De Gennes Research Articles

Josephson Critical Currents and Related Effects in Ultracold Atomic Superfluid Sytems

The Josephson and Proximity effects play a pivotal role in the design of superconducting devices for the implementation of quantum technology, ranging from the standard Al based to the more exotic twisted high-Tc junctions. Josephson critical currents have been recently investigated also in ultracold atomic systems where a potential barrier acts as a weak link. The unifying feature of the above systems, apart from being superconducting/superfluid, is the presence of spatial inhomogeneity, a feature that has to be properly taken into account in any theoretical approach employed to investigate them. In this work, we review the novel (dubbed LPDA for Local Phase Density Approximation) approach based on a coarse graining of the Bogoliubov–de Gennes (BdG) equations. Non-local and local forms of this coarse graining were utilized when investigating Proximity and Josephson effects. Moreover, the LPDA approach was further developed to include pairing fluctuations at the level of the non-self-consistent t-matrix approximation. The resulting approach, dubbed mLPDA (modified LPDA), can be used whenever inhomegeneity and fluctuations effects simultaneously play an important role.

Topological Defect Evolutions Guided by Varying the Initial Azimuthal Orientation

Topological defects are a key concern in numerous branches of physics. It is meaningful to exploit the topological defect evolutions during the phase transitions of condensed matter. Here, via varying the initial azimuthal orientation of the square alignment lattice in a hybrid cell, the topological defect evolution of liquid crystal during the nematic (N)–smectic A (SmA) phase transition is investigated. The director fields surrounding ±1 point defects are manipulated by predesigning the initial azimuthal orientation. When further cooled to the SmA phase, spiral toric focal conic domain (TFCD) arrays are formed as a result of twisted deformation suppression and unique symmetry breaking after the phase transition. The variation in the azimuthal orientation causes the TFCDs to degenerate from infinite rotational symmetry to quadruple rotational symmetry, thus releasing new textures for the SmA phase. Landau–de Gennes numerical modeling is adopted to reproduce the director distributions in the N phase and reveal the evolution of the topological defects. This work enriches the knowledge on the self-organization of soft matter, enhances the capability for the manipulations of topological defects, and may inspire new intriguing applications.

Bound States and Scattering of Magnons on a Superconducting Vortex in Ferromagnet-superconductor Heterostructures

We study the magnon spectrum in a thin ferromagnetic-superconductor heterostructure in the presence of a single superconducting vortex. We employ the Bogolubov–de Gennes Hamiltonian which describes the magnons in the presence of the stray magnetic field and the non-uniform magnetic texture induced by the vortex. We find that the vortex localizes magnon states approximately in the same way as a charge center produces electron bound states due to screened Coulomb interaction in the two-dimensional electron gas. The number of these localized states is substantially determined by the material parameters of the ferromagnetic film only. We solve the scattering problem for an incident plane spin wave and compute the total and transport cross sections. We demonstrate that the vortex-induced non-uniform magnetic texture in chiral ferromagnetic film produces a skew scattering of magnons. We explore the peculiarities of the quantum scattering problem that correspond to orbiting in the classical limit.

Superconducting density of states and vortex lattice of LaRu2P2 observed by scanning tunneling spectroscopy

We provide the superconducting density of states of the pnictide superconductor LaRu2P2(Tc= 4.1 K), measured using millikelvin scanning tunneling microscopy. From the tunneling conductance, we extract a density of states which shows the opening of a s-wave single superconducting gap. The temperature dependence of the gap also follows BCS theory. Under magnetic fields, vortices present Caroli de Gennes Matricon states, although these are strongly broadened by defect scattering. From the vortex core size we obtain a superconducting coherence length ofξ = 50 nm, compatible with the value extracted from macroscopicHc2measurements. We discuss the comparison between s-wave LaRu2P2and pnictide unconventional multiple gap and strongly correlated Fe based superconductors.

