two-body Smoluchowski advection-diffusion equation. The singularly perturbed PDE problem is solved by performing an angular averaging over the extensional and compressing sectors and by the rigorous application of boundary-layer theory (intermediate asymptotics). This allows us to expand the solution to a higher order in Péclet with respect to previous methods. The scheme is independent of the type of interaction potential. We apply it to the example of charge-stabilized colloidal particles interacting via the repulsive Yukawa potential and study the distortion of the structure factor. It is predicted that the distortion is larger at small wavevectors $k$ and its dependence on $Pe$ is a simple power law. At increasing $Pe$, the main peak of the structure factor displays a broadening and shift towards lower $k$ in the extensional sectors, which indicates shear-induced spreading out of particle correlations and neighbor particles locally being dragged away from the reference one. In the compressing sectors, instead, a narrowing and shift towards high $k$ is predicted, reflecting shear-induced ordering near contact and concomitant depletion in the medium-range. An overall narrowing of the peak is also predicted for the structure factor averaged over the whole solid angle. Calculations are also performed for hard spheres, showing good overall agreement with experimental data. It is also shown that the shear-induced structure factor distortion is orders of magnitude larger for the Yukawa repulsion than for the hard spheres.

cond-mat.soft↗
arXiv2022

The $ω^3$ scaling of the vibrational density of states in quasi-2D nanoconfined solids

Atomic vibrations play a vital role in the functions of various physical, chemical, and biological systems. The vibrational properties and the specific heat of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic $ω^{2}$ low-frequency scaling of the vibrational density of states (VDOS) in bulk ordered solids from few fundamental assumptions. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the VDOS of amorphous ice confined to a thickness of $\approx 1$ nm inside graphene oxide membranes and we observe a crossover from the Debye $ω^2$ scaling to an anomalous $ω^3$ behaviour upon reducing the confinement size $L$. Additionally, using molecular dynamics simulations, we confirm the experimental findings and also prove that such a scaling of the VDOS appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency $ω^3$ law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency $ω_\times= v L/2π$, with $v$ the speed of sound of the material, and we confirm this quantitative estimate with simulations. This new physical phenomenon, revealed by combining theoretical, experimental and simulations results, is relevant to a myriad of systems both in synthetic and biological contexts and it could impact various technological applications for systems under confinement such as nano-devices or thin films.

cond-mat.mtrl-sci↗
arXiv2022

Analytical theory of enhanced Bose-Einstein condensation in thin films

We present an analytically solvable theory of Bose-Einstein condensation in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-to-moderate confinement regime (where the film thickness $L$ is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature $T_{c} \sim L^{-1/2}$. For cold Bose gases, this implies an enhancement up to two orders of magnitude in $T_{c}$ for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. $C \sim T^{2}$, is predicted for nano-scale films, which implies a different $λ$ point behaviour with respect to bulk systems, while the condensate fraction is predicted to follow a $[1- (T/T_{c})^{2}]$ law.

cond-mat.quant-gas↗
arXiv2022

Theory of sound attenuation in amorphous solids from nonaffine motions

We present a theoretical derivation of acoustic phonon damping in amorphous solids based on the nonaffine response formalism for the viscoelasticity of amorphous solids. The analytical theory takes into account the nonaffine displacements in transverse waves and is able to predict both the ubiquitous low-energy diffusive damping $\sim k^{2}$, as well as a novel contribution to the Rayleigh damping $\sim k^{4}$ at higher wavevectors and the crossover between the two regimes observed experimentally. The coefficient of the diffusive term is proportional to the microscopic viscous (Langevin-type) damping in particle motion (which arises from anharmonicity), and to the nonaffine correction to the static shear modulus, whereas the Rayleigh damping emerges in the limit of low anharmonicity, consistent with previous observations and macroscopic models. Importantly, the $k^4$ Rayleigh contribution derived here does not arise from harmonic disorder or elastic heterogeneity effects and it is the dominant mechanism for sound attenuation in amorphous solids as recently suggested by molecular simulations.

