Paramagnetic Singularities of the Orbital Magnetism in Graphene with a Moiré Potential.

The recent detection of the singular diamagnetism of Dirac electrons in a single graphene layer paved a new way of probing 2D quantum materials through the measurement of equilibrium orbital currents which cannot be accessed in usual transport experiments. Among the theoretical predictions is an intriguing orbital paramagnetism at saddle points of the dispersion relation. Here we present magnetization measurements in graphene monolayers aligned on hexagonal boron nitride crystals. Besides the sharp diamagnetic McClure response at the Dirac point, we detect extra diamagnetic singularities at the satellite Dirac points of the moiré lattice. Surrounding these diamagnetic satellite peaks, we also observe paramagnetic peaks located at the chemical potential of the saddle points of the graphene moiré band structure and relate them to the presence of van Hove logarithmic singularities in the density of states. These findings reveal the long ago predicted anomalous paramagnetic orbital response in 2D systems when the Fermi energy is tuned to the vicinity of saddle points.

Spin-Orbit-Enhanced Robustness of Supercurrent in Graphene/WS_{2} Josephson Junctions.

We demonstrate the enhanced robustness of the supercurrent through graphene-based Josephson junctions in which strong spin-orbit interactions (SOIs) are induced. We compare the persistence of a supercurrent at high out-of-plane magnetic fields between Josephson junctions with graphene on hexagonal boron-nitride and graphene on WS_{2}, where strong SOIs are induced via the proximity effect. We find that in the shortest junctions both systems display signatures of induced superconductivity, characterized by a suppressed differential resistance at a low current, in magnetic fields up to 1 T. In longer junctions, however, only graphene on WS_{2} exhibits induced superconductivity features in such high magnetic fields, and they even persist up to 7 T. We argue that these robust superconducting signatures arise from quasiballistic edge states stabilized by the strong SOIs induced in graphene by WS_{2}.

Microwave Signature of Topological Andreev level Crossings in a Bismuth-based Josephson Junction.

Demonstrating the topological protection of Andreev states in Josephson junctions is an experimental challenge. In particular the telltale 4π periodicity expected for the current phase relation has remained elusive, because of fast parity breaking processes. It was predicted that low temperature ac susceptibility measurements could reveal the topological protection of quantum spin Hall edge states by probing their low energy Andreev spectrum at finite frequency. We have performed such a microwave probing of a phase-biased Josephson junction built around a bismuth nanowire, a predicted second order topological insulator, and which was previously shown to host one-dimensional ballistic edge states. We find absorption peaks at the Andreev level crossings, whose temperature and frequency dependencies point to protected topological crossings with an accuracy limited by the electronic temperature of our experiment.

Strong Anisotropic Spin-Orbit Interaction Induced in Graphene by Monolayer WS_{2}.

We demonstrate strong anisotropic spin-orbit interaction (SOI) in graphene induced by monolayer WS_{2}. Direct comparison between graphene-monolayer WS_{2} and graphene-bulk WS_{2} systems in magnetotransport measurements reveals that monolayer transition metal dichalcogenide can induce much stronger SOI than bulk. Detailed theoretical analysis of the weak antilocalization curves gives an estimated spin-orbit energy (E_{so}) higher than 10 meV. The symmetry of the induced SOI is also discussed, and the dominant z→-z symmetric SOI can only explain the experimental results. Spin relaxation by the Elliot-Yafet mechanism and anomalous resistance increase with temperature close to the Dirac point indicates Kane-Mele SOI induced in graphene.

Dissipation and supercurrent fluctuations in a diffusive normal-metal-superconductor ring.

A mesoscopic hybrid normal-metal-superconductor ring is characterized by a dense Andreev spectrum with a flux dependent minigap. To probe the dynamics of such a ring, we measure its linear response to a high frequency flux, in a wide frequency range, with a multimode superconducting resonator. We find that the current response contains, besides the well-known dissipationless Josephson contribution, a large dissipative component. At high frequency compared to the minigap and low temperature, we find that the dissipation is due to transitions across the minigap. In contrast, at lower frequency there is a range of temperature for which dissipation is caused predominantly by the relaxation of the Andreev states' population. This dissipative response, related via the fluctuation dissipation theorem to a nonintuitive zero frequency thermal noise of supercurrent, is characterized by a phase dependence dominated by its second harmonic, as predicted long ago but never observed thus far.

Detection of graphene's divergent orbital diamagnetism at the Dirac point.

The electronic properties of graphene have been intensively investigated over the past decade. However, the singular orbital magnetism of undoped graphene, a fundamental signature of the characteristic Berry phase of graphene's electronic wave functions, has been challenging to measure in a single flake. Using a highly sensitive giant magnetoresistance (GMR) sensor, we have measured the gate voltage­dependent magnetization of a single graphene monolayer encapsulated between boron nitride crystals. The signal exhibits a diamagnetic peak at the Dirac point whose magnetic field and temperature dependences agree with long-standing theoretical predictions. Our measurements offer a means to monitor Berry phase singularities and explore correlated states generated by the combined effects of Coulomb interactions, strain, or moiré potentials.