Inhomogeneous stripe phase and tunable Majorana zero modes in Rashba s-wave superconducting systems in the presence of in-plane Zeeman field

Based on the extended Bogoliubov–de Gennes theory, the inhomogeneous stripe order and Majorana bound states are demonstrated in s-wave superconducting systems with Rashba spin–orbit interaction when the in-plane Zeeman field is applied. For a fully open square sample, topological phase transitions can be driven by the Zeeman field, and the stripe phase with spatially oscillating order parameter shows up across a critical field strength. The topological channels arise in this phase, which can be utilized to create and manipulate Majorana zero modes. Interestingly, (quasi-)one-dimensional channels with diminished pairing amplitude can be formed in narrow arms of a square loop, accompanied by the reconstruction of energy spectra of the condensate and the realization of robust Majorana zero-energy states at the ends of channels. The associated evolution of topological phases and the location of Majorana zero modes are highly sensitive to the field direction. Moreover, the effects of the rectangular aspect-ratio and the off-centered hole as well as the surface defects on Majorana end modes are explored in Rashba asymmetric loops. In comparison, the field-dependent evolution processes of low-energy levels behave more complicated because the emergence of confined topological channels can be effectively tuned by the length and width of loop arms as well as the size and position of an introduced small indentation at the outer edge. Rich patterns of Majorana corner-like states are generated for such asymmetric systems. Our theoretical predictions may shed new light on the tunability of Majorana zero modes and provide useful guidance for future experiments and applications.

Twist elastic constant of chiral nematic cellulose nanocrystals determined by tactoid reconfiguration in electric field

Lyotropic chiral nematic cellulose nanocrystals (CNCs) have attracted significant attention and great progress has been made. Investigating their physical parameters, especially the twist elastic constant (K22), is pivotal for advancing our comprehension of fundamental viscoelastic property of chiral nematic phase. In this study, we demonstrate a straightforward method to simultaneously estimate K22 and helical twisting power (Kt) of chiral nematic CNCs. This method involves analyzing rheology properties and electro-response of CNCs, focusing on the rotational dynamics and structural reconfiguration of CNC tactoids under an electric field. By examining the rotation dynamics of CNC tactoids under an electric field, together with the viscosity characterization, the anisotropic dielectric susceptibility (∆χ) of chiral nematic CNC along the helix axis was determined. Subsequently, K22/∆χn was extracted by analyzing CNC tactoid pitch evolution under an electric field, employing the de Gennes model. The K22 for different concentrated CNCs is finally estimated by integrating experimental results and theory. It is shown that the chiral nematic CNCs present concentration-dependent K22, ranging from 0.05 to 0.14 pN, while Kt spans from 0.06 to 0.14 pN/μm. This study offers a comprehensive understanding of the CNC fundamental viscoelastic property and opens up new avenues for K22 measurement in other lyotropic liquid crystals.

Microscopic solutions for vortex clustering in two-band type-1.5 superconductors

Two-band superconductors exhibit a distinct phase characterized by two correlation lengths, one smaller and the other larger than the magnetic field penetration length. This regime was coined type-1.5 superconductivity, with several unconventional properties, such as vortex clustering. However, a fully microscopic solution for vortex clusters has remained challenging due to computational complexities beyond quasiclassical models. This work presents numerical solutions obtained in a fully self-consistent two-band Bogoliubov–de Gennes model. We show the presence of discrepant correlation lengths leading to vortex clustering in two-band superconductors. Published by the American Physical Society 2024

Effect of arm-length polydispersity on the phase behaviour of V-shaped molecules

Phase behaviour of a melt of polydisperse V-shaped particles is considered within the Landau theory of phase transitions. It is assumed that particles are composed of two semi-flexible segments, one of which has a constant length, while the other has an arbitrary length distribution; the segments are joined at an external angle. The contributions up to the sixth order into the Landau–de Gennes free energy expansion in terms of the alignment tensor are presented in a diagrammatic form. The phase diagrams have been obtained for a special case characterised by rigid segments and Schulz–Zimm distribution for the length of the segment. It is shown that an increase in the polydispersity index of the segment leads to an increase of the isotropic–nematic transition temperature, substantial increase of the stability region of a uniform biaxial nematic ( N B ) phase, and a decrease in the area occupied by a uniform oblate nematic phase.

