De Gennes Research Articles

On standing waves and gradient-flow for the Landau–De Gennes model of nematic liquid crystals

The article treats the existence of standing waves and solutions to gradient-flow equation for the Landau–De Gennes models of liquid crystals, a state of matter intermediate between the solid state and the liquid one. The variables of the general problem are the velocity field of the particles and the Q-tensor, a symmetric traceless matrix which measures the anisotropy of the material. In particular, we consider the system without the velocity field and with an energy functional unbounded from below. At the beginning we focus on the stationary problem. We outline two variational approaches to get a critical point for the relative energy functional: by the Mountain Pass Theorem and by proving the existence of a least energy solution. Next we describe a relationship between these solutions. Finally we consider the evolution problem and provide some Strichartz-type estimates for the linear problem. By several applications of these results to our problem, we prove via contraction arguments the existence of local solutions and, moreover, global existence for initial data with small L^2-norm.

Orientation-dependent crossover from retro to specular Andreev reflections in semi-Dirac materials

In the framework of Bogoliubov–de Gennes equation, we theoretically study the transport properties in normal-superconducting junctions based on semi-Dirac materials (SDMs). Owing to the intrinsic anisotropy of SDMs, the configuration of Andreev reflection (AR) and the differential conductance are strongly orientation-dependent. For the transport along the linear dispersion direction, the differential conductance exhibits a clear crossover from retro AR to specular AR with increasing the bias-voltage, and the differential conductance oscillates with the interfacial barrier strength without a decaying profile. Conversely, for the transport along the quadratic dispersion direction, the boundary between the retro AR and specular AR becomes ambiguous when the orientation angle increases, and the differential conductance decays with increasing the momentum mismatch or the interfacial barrier strength. We illustrate the pseudo-spin textures to reveal the underling physics behind the anisotropic coherent transport properties. These results enrich the understanding of the superconducting coherent transport in SDMs.

Elastic anisotropy in the reduced Landau-de Gennes model.

We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter, , and the critical points are described by 3 d.f. We analytically construct a symmetric critical point for all admissible values of , which is necessarily globally stable for small domains, i.e. when the square edge length, , is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the , , and solutions, of which the , and solutions can be stable. Furthermore, we demonstrate that the novel solution is energetically preferable for large and large , and prove associated stability results that corroborate the stabilizing effects of for reduced Landau–de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of , which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.

Mechanisms of Flow-Induced Polymer Translocation

Flow-induced translocation of linear and ring polymers is studied by using a combination of multiparticle collision dynamics and molecular dynamics. The results show that both end capture and fold capture are present in the capture process of linear chains in weak flows, whereas fold capture becomes dominant in strong flows, resulting in similar behavior for the linear and ring chains in the strong flow regime. For narrow channels, the critical flux decreases with the increase of channel size, which is qualitatively consistent with the prediction by Wu et al.; for large channel sizes (which are still smaller than the polymer size), the critical flux is independent of channel size, in agreement with an earlier prediction by de Gennes et al. The presence of these two scaling regimes indicates that the confined blob exhibits a crossover from free draining to nondraining as the channel size increases. Moreover, we found that the conformation of the polymer exhibits a flow-induced coil–compact–stretch transition, and the transition does not appear to be first order. In addition, we observed that the monomers far from the channel and in the channel exhibit independent dynamics.

Orbital vortices in s -wave spin-singlet superconductors in zero magnetic field

Breaking of time-reversal and point-group spatial symmetries can have a profound impact on superconductivity. One of the most extraordinary effects, due to the application of a magnetic field, is represented by the Abrikosov vortices with charged supercurrents circulating around their cores. Whether a similar phenomenon can be obtained by exploiting spatial symmetry breaking, e.g. through electric fields or mechanical strain, is a fundamentally relevant but not yet fully settled problem. Here, we show that in two-dimensional spin-singlet superconductors with unusually low degree of spatial symmetry content, vortices with supercurrents carrying angular momentum around the core can form and be energetically stable. The vortex has zero net magnetic flux since it is made up of counter-propagating Cooper pairs with opposite orbital moments. By solving self-consistently the Bogoliubov - de Gennes equations in real space, we demonstrate that the orbital vortex is stable and we unveil the spatial distribution of the superconducting order parameter around its core. The resulting amplitude has a characteristic pattern with a pronounced angular anisotropy that deviates from the profile of conventional magnetic vortices. These hallmarks guide predictions and proposals for the experimental detection.