Conductance fluctuations and field asymmetry of rectification in graphene.

We investigate conductance fluctuations as a function of carrier density n and magnetic field in diffusive mesoscopic samples made from monolayer and bilayer graphene. We show that the fluctuations' correlation energy and field, which are functions of the diffusion coefficient, have fundamentally different variations with n, illustrating the contrast between massive and massless carriers. The field dependent fluctuations are nearly independent of n, but the n-dependent fluctuations are not universal and are largest at the charge neutrality point. We also measure the second-order conductance fluctuations (mesoscopic rectification). Its field asymmetry, due to electron-electron interaction, decays with conductance, as predicted for diffusive systems.

Transport and elastic scattering times as probes of the nature of impurity scattering in single-layer and bilayer graphene.

Transport and elastic scattering times, tau{tr} and tau{e}, are experimentally determined from the carrier density dependence of the magnetoconductance of monolayer and bilayer graphene. Both times and their dependences on carrier density are found to be very different in the monolayer and the bilayer. However, their ratio tau{tr}/tau{e} is found to be close to 1.8 in the two systems and nearly independent of the carrier density. These measurements give insight on the nature (neutral or charged) and range of the scatterers. Comparison with theoretical predictions suggests that the main scattering mechanism in our samples is due to strong (resonant) scatterers of a range shorter than the Fermi wavelength, likely candidates being vacancies, voids, adatoms or short-range ripples.

Proximity-induced superconductivity in DNA.

Conductivity measurements on double-stranded DNA molecules deposited by a combing process across a submicron slit between rhenium/carbon metallic contacts reveal conduction to be ohmic between room temperature and 1 kelvin. The resistance per molecule is less than 100 kilohm and varies weakly with temperature. Below the superconducting transition temperature (1 kelvin) of the contacts, proximity-induced superconductivity is observed. These results imply that DNA molecules can be conducting down to millikelvin temperature and that phase coherence is maintained over several hundred nanometers.

A three-dimensional model for ciliary motion based on the internal 9+2 structure.

Here we present, to our knowledge, the first modelling platform that enables simulations of three-dimensional (3D) motion of multicilia arrays at a detailed level. It consists of three building blocks: (i) geometric equations for tracking the 3D motion of the cilia, (ii) a hydrodynamic description of the ciliary system, and (iii) model equations for the internal bend generating based on the 9 + 2 structure. The model generates seemingly realistic 3D beat patterns and demonstrates metachronal coordination that evolves autonomously as a result of the hydrodynamic coupling between the cilia. We study the effect of the twisting motion within the cilia and propose a conjecture on a possible role of the radial spokes system.

The dynamics of group formation.

A general continuous model is presented for animal group size distribution. Attention is restricted to a fixed size population divided into groups of various dynamic sizes, but the approach extends easily to populations of variable size. The basic idea is to relate group size distribution to two functions, the (density-dependent) rates of fusion and fission. These functions can be estimated from data and can ultimately be related to the behavior of individuals and the dynamics of groups. For various functional forms, the stationary distributions of group sizes are sought. In several prototype cases, the stationary distribution has a peak value, the "most frequent group size," which emerges endogenously from the dynamics. The authors determine when such a peak emerges and more generally show the existence and uniqueness of the stationary distribution. Stability of stationary solutions is discussed. Progress is shown, but a general treatment remains refractory.

Probing the dynamics of Andreev states in a coherent normal/superconducting ring.

The supercurrent that establishes between two superconductors connected through a normal N mesoscopic link is carried by quasiparticule states localized within the link, the "Andreev bound states (ABS)". Whereas the dc properties of this supercurrent in SNS junctions are now well understood, its dynamical properties are still an unresolved issue. In this letter we probe this dynamics by inductively coupling an NS ring to a multimode superconducting resonator, thereby implementing both a phase bias and current detection at high frequency. Whereas at very low temperatures we essentially measure the phase derivative of the supercurrent, at higher temperature we find a surprisingly strong frequency dependence in the current response of the ring: the ABS do not follow adiabatically the phase modulation. This experiment also illustrates a new tool to probe the fundamental time scales of phase coherent systems that are decoupled from macroscopic normal contacts and thermal baths.

Geometrical dependence of decoherence by electronic interactions in a GaAs/GaAlAs square network.