Manipulating chiral Majorana mode with additional potential in superconductor-Chern insulator heterostructures

We employed the self-consistent Bogoliubov–de Gennes equations to explore the states of chiral Majorana mode in quantum anomalous Hall insulators in proximity to a superconductor, leading to the development of an extensive topological phase diagram. Our investigation focused on how an additional potential affects the separation of chiral Majorana modes across different phase conditions. We substantiated our findings by examining the zero-energy Local Density of States spectrum and the probability distribution of the chiral Majorana modes. We established the universality of chiral Majorana mode separation by applying an additional potential. This finding serves as a vital resource for future endeavors aimed at controlling and detecting these particles, thereby contributing to the advancement of quantum computing and condensed matter physics.

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Minimizers for the de Gennes–Cahn–Hilliard energy under strong anchoring conditions

AbstractIn this article, we use the Nehari manifold and the eigenvalue problem for the negative Laplacian with Dirichlet boundary condition to analytically study the minimizers for the de Gennes–Cahn–Hilliard energy with quartic double‐well potential and Dirichlet boundary condition on the bounded domain. Our analysis reveals a bifurcation phenomenon determined by the boundary value and a bifurcation parameter that describes the thickness of the transition layer that segregates the binary mixture's two phases. Specifically, when the boundary value aligns precisely with the average of the pure phases, and the bifurcation parameter surpasses or equals a critical threshold, the minimizer assumes a unique form, representing the homogeneous state. Conversely, when the bifurcation parameter falls below this critical value, two symmetric minimizers emerge. Should the boundary value be larger or smaller from the average of the pure phases, symmetry breaks, resulting in a unique minimizer. Furthermore, we derive bounds of these minimizers, incorporating boundary conditions and features of the de Gennes–Cahn–Hilliard energy.

Wetting Effect Induced Depletion and Adsorption Layers: Diffuse Interface Perspective.

When a multi-component fluid contacts arigid solid substrate, the van der Waals interaction between fluids and substrate induces a depletion/adsorption layer depending on the intrinsic wettability of the system. In this study, we investigate the depletion/adsorption behaviors of A-B fluid system. We derive analytical expressions for the equilibrium layer thickness and the equilibrium composition distribution near the solid wall, based on the theories of de Gennes and Cahn. Our derivation is verified through phase-field simulations, wherein the substrate wettability, A-B interfacial tension, and temperature are systematically varied. Our findings underscore two pivotal mechanisms governing the equilibrium layer thickness. With an increase in the wall free energy, the substrate wettability dominates the layer formation, aligning with de Gennes' theory. When the interfacial tension increases, or temperature rises, the layer formation is determined by the A-B interactions, obeying Cahn's theory. Additionally, we extend our study to non-equilibrium systems where the initial composition deviates from the binodal line. Notably, macroscopic depletion/adsorption layers form on the substrate, which are significantly thicker than the equilibrium microscopic layers. This macroscopic layer formation is attributed to the interplay of phase separation and Ostwald ripening. We anticipate that the present finding could deepen our knowledge on the depletion/adsorption behaviors of immiscible fluids.

