Mesoscopic Regime Research Articles

Flux flow in current driven mesoscopic superconductors: size effects

Flux-flow phenomena in a superconducting mesoscopic stripe submitted to an applied current and external magnetic field is studied. The time-dependent Ginzburg-Landau equations are solved numerically to obtain the electric and magnetic response of the system. It is shown that the I-V curves, for the wider strips, present a universal behaviour. The dependence of the flux-flow resistivity on the magnetic field and width allow us to propose a criterion characterizing, both, the macroscopic and mesoscopic regimes. The power spectrum of the average voltage permits identifying the effect of surface currents in vortices movement. Based on the maximum value of the power spectrum first harmonic we propose a geometric condition for matching between the sample dimensions and the vortex lattice parameter.

Correlation between piezoresponse nonlinearity and hysteresis in ferroelectric crystals at the nanoscale

The nonlinear response of a ferroic to external fields has been studied for decades, garnering interest for both understanding fundamental physics, as well as technological applications such as memory devices. Yet, the behavior of ferroelectrics at mesoscopic regimes remains poorly understood, and the scale limits of theories developed for macroscopic regimes are not well tested experimentally. Here, we test the link between piezo-nonlinearity and local piezoelectric strain hysteresis, via AC-field dependent measurements in conjunction with hysteresis measurements with varying voltage windows on (K,Na)NbO3 crystals with band-excitation piezoelectric force microscopy. The correlation coefficient between nonlinearity amplitude and the amplitude during hysteresis loop acquisition shows a clear decrease with increasing AC bias. Further, correlation of polynomial fitting terms from the nonlinear measurements with the hysteresis loop area reveals that the largest correlations are reserved for the quadratic terms, which is expected for irreversible domain wall motion contributions that impact both piezoelectric behavior as well as minor loop formation. This study suggests applicability at local length scales of fundamental principles of Rayleigh behavior, with associated implications for future nanoscale ferroic devices.

A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

We use the coordinate Bethe ansatz to exactly calculate matrix elements between eigenstates of the Lieb–Liniger model of one-dimensional bosons interacting via a two-body delta-potential. We investigate the static correlation functions of the zero-temperature ground state and their dependence on interaction strength, and analyze the effects of system size in the crossover from few-body to mesoscopic regimes for up to seven particles. We also obtain time-dependent nonequilibrium correlation functions for five particles following quenches of the interaction strength from two distinct initial states. One quench is from the noninteracting ground state and the other from a correlated ground state near the strongly interacting Tonks–Girardeau regime. The final interaction strength and conserved energy are chosen to be the same for both quenches. The integrability of the model highly constrains its dynamics, and we demonstrate that the time-averaged correlation functions following quenches from these two distinct initial conditions are both nonthermal and moreover distinct from one another.

Condensate fluctuation and thermodynamics of mesoscopic Bose-Einstein condensates: A correlated many-body approach

We present a correlated many-body approach to calculate the distribution function and fluctuations for a Bose-Einstein condensate with $N$ interacting atoms in the harmonic confinement. The present formulation uses the recursion relation for the canonical ensemble partition function $(Z)$. $Z$ is calculated from the energy spectrum of the many-body effective potential, which keeps all possible two-body correlations and uses the realistic interatomic interaction. The condensate statistics are in very good agreement with earlier results of an ideal gas for which exact statistical moments for all temperature are known. We also present the numerical results of condensate statistics for real experimental situations. The calculated moments nicely exhibit the mesoscopic effect for a few hundred atoms, whereas the sharp fall in the variance for the large condensate near the critical temperature shows the possibility of phase transition. We also calculate the critical temperature for the mesoscopic regime. Our present calculation mimics the JILA experiment with $^{87}\mathrm{Rb}$ atoms.