Vortex state in a superconducting mesoscopic irregular octagon

Our study sample is a superconducting bi-dimensional octagon with different boundary conditions immersed in a magnetic external field [Formula: see text]. The boundary conditions are simulated by considering different values of the de Gennes extrapolation length [Formula: see text] on different surfaces of the sample. Our investigation was carried out by solving the time-dependent Ginzburg–Landau equations. We analyzed the superconducting electron density and the magnetization curves as functions of [Formula: see text] and temperature [Formula: see text] in field-cooling and in zero-field-cooling processes for different values of [Formula: see text] and size of the sample. We found a strong dependence of the critical fields on [Formula: see text] and size of the sample.

Stability of a split-core configuration induced by saddle-splay elasticity in a submicron nematic liquid crystal spherical droplet

ABSTRACT We use Landau–de Gennes theory to investigate the configurations of liquid crystals confined to a submicron spherical droplet subject to weak homeotropic anchoring. The results show that in a one-constant approximation, there are three equilibrium configurations: radial hedgehog, ring disclination and uniform, where the radial hedgehog configuration is a stable state. With increasing elastic anisotropy, which is essentially an increase in the splay elastic constant, the radial hedgehog configuration transforms into a split-core configuration, which is metastable. The split-core configuration becomes the lowest-energy state induced by saddle-splay elasticity within appropriate ranges of the radius and elastic anisotropy.

Quantum Turbulence and Planckian Dissipation

The notion of the Planckian dissipation is extended to the system of the Caroli–de Gennes–Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time τ is comparable with the quantum Heisenberg time {{t}_{H}} = hbar {text{/}}Delta E, where Delta E is the interlevel distance in the vortex core (the minigap). This type of Planck dissipation has two important physical consequences. First, it determines the regime, when the effect of the axial anomaly becomes important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli–de Gennes–Matricon states becomes important in the super-Planckian region, i.e., when tau < hbar {text{/}}Delta E. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at tau < hbar {text{/}}Delta E and the vortex turbulence regime at tau > hbar {text{/}}Delta E.

Inducing chiral superconductivity on honeycomb lattice systems

Superconductivity in graphene-based systems has recently attracted much attention, as either intrinsic behavior or induced by proximity to a superconductor may lead to interesting topological phases and symmetries of the pairing function. A prominent system considers the pairing to have chiral symmetry. The question arises as to the effect of possible spin–orbit coupling on the resulting superconducting quasiparticle (QP) spectrum. Utilizing a Bogolyubov–de Gennes (BdG) Hamiltonian, we explore the interplay of different interaction terms in the system, and their role in generating complex Berry curvatures in the QP spectrum, as well as non-trivial topological behavior. We demonstrate that the topology of the BdG Hamiltonian in these systems may result in the appearance of edge states along the zigzag edges of nanoribbons in the appropriate regime. For suitable chemical potential and superconducting pairing strength, we find the appearance of robust midgap states at zigzag edges, well protected by large excitation gaps and momentum transfer.

Superfast-Expanding Porous Hydrogels: Pushing New Frontiers in Converting Chemical Potential into Useful Mechanical Work.