Andreev reflection, Andreev states, and long ballistic SNS junction

The analysis in the present paper is based on the most known concept introduced by the brilliant physicist Alexander Andreev: Andreev bound states in a normal metal sandwiched between two superconductors. The paper presents results of direct calculations of ab initio expressions for the currents in a long ballistic SNS junction. The expressions are expanded in 1/L (L is the thickness of the normal layer). The main contribution ∝1/L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\propto 1/L$$\\end{document} to the current agrees with the results obtained in the past, but the analysis suggests a new physical picture of the charge transport through the junction free from the problem with the charge conservation law. The saw-tooth current-phase relation at T=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=0$$\\end{document} directly follows from the Galilean invariance of the Bogolyubov–de Gennes equations proved in the paper. The proof is valid for any variation of the energy gap in space if the Andreev reflection is the only scattering process. The respective roles of the contributions of bound and continuum states to the current are clarified. They depend on the junction dimensionality.

Geometric modeling of phase ordering for the isotropic–smectic A phase transition

BackgroundLiquid crystal (LC) mesophases have an orientational and positional order that can be found in both synthetic and biological materials. These orders are maintained until some parameter, mainly the temperature or concentration, is changed, inducing a phase transition. Among these transitions, a special sequence of mesophases has been observed, in which priority is given to the direct smectic liquid crystal transition. The description of these transitions is carried out using the Landau–de Gennes (LdG) model, which correlates the free energy of the system with the orientational and positional order.MethodologyThis work explored the direct isotropic-to-smectic A transition studying the free energy landscape constructed with the LdG model and its relation to three curve families: (I) level-set curves, steepest descent, and critical points; (II) lines of curvature (LOC) and geodesics, which are directly connected to the principal curvatures; and (III) the Casorati curvature and shape coefficient that describe the local surface geometries resemblance (sphere, cylinder, and saddle).ResultsThe experimental data on 12-cyanobiphenyl were used to study the three curve families. The presence of unstable nematic and metastable plastic crystal information was found to add information to the already developed smectic A phase diagram. The lines of curvature and geodesics were calculated and laid out on the energy landscape, which highlighted the energetic pathways connecting critical points. The Casorati curvature and shape coefficient were computed, and in addition to the previous family, they framed a geometric region that describes the phase transition zone.Conclusion and significanceA direct link between the energy landscape’s topological geometry, phase transitions, and relevant critical points was established. The shape coefficient delineates a stability zone in which the phase transition develops. The methodology significantly reduces the impact of unknown parametric data. Symmetry breaking with two order parameters (OPs) may lead to novel phase transformation kinetics and droplets with partially ordered surface structures.

Polymer physics view of peripheral chromatin: de Gennes' self-similar carpet.

Using scaling arguments to model peripheral chromatin localized near the inner surface of the nuclear envelope (NE) as a flexible polymer chain, we discuss the structural properties of the peripheral chromatin composed of alternating lamin-associated domains (LADs) and inter-LADs. Modeling the attraction of LADs to NE by de Gennes' self-similar carpet, which treats the chromatin layer as a polymer fractal, explains two major experimental observations. (i) The high density of chromatin close to the nuclear periphery decays to a constant density as the distance to the periphery increases. (ii) Due to the decreasing mesh size towards the nuclear periphery, the chromatin carpet inside NE excludes molecules (via nonspecific interactions) above a threshold size that depends on the distance from the nuclear periphery.

Hidden symmetry of Bogoliubov de Gennes quasi-particle eigenstates and universal relations in flat band superconducting bipartite lattices

Unconventional flat band (FB) superconductivity, as observed in van der Waals heterostructures, could open promising avenues towards high-T_cc materials. In FBs, pairings and superfluid weight scale linearly with the interaction parameter, such an unusual behaviour justifies and encourages strategies to promote FB engineering. Bipartite lattices (BLs) which naturally host FBs could be particularly interesting candidates. Within Bogoliubov de Gennes theory and in the framework of the attractive Hubbard model in BLs, a hidden symmetry of the quasi-particle eigenstates is revealed. As a consequence, we demonstrate universal relations for the pairings and the superfluid weight that are independent of the characteristics of the hopping term. Remarkably, it is shown that these general properties are insensitive to disorder as long as the bipartite character is protected.