Fluctuating Finite Element Analysis: Development and Applications to Cytoplasmic Dynein

The number of structures in the Electron Microscopy Database (EMDB) is growing rapidly due to improvements in cryo-electron microscopy and tomography [1]. This database is complementary to the Protein Data Base (PDB), in that it contains volumetric information about the overall shape of a biomolecule, rather than fully atomistic structures. Fluctuating Finite Element Analysis (FFEA) [2] is a new computer simulation technique that simulates the dynamic behaviour of bio-molecular structures in the EMDB, in an analogous manner to the use of atomistic molecular dynamics trajectories based on structures deposited in the PDB. As FFEA uses a continuum representation of biomolecules it has no upper length-scale limit, and provides access to mesoscopic regimes (50-1000nm) inaccessible to more detailed modelling techniques.To model the action of molecular motors using FFEA, we account for atomistic processes such as ATP binding, hydrolysis and changes in protein secondary structure by including them as instantaneous events occurring at a given rate. Coupling the temperature driven dynamics of the motor with the probability that a transition will occur ensures that the internal strain energy influences the rate of the chemical processes driving the action of the motor. We are currently applying this coupled simulation to cytoplasmic dynein, which is a dimeric molecular motor involved in intracellular cargo transport, to study how mechanical communication and gating between the two subunits enables the motor to walk without moving backwards, stalling or releasing from the microtubule completely.[1] Kuehlbrandt, W., The Resolution Revolution, Science. 2014, 343(6178), 1443-4.[2] Oliver, R. C., Read, D. J., Harlen, O. G. And Harris, S. A., A stochastic finite element model for the dynamics of globular macromolecules, J. Comp. Phys. 2013, 239, 147-65.

Mesoscopic transport and quantum chaos

The field of Quantum Chaos, addressing the quantum manifestations of an underlying classically chaotic dynamics, was developed in the early eighties, mainly from a theoretical perspective. Few experimental systems were initially recognized to exhibit the versatility of being sensitive, at the same time, to their classical and quantum dynamics. Rydberg atoms provided the main testing ground of Quantum Chaos concepts until the early nineties, marked by the development of microwave billiards, ultra-cold atoms in optical lattices, and low-temperature transport in mesoscopic semiconductor structures. The mesoscopic regime is attained in small condensed matter systems at sufficiently low temperatures for the electrons to propagate coherently across the sample. The quantum coherence of electrons, together with the ballistic motion characteristic of ultra-clean microstructures, motivated the proposal of mesocopic systems as a very special laboratory for performing measurements and testing the theoretical ideas of Quantum Chaos. Experimental realizations and many important developments, reviewed in this article, followed from such a connection.

Dissipative dynamics of quantum fluctuations

One way to look for complex behaviours in many‐body quantum systems is to let the number N of degrees of freedom become large and focus upon collective observables. Mean‐field quantities scaling as tend to commute, whence complexity at the quantum level can only be inherited from complexity at the classical level. Instead, fluctuations of microscopic observables scale as and exhibit collective Bosonic features, typical of a mesoscopic regime half‐way between the quantum one at the microscopic level and the classical one at the level of macroscopic averages. Here, we consider the mesoscopic behaviour emerging from an infinite quantum spin chain undergoing a microscopic dissipative, irreversible dynamics and from global states without long‐range correlations and invariant under lattice translations and dynamics. We show that, from the fluctuations of one site spin observables whose linear span is mapped into itself by the dynamics, there emerge bosonic operators obeying a mesoscopic dissipative dynamics mapping Gaussian states into Gaussian states. Instead of just depleting quantum correlations because of decoherence effects, these maps can generate entanglement at the collective, mesoscopic level, a phenomenon with no classical analogue that embodies a peculiar complex behaviour at the interface between micro and macro regimes.

Gelation Kinetics and Polymer Network Dynamics of Homogeneous Tetra‐PEG Gels

SummaryTetra‐PEG gels made via cross‐end‐coupling of tetra‐arm poly(ethylene glycol) chains having complementary functional groups have been recognized to have a very homogeneous network structure free from inhomogeneities and entanglements. Their unique network structure provides advanced mechanical properties, such as high deformability and toughness. The origin of these unique structure and properties is investigated from the viewpoints of gelation kinetics and polymer network dynamics. Spectroscopic studies on gelation kinetics of Tetra‐PEG gels indicate that the gelation kinetics is classified to reaction‐limited process, leading to formation of uniform polymer network with high yield. Polymer dynamics studied with neutron spin echo (NSE) and dynamic light scattering (DLS) shows that the dynamic is classified to Zimm mode in the microscopig regime (NSE window), and to collective diffusion mode in mesoscopic regime (DLS window). The crossover was found to correspond to the mesh size of the network. The absence of the offset in the intermediate scattering function also indicates homogeneity and uniformity of Tetra‐PEG gel networks.