cond-mat.soft↗
arXiv2022

Theory of Superconductivity Mediated by Topological Phonons

Topological phononic insulators are the counterpart of three-dimensional quantum spin Hall insulators in phononic systems and, as such, their topological surfaces are characterized by Dirac cone-shaped gapless edge states arising as a consequence of a bulk-boundary correspondence. We propose a theoretical framework for the possible superconducting phase in these materials, where the attractive interaction between electrons is mediated by topological phonons in nontrivial boundary modes. Within the BCS limit, we develop a self-consistent two-band gap equation, whose solutions show that the superconducting critical temperature has a non-monotonic behaviour with respect to the phononic frequency in the Kramers-like point. This remarkable behaviour is produced by a resonance, that occurs when electrons and phonons on the topological surfaces have the same energy: this effectively increases the electron-phonon interaction and hence the Cooper pair binding energy, thus establishing an optimal condition for the superconducting phase. With this mechanism, the $T_{c}$ can be increased by well over a factor two, and the maximum enhancement occurs in the degenerate phononic flat-band limit.

cond-mat.supr-con↗
arXiv2022

Reply to Chen and Ni on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"

We show that very clear answers to the queries raised by D. Chen and R. Ni in their Comment on our recent paper [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] can be found in our original paper already. The paper [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is free of mathematical errors, as anyone can easily verify, and all the assumptions were carefully, and critically discussed in the paper.

cond-mat.soft↗
arXiv2022

Superconducting dome in ferroelectric-type materials from soft mode instability

We present a minimal theory of superconductivity enhancement in ferroelectric-type materials. Simple expressions for the optical mode responsible for the soft mode transition are assumed. A key role is played by the anharmonic phonon damping which is modulated by an external control parameter (electron doping or mechanical strain) causing the appearance of the soft mode. It is shown that the enhancement in the superconducting critical temperature $T_{c}$ upon approaching the ferroelectric transition from either side is due to the Stokes electron-phonon scattering processes promoted by strong phonon damping effects.

cond-mat.supr-con↗
arXiv2022

Reply to Morse and Charbonneau on "Explicit analytical solution for random close packing in $d=2$ and $d=3$"

A Comment by Morse and Charbonneau shows that our recent analytical solution to the random close packing (RCP) problem is in good agreement with packings data in dimensions $d<6$ but deviates from the data for $d\geq6$. In this Reply we argue, using results related to the $E_{8}$ Lie group, that no RCP solution based on contact numbers and marginal stability is expected to capture RCP in large space dimensions $d \geq 8$ where a large gap exists between nearest neighbours already at $d=8$. The fact remains that the result in [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is currently the only simple analytical solution to the RCP problem based on statistical arguments, which captures a good deal of the underlying physics in $d=2,3,4,5$.

cond-mat.stat-mech↗
arXiv2022

Correlation between vibrational anomalies and emergent anharmonicity of local potential energy landscape in metallic glasses

The boson peak (BP) is a universal feature in the Raman and inelastic scattering spectra of both disordered and crystalline materials. The current paradigm presents the boson peak as the result of a Ioffe-Regel crossover between ballistic (phonon) and diffusive-type excitations, where the loss of coherence of phonons is described as a purely harmonic process due to structural disorder. This "harmonic disorder" paradigm for the BP has never been challenged or tested at the atomistic level. Here, through a set of atomistically-resolved characterizations of amorphous metallic alloys, we uncover a robust inverse proportionality between the intensity of boson peak and the activation energy of excitations in the potential energy landscape (PEL). Larger boson peak is linked with shallower basins and lower activation barriers and, consequently, with strongly anharmonic sectors of the PEL. Numerical evidence from atomistic simulations indicates that THz atomic vibrations contributing the most to the BP in atomic glasses are strongly anharmonic, as evidenced through very large values of the atomic- and mode-resolved Grüneisen parameter found for the atomic vibrations that constitute the BP. These results provide a direct bridge between the vibrational spectrum and the topology of the PEL in solids, and point towards a new "giant anharmonicity" paradigm for both generic disordered materials and for the phonon-glass problem in emerging materials for energy applications. In this sense, disorder and anharmonicity emerge as the two sides of the same coin.