Temperature-dependent storage modulus of polymer nanocomposites, blends and blend-based nanocomposites based on percolation and De Gennes’s self-similar carpet theories

Temperature-dependent storage modulus of polymer nanocomposites, blends and blend-based nanocomposites based on percolation and De Gennes’s self-similar carpet theories

Theoretical models for the nematic twist-bend phase and the Landau de Gennes theory of Longa and Tomczyk

ABSTRACT We present a critical analysis of the existing phenomenological theories of the nematic twist-bend phase including the models proposed by Dozov and Selinger and the more general Landau de Gennes theory of L. Longa and W. Tomczyk. The role of the flexoelectric polarisation is considered in detail as well as the stabilisation of the nanoscale helical structure of the twist-bend phase. In particular we focus into the mechanism of the reduction of the bend elastic constant determined by negative flexoelectric corrections and discuss why the splay elastic constant is not reduced at all. A molecular theory of elasticity of bent-core nematics, which also enables one to describe the reduction of the bend elastic constant, is considered in detail as well. Finally we consider two different tensor orientational order parameters of the twist-bend phase which describe all kinds of uniaxial and local biaxial ordering of bent-core molecules in the twist-bend phase.

Ensemble structure of the N-terminal domain (1–267) of FUS in a biomolecular condensate

Solutions of some proteins phase separate into a condensed state of high protein concentration and a dispersed state of low concentration. Such behavior is observed in living cells for a number of RNA-binding proteins that feature intrinsically disordered domains. It is relevant for cell function via the formation of membraneless organelles and transcriptional condensates. On a basic level, the process can be studied in vitro on protein domains that are necessary and sufficient for liquid-liquid phase separation (LLPS). We have performed distance distribution measurements by electron paramagnetic resonance for 13 sections in an N-terminal domain (NTD) construct of the protein fused in sarcoma (FUS), consisting of the QGSY-rich domain and the RGG1 domain, in the denatured, dispersed, and condensed state. Using 10 distance distribution restraints for ensemble modeling and three such restraints for model validation, we have found that FUS NTD behaves as a random-coil polymer under good-solvent conditions in both the dispersed and condensed state. Conformation distribution in the biomolecular condensate is virtually indistinguishable from the one in an unrestrained ensemble, with the latter one being based on only residue-specific Ramachandran angle distributions. Over its whole length, FUS NTD is slightly more compact in the condensed than in the dispersed state, which is in line with the theory for random coils in good solvent proposed by de Gennes, Daoud, and Jannink. The estimated concentration in the condensate exceeds the overlap concentration resulting from this theory. The QGSY-rich domain is slightly more extended, slightly more hydrated, and has slightly higher propensity for LLPS than the RGG1 domain. Our results support previous suggestions that LLPS of FUS is driven by multiple transient nonspecific hydrogen bonding and π−sp2 interactions.

Melted grain boundaries in smectic A under imposed bend: role of the anisotropy

ABSTRACT The well-known de Gennes analogy between smectics and superconductors predicts two types of smectic A behaviour under imposed bend. In Type I smectics, the smectic order melts, expelling all of the bend in a bulk nematic region (3D ‘defect’). In Type II smectics, the order melts on 1D defects, edge dislocation lines, which form an Abrikosov-like lattice. Here, I discuss how the strong anisotropy of the smectic coherence lengths influence the smectic A behaviour under imposed bend distortion. I show analytically and numerically that, as proposed previously, a third type of behaviour is possible close to a second-order nematic–smectic A transition, with smectic order melting on the plane of the grain boundary (2D defects). This third kind of behaviour, Melted Grain Boundary (MGB), which has been previously reported experimentally in the smectic A material 9CB, is intermediate between the Type I and Type II behaviours and can be considered as Type ‘one-and-a-half’ smectic A. I define the domain of material parameters in which the planar MGB defect is energetically and topologically stable. I discuss also if similar planar defects may exist, or not, in other anisotropic materials, e.g. superconductors, chiral smectic A, cholesterics and twist-bend nematics.