Superabsorbent polymer gels can absorb large amounts of water (100-1000× their dry weight). For the past 50 years, many scientists such as de Gennes have proposed to extract mechanical work from gel expansion/contraction, which could pave the way for "artificial muscles". However, slow rates of gel expansion have limited these efforts: macroscale (∼cm) gels take over 24 h to expand to their equilibrium size. Gels can be made to expand faster if their characteristic length scale is reduced, e.g., by making a macroscopic gel porous. Still, gels that are both superabsorbent and able to expand rapidly have not yet been realized. Here, we create gels at the macroscale (∼cm or larger) that are porous, highly robust, superabsorbent and expand much faster than any gels thus far. Our approach involves the in situ foaming of a monomer solution (acrylic acid and acrylamide) using a double-barreled syringe that has acid and base in its two barrels. Gas (CO2) is generated at the mixing tip of the syringe by the acid-base reaction, and gas bubbles are stabilized by an amphiphilic polymer in one of the barrels. The monomers are then polymerized by ultraviolet (UV) light to form the gel around the bubbles, and the material is dried under ambient conditions to give a porous solid. When this dry gel is added to water, it absorbs water at a rate of 20 g/g·s until an equilibrium is achieved at ∼300× its weight. In the process, each gel dimension increases by ∼20%/s until its final dimensions are more than 3× larger. Such rapid and appreciable expansion can be easily observed by the eye, and remarkably, the swollen gel is robust enough to be picked up by hand. SEM images reveal a porosity of >90% and an interconnected network of pores. The gels are responsive to pH, and a full cycle of expansion (in regular water) and contraction (at pH 10 or in ethanol) can be completed within about 60 s. We use gel expansion to rapidly lift weights against gravity, resulting in ∼0.4 mJ of work being done over 40 s, which translates to a power density of 260 mW/kg. This ability to harness the chemical potential energy from the gel to do useful mechanical work could enable new designs for mechano-chemical engines─and potentially for artificial muscles.

In-gap states of vortices at the surface of a topological insulator

By solving the Bogoliubov–de Gennes equations we study fermion bound states in the core of a vortex of a two-dimensional superconductor. The metallic surface states of a strong topological insulator become superconducting via proximity effect with an s-wave superconductor. The strong spin-orbit coupling locks the spin perpendicular to the momentum (Rashba interaction) giving rise to a zero-energy Majorana state. We investigate the case of a large first excitation energy of the order of the superconducting gap (Δ∞), i.e. for the Fermi level close to the apex of the Dirac cone. We obtain the local density of states (LDOS) for the bulk and the bound states. The particle-hole symmetry is broken in the LDOS for up-spin as a consequence of the spin-orbit coupling and the chirality of the vortex. On the other hand, the down-spin LDOS is particle-hole symmetric. The spin-polarization of the bound state peaks is studied in detail. We present a waterfall-like spectrum that shows that for a distance less than 3 times the coherence length ξ from the core, the bound states can be observed.

Influence of Rashba spin-orbit coupling on Josephson effect in triplet superconductor/two-dimensional semiconductor/triplet superconductor junctions

We study theoretically Josephson effect in a planar ballistic junction between two triplet superconductors with p-wave orbital symmetries and separated by a two-dimensional (2D) semiconductor channel with strong Rashba spin–orbit coupling. In triplet superconductors, three types of orbital symmetries are considered. We use Bogoliubov–de Gennes formalism to describe quasiparticle propagations through the junction and the supercurrents are calculated in terms of Andreev reflection coefficients. The features of the variation of the supercurrents with the change of the strength of Rashba spin–orbit coupling are investigated in some detail. It is found that for the three types of orbital symmetries considered, both the magnitudes of supercurrent and the current-phase relations can be manipulated effectively by tuning the strength of Rashba spin–orbit coupling. The interplay of Rashba spin–orbit coupling and Zeeman magnetic field on supercurrent is also investigated in some detail.

Evidence of Many-Body Interactions in the Virial Coefficients of Polyelectrolyte Gels.