Size-Dependent Silicon Epitaxy at Mesoscale Dimensions

New discoveries on collective processes in materials fabrication and performance are emerging in the mesoscopic size regime between the nanoscale, where atomistic effects dominate, and the macroscale, where bulk-like behavior rules. For semiconductor electronics and photonics, dimensional control of the architecture in this regime is the limiting factor for device performance. Epitaxial crystal growth is the major tool enabling simultaneous control of the dimensions and properties of such architectures. Although size-dependent effects have been studied for many small-scale systems, they have not been reported for the epitaxial growth of Si crystalline surfaces. Here, we show a strong dependence of epitaxial growth rates on size for nano to microscale radial wires and planar stripes. A model for this unexpected size-dependent vapor phase epitaxy behavior at small dimensions suggests that these effects are universal and result from an enhanced surface desorption of the silane (SiH4) growth precursor near facet edges. Introducing phosphorus or boron dopants during the silicon epitaxy further decreases the growth rates and, for phosphorus, gives rise to a critical layer thickness for single crystalline epitaxial growth. This previously unknown mesoscopic size-dependent growth effect at mesoscopic dimensions points to a new mechanism in vapor phase growth and promises greater control of advanced device geometries.

Absolute calibration of a charge-coupled device camera with twin beams

We report on the absolute calibration of a Charge-Coupled Device (CCD) camera by exploiting quantum correlation. This method exploits a certain number of spatial pairwise quantum correlated modes produced by spontaneous parametric-down-conversion. We develop a measurement model accounting for all the uncertainty contributions, and we reach the relative uncertainty of 0.3% in low photon flux regime. This represents a significant step forward for the characterization of (scientific) CCDs used in mesoscopic light regime.

Localization and field-periodic conductance fluctuations in trilayer graphene

We have systematically studied quantum transport in a short trilayer-graphene field-effect transistor. Close to the charge neutrality point, our magnetoconductance data are well described by the theory of weak localization in monolayer graphene. However, as the carrier density is increased we find a complex evolution of the low field magnetoconductance that originates from a combination of the monolayer-like and bilayer-like band structures. The increased phase coherence length at high hole densities takes our shortest devices into the mesoscopic regime with the appearance of significant conductance fluctuations on top of the localization effects. Although these are aperiodic in gate voltage, they exhibit a quasi-periodic behaviour as a function of magnetic field. We show that this is consistent with the interference of discrete trajectories in open quantum dots and discuss the possible origin of these in our devices.

Radial Epitaxy of Silicon for Optoelectronic Applications

At the heart of the dramatic transition in semiconductor device technology from planar to three-dimensional (3D) architectures is the ability to shrink devices to nanoscale dimensions with near atomic level control of materials’ structure and composition. The 3D structures serve as building blocks for high-performance electronic and photonic devices such as photovoltaic cells, light-emitting diodes, multi-gate field effect transistors and require unprecedented control in dimensions and materials properties. Epitaxial crystal growth, along with lithographic and etching technologies, provides one of the enabling approaches to create such structures. The standard for epitaxy in electronics technology is chemical vapor deposition (CVD) growth, which enables preparation of 3D semiconducting nanomaterials with modulated composition and electrical dopant profiles, with silicon (Si) epitaxy being arguably the world’s best studied crystal growth system. It is thus important to understand Si epitaxy on nanoscale structures, since any change in crystal growth kinetics at small sizes would have a large effect on dimensional control from a technological perspective and would also be of great interest from a fundamental perspective for understanding atomic scale processes and fabricating novel structures. We show that Si epitaxial growth at the nanoscale becomes size dependent at dimensions significantly larger than the onset of thermodynamic limits, and that this previously unknown behavior within the mesoscopic size regime for one of the best known crystal growth systems is a general phenomenon. A monotonic reduction in homoepitaxial growth rate with size is observed for facet widths below certain scale and the results modeled by an area-dependent precursor incorporation rate. The presence of n and p type dopants results in even greater reductions in low temperature radial growth rates, and a critical thicknesses for Si single crystal radial epitaxy is found for phosphorus. The results provide new insights on the nature of CVD crystal growth at small dimensions and have significant implications for 3D nanoscale fabrication of technologically important Si electronic device architectures. Si radial p-i-n junction nanowire structure is a suitable platform to integrate fundamental understanding and applications since the structure provides an approach for realizing concurrent maximization of light absorption and photogenerated carrier separation in photovoltaic (PV) devices. Additionally, NW arrays embedding radial p-(i)-n junctions enhance light absorption significantly in wide range of wavelengths. Si radial p-i-n junctions consisted of core Si NWs and Si shells. Core Si NWs were prepared by top-down consisting of lithographic technique and deep reactive ion etching. After formation of Si NWs, the color of Si substrate in NW regions turned to be black from shiny metallic surface. The change of color indicates enhanced light absorption in visible wavelengths. Electrically doped Si radial shell was prepared by epitaxial growth on the surfaces of Si NWs via low-pressure chemical vapor deposition. PV characteristics of crystalline Si radial p-i-n junction arrays prepared by top-down approach and epitaxial shell growth were investigated by current–voltage measurements under dark and Air Mass 1.5G conditions. Though the unoptimal dimensions of NWs and top electrode configuration, the open circuit voltage, short circuit current density, and photoconversion efficiency of the device were 0.46 V, 40 mA/cm2, and 10%, respectively. The high short circuit current density comparable to that of commercialized Si PV cell indicates that efficient photogenerated generation/collection is occurred in Si radial p-i-n junction.