cond-mat.dis-nn↗
arXiv2022

Explicit Analytical Solution for Random Close Packing in d=2 and d=3

We present an analytical derivation of the volume fractions for random close packing (RCP) in both $d=3$ and $d=2$, based on the same methodology. Using suitably modified nearest neigbhour statistics for hard spheres, we obtain $ϕ_{\mathrm{RCP}}=0.65896$ in $d=3$ and $ϕ_{\mathrm{RCP}}=0.88648$ in $d=2$. These values are well within the interval of values reported in the literature using different methods (experiments and numerical simulations) and protocols. This order-agnostic derivation suggests some considerations related to the nature of RCP: (i) RCP corresponds to the onset of mechanical rigidity where the finite shear modulus emerges, (ii) the onset of mechanical rigidity marks the maximally random jammmed state and dictates $ϕ_{\mathrm{RCP}}$ via the coordination number $z$, (iii) disordered packings with $ϕ>ϕ_{\mathrm{RCP}}$ are possible at the expense of creating some order, and $z=12$ at the FCC limit acts as a boundary condition.

cond-mat.soft↗
arXiv2022

Relativistic Langevin Equation derived from a particle-bath Lagrangian

We show how a relativistic Langevin equation can be derived from a Lorentz-covariant version of the Caldeira-Leggett particle-bath Lagrangian. In one of its limits, we identify the obtained equation with the Langevin equation used in contemporary extensions of statistical mechanics to the near-light-speed motion of a Brownian particle in non-relativistic dissipative fluids. The proposed framework provides a more rigorous and first-principles form of the Langevin equation often quoted or postulated as ansatz in previous works. We then refine the aforementioned results by considering more terms in the particle-bath coupling, which improves the precision of the approximation for fully relativistic settings where not only the tagged particle but also the thermal bath motion is relativistic. We discuss the implications of the apparent breaking of space-time translation and parity invariance, showing that these effects are not necessarily in contradiction with the assumptions of statistical mechanics. The intrinsically non-Markovian character of the fully relativistic generalized Langevin equation derived here, and of the associated fluctuation-dissipation theorem, is also discussed.

cond-mat.stat-mech↗
arXiv2021

Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory

We combine hydrodynamic and field theoretic methods to develop a general theory of phonons as Goldstone bosons in crystals, glasses and liquids based on non-affine displacements and the consequent Goldstones phase relaxation. We relate the conservation, or lack thereof, of specific higher-form currents with properties of the underlying deformation field -- non-affinity -- which dictates how molecules move under an applied stress or deformation. In particular, the single-valuedness of the deformation field is associated with conservation of higher-form charges that count the number of topological defects. Our formalism predicts, from first principles, the presence of propagating shear waves above a critical wave-vector in liquids, thus giving the first formal derivation of the phenomenon in terms of fundamental symmetries. The same picture provides also a theoretical explanation of the corresponding "positive sound dispersion" phenomenon for longitudinal sound. Importantly, accordingly to our theory, the main collective relaxation timescale of a liquid or a glass (known as the $α$ relaxation for the latter) is given by the phase relaxation time, which is not necessarily related to the Maxwell time. Finally, we build a non-equilibrium effective action using the in-in formalism defined on the Schwinger-Keldysh contour, that further supports the emerging picture. In summary, our work suggests that the fundamental difference between solids, fluids and glasses has to be identified with the associated generalized higher-from global symmetries and their topological structure, and that the Burgers vector for the displacement fields serves as a suitable topological order parameter distinguishing the solid (ordered) phase and the amorphous ones (fluids, glasses).

cond-mat.soft↗