Simulation studies of aqueous polymer solutions, and heuristic arguments by De Gennes for aqueous polyethylene oxide polymer solutions, have suggested that many-body interactions can give rise to the ‘anomalous’ situation in which the second osmotic virial coefficient is positive, while the third virial coefficient is negative. This phenomenon was later confirmed in analytic calculations of the phase behavior and the osmotic pressure of complex fluids exhibiting cooperative self-assembly into extended dynamic polymeric structures by Dudowicz et al. In the present study, we experimentally confirm the occurrence of this osmotic virial sign inversion phenomenon for several highly charged model polyelectrolyte gels (poly(acrylic acid), poly(styrene sulfonate), DNA, hyaluronic acid), where the virial coefficients are deduced from osmotic pressure measurements. Our observations qualitatively accord with experimental and simulation studies indicating that polyelectrolyte materials exhibit supramolecular assembly in solution, another symptomatic property of fluids exhibiting many-body interactions. We also find that the inversion in the variation of the second (A2) and third (A2) virial coefficients upon approach to phase separation does not occur in uncharged poly(vinyl acetate) gels. Finally, we briefly discuss the estimation of the osmotic compressibility of swollen polyelectrolyte gels from neutron scattering measurements as an alternative to direct, time-consuming and meticulous osmotic pressure measurements. We conclude by summarizing some general trends and suggesting future research directions of natural and synthetic polyelectrolyte hydrogels.

From spatial to temporal patterns: cooperativity across ion channels in supercritical membranes

Theoretically predicted by Fisher and de Gennes in 1978, critical Casimir forces are the thermodynamic analogues of the Casimir-Polder attraction forces due to quantum fluctuations of confined electromagnetic field in vacuum. In the context of lipid membranes close to a miscibility transition, critical Casimir interactions are thought to be responsible for clustering of membrane proteins. Here we explore the hypothesis that these effective statistical-field mediated interactions can explain the observed ion channel cooperativity that has been suggested to promote multistability of the membrane potential and thus “cellular memory”.

Study of the Droplet Pinning Force in the Transition from Dry to Liquid-Infused Thin Polymer Films.

The change in the pinning force during the transition from dry to oil-impregnated thin polymer films is studied for droplets of water and hexadecane. A careful variation of the oil amount in the films is performed by means of supercritical impregnation. The film thickness dependence on the oil content is measured using ellipsometry and compared to gel swelling theory estimates. Depending on the oil content, two cases of pinning force behavior have been identified. For each case, the factors that determine the pinning force are discussed. The pinning force in the transition from dry to equilibrium swollen gel films is well approximated by the Joanny and de Gennes hysteresis model of dilute defects.

Study of effective de-Gennes factor and effect of doping on superconductivity in rare-earth nickel borocarbide superconductors

We theoretically study the effective de Gennes factor and effect of doping on the critical temperature in RNi2B2C (R = Ho). We formulate a mean-field Hamiltonian model where a BCS type of Cooper pair mechanism is considered. We self-consistently solve SC order parameter, AFM order parameter and dopant concentration. The de Gennes scaling on critical temperature and Neel temperature for different Nickel borocarbide compounds gives an idea about the competition between superconductivity and antiferromagnetism in rare earth quaternary borocarbide superconductors RNi2B2C. We study here the effect of doping on the parent borocarbide superconductor HoNi2B2C. We plot the effective de-Gennes factor vs. SC critical temperature for the pseudo quaternary borocarbide compound HoxLa1-xNi2B2C for different dopant concentrations which agrees well with experimental findings.

Alignment of carbon nanotubes under the influences of nematic liquid crystals and electric fields — an analytical study

Carbon nanotubes (CNTs) have benefits in various fields, they are disadvantageous due to their tendency to form aggregates and poorly controlled alignment of the CNT molecules (characterized by order parameters). These deficiencies can be overcome by dispersing the CNTs in nematic liquid crystal (LC) and placing the mixture under the influence of an electric field. In this study, Doi and Landau–de Gennes free energy density equations are used to analytically confirm that an electric field increases the order parameters of CNTs and LCs in a dispersion mixture. The anchoring strength of the nematic LC is also found to affect the order parameters of the CNTs and LC. Further, increasing the length-to-diameter ratio of the CNTs increases their alignment without affecting the LC alignment. These findings indicate that CNT molecular alignment can be controlled by adjusting the CNT length-to-diameter ratio, anchoring the LCs, and adjusting the electric field strength.