The physics of quantum computation

Quantum computation has emerged in the past decades as a consequence of down-scaling of electronic devices to the mesoscopic regime and of advances in the ability of controlling and measuring microscopic quantum systems. Quantum computation has many interdisciplinary aspects, ranging from physics and chemistry to mathematics and computer science. In this paper, we focus on physical hardware, present day challenges and future directions for design of quantum architectures.

Free standing yttria-doped zirconia membranes: Geometrical effects on stability

Professor Arthur Nowick made seminal contributions to the areas of ionic conduction mechanisms in crystalline and disordered systems. An area of emerging interest in the solid state ionics community is investigating conduction in the mesoscopic regime. With free standing membranes, one can probe low-dimensional effects such as confinement without interference from substrates. Membranes have potential relevance to solid state devices that benefit from reduced ionic resistance, for example sensors and solid oxide fuel cells. Membranes with varying lateral dimensions have been previously reported in literature; however, understanding of stress interactions in suspended oxide structures is in early stages. In this paper, we demonstrate self-supported, i.e. in the absence of any additional mechanical support layers, square and circular membranes of 100 nm thick yttria-doped zirconia (YDZ) having side length and diameters of 0.15–2 mm. The buckled membrane shape is intimately linked to the fabrication processes arising from dry versus wet etching protocols. Geometrical considerations associated with buckling and stability are discussed. Thin film solid oxide fuel cells utilizing circular membranes are fabricated, exhibiting open circuit voltages between 0.8 and 1 V that correlate with membrane size and exhibit a total power output on the order of several mW. These results contribute to advancing experimental techniques to fabricate free standing oxide membranes for fundamental and applied studies pertaining to ionic and electronic conduction.

A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION

On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Spohn and Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.

Approach to structural anisotropy in compacted cohesive powder

We investigate the mesoscopic regime between microscopic particle properties and macroscopic bulk behavior and present a complementary approach of physical experiments and discrete element method simulations to explore the development of the microstructure of cohesive powders during compaction. On the experimental side, a precise micro shear tester $$(\mu \hbox {ST})$$ for very small powder samples has been developed and integrated into a high resolution X-ray microtomography (XMT) system. The combination of $$\mu \hbox {ST}$$ and XMT provides the unique possibility to access the 3D microstructure and the particle network inside manipulated powder samples experimentally. In simulations we explore the structural changes resulting from compaction: a Hertzian contact model is utilized for compaction of an isotropic initial configuration created by a geometrical algorithm. As a first result of this approach we present the analysis of the compaction of slightly cohesive $$\hbox {SiO}_2$$ particles with special regard to bulk density, heterogeneity, compaction law and structural anisotropy.

Multiple scattering of light in cold atomic clouds in a magnetic field

Starting from a microscopic theory for atomic scatterers, we describe the scattering of light by a single atom and study the coherent propagation of light in a cold atomic cloud in the