We investigate weak localization in metallic networks etched in a two-dimensional electron gas between 25 and 750 mK when electron-electron (e-e) interaction is the dominant phase breaking mechanism. We show that, at the highest temperatures, the contributions arising from trajectories that wind around the rings and trajectories that do not are governed by two different length scales. This is achieved by analyzing separately the envelope and the oscillating part of the magnetoconductance. For T > or approximately 0.3 K we find L phi env proportional T(-1/3) for the envelope and L phi osc proportional, T(-1/2) for the oscillations, in agreement with the prediction for a single ring [T. Ludwig and A. D. Mirlin, Phys. Rev. B 69, 193306 (2004); 10.1103/PhysRevB.69.193306C. Texier and G. Montambaux, Phys. Rev. B 72, 115327 (2005); 10.1103/PhysRevB.72.115327C. Texier, Phys. Rev. B76, 153312 (2007)10.1103/PhysRevB.76.153312]. This is the first experimental confirmation of the geometry dependence of decoherence due to e-e interaction.

Simulations of three-dimensional ciliary beats and cilia interactions.

A new set of equations describing the time evolution of torsion and curvature for an inextensible curve is developed. Combined with our recently developed Slender Body Theory approach to such problems, these equations were applied to simulate three-dimensional ciliary beats, while allowing for cilia interactions. The computer animation technique, which was originally designed to display two-dimensional beats, has been enhanced to accommodate the new three-dimensional results.

A model of herd grazing as a travelling wave, chemotaxis and stability.

Possible constitutive models are examined for the formation of a herd, under the assumption that a herd forms a travelling wave while grazing. Under quite general conditions, it is found that the only possibility for a travelling wave is a balance between food seeking and natural dispersion, such as in chemotaxis. The stability of the travelling wave previously conjectured, is shown both for one- and two-dimensional perturbations.

Ciliary motion modeling, and dynamic multicilia interactions.

This paper presents a rigorous and accurate modeling tool for ciliary motion. The hydrodynamics analysis, originally suggested by Lighthill (1975), has been modified to remove computational problems. This approach is incorporated into a moment-balance model of ciliary motion in place of the previously used hydrodynamic analyses, known as Resistive Force Theory. The method is also developed to include the effect of a plane surface at the base of the cilium, and the effect of the flow fields produced by neighboring cilia. These extensions were not possible with previous work using the Resistive Force Theory hydrodynamics. Performing reliable simulations of a single cilium as well as modeling multicilia interactions is now possible. The result is a general method which could now be used for detailed modeling of the mechanisms for generating ciliary beat patterns and patterns of metachronal interactions in arrays of cilia. A computer animation technique was designed and applied to display the results.

Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions.

This paper presents a simple and reasonable method for generating a phenomenological model of the internal mechanism of cilia. The model uses a relatively small number of parameters whose values can be obtained by fitting to ciliary beat shapes. Here, we use beat patterns observed in Paramecium. The forces that generate these beats are computed and fit to a simple functional form called the "engine." This engine is incorporated into a recently developed hydrodynamic model that accounts for interactions between neighboring cilia and between the cilia and the surface from which they emerge. The model results are compared to data on ciliary beat patterns of Paramecium obtained under conditions where the beats are two-dimensional. Many essential features of the motion, including several properties that are not built in explicitly, are shown to be captured. In particular, the model displays a realistic change in beat pattern and frequency in response to increased viscosity and to the presence of neighboring cilia in configurations such as rows of cilia and two-dimensional arrays of cilia. We found that when two adjacent model cilia start beating at different phases they become synchronized within several beat periods, as observed in experiments where two flagella are brought into close proximity. Furthermore, examination of various multiciliary configurations shows that an approximately antiplectic wave pattern evolves autonomously. This modeling evidence supports earlier conjectures that metachronism may occur, at least partially, as a self-organized phenomenon due to hydrodynamic interactions between neighboring cilia.

Energetic considerations of ciliary beating and the advantage of metachronal coordination.

The internal mechanism of cilia is among the most ancient biological motors on an evolutionary scale. It produces beat patterns that consist of two phases: during the effective stroke, the cilium moves approximately as a straight rod, and during the recovery stroke, it rolls close to the surface in a tangential motion. It is commonly agreed that these two phases are designed for efficient functioning: the effective stroke encounters strong viscous resistance and generates thrust, whereas the recovery stroke returns the cilium to starting position while avoiding viscous resistance. Metachronal coordination between cilia, which occurs when many of them beat close to each other, is believed to be an autonomous result of the hydrodynamical interactions in the system. Qualitatively, metachronism is perceived as a way for reducing the energy expenditure required for beating. This paper presents a quantitative study of the energy expenditure of beating cilia, and of the energetic significance of metachronism. We develop a method for computing the work done by model cilia that beat in a viscous fluid. We demonstrate that for a single cilium, beating in water, the mechanical work done during the effective stroke is approximately five times the amount of work done during the recovery stroke. Investigation of multicilia configurations shows that having neighboring cilia beat metachronally is energetically advantageous and perhaps even crucial for multiciliary functioning. Finally, the model is used to approximate the number of dynein arm attachments that are likely to occur during the effective and recovery strokes of a beat cycle, predicting that almost all of the available dynein arms should participate in generating the motion.