Steady state crack growth in viscoelastic solids: A comparative study

We compare the predictions of different theories on the steady state growth of a Mode I crack in linear viscoelastic solids. The theories studied in this work include those by Knauss, Schapery, Persson and Brener. The comparisons focus on the fractional dissipation rate and the relationship between crack growth velocity and fracture energy. Analytical solutions are carried out using realistic constitutive models such as the Generalized Maxwell Solid (GMS) and the Power Law Solid (PLS). These theories are tested against two different sets of experimental data reported in the literature. We also present new results such as the strain field directly ahead of the crack tip, the residual strain on the crack surfaces and the crack opening displacement (COD). We use the expressions for COD to study the shape and size of the “viscoelastic trumpet” proposed by de Gennes. Using a new approach, we study the shape and size of the viscoelastic dissipation zone around the crack tip and discuss its dependence on the crack growth velocity.

Shape resonances and the T c dependence on film thickness of Ni/Bi systems

We report on the experimentally observed variation of the superconducting critical temperature (T c ) of Ni/Bi systems as a function of the total deposited film thickness and on its explanation using a theoretical model. Two series of Ni/Bi systems have been analyzed which were obtained by depositions of Ni onto Bi in the proportions Ni3Bix (3 nm of Ni onto x nm of Bi) and NiyBi6y (y nm Ni onto 6 y nm of Bi). As shown recently, the formation of the superconducting compound NiBi3 at Ni/Bi interfaces in the resulting NiBi3-Bi films is thermodynamically favored by a volume contraction. Here we corroborate this result and estimate the thickness of the resulting NiBi3 and of the remaining Bi layers for the Ni3Bix and NiyBi6y series using the laws of mass and conservation of number of atoms. We consider the resulting film as being made up of two homogeneous and uniform layers of NiBi3 and Bi, respectively, and study this idealizing model using the Bogoliubov de Gennes (BdG) equations. It is assumed that superconductivity originates in the NiBi3 layer and penetrates the Bi layers via a potential barrier. Our theoretical calculations predict the dependence of T c with respect to the thicknesses of the NiBi3 and Bi layers, and also with the strength of the potential barrier that blocks the migration of electrons from the NiBi3 to the Bi layer. The calculations show that the superconducting gap also exists in Bi, although much weaker than in the NiBi3 layer. We compare the predicted T c values with the experimental data and find sufficient agreement to suggest that our model can explain the experimentally observed variation of T c with thickness. We interpret this dependence as shape resonance oscillations which are derived from the BdG theory applied to thin superconducting films.

Structural, magnetic and magnetocaloric properties of (Pr,Sm)2Fe17 compound at room temperature

In the present work, we report on the structural, magnetic, and magnetocaloric properties of the (Pr, Sm)2Fe17 system prepared by arc melting under high pure argon and homogenized at 1073 K to minimize other possible impurity phases. X-ray diffraction (XRD) coupled with Rietveld analysis with FullProf computer code reveals the presence of a single-phase of (Pr, Sm)2Fe17. This compound crystallizes in the rhombohedral Th2Zn17 type structure. The lattice parameters decrease when Sm substitutes Pr. Hence, the temperature dependence of the magnetization is determined. The Curie temperature increases from 285 K to 299 K after the Pr substitution. This increase in TC is mainly due to the de Gennes factor. The Arrott plot around second-order magnetic transition, magnetic entropy changes ΔSM, the relative cooling power, and temperature-averaged entropy change (TEC) are reported. This compound is considered a magnetic refrigerant for use at a low magnetic field based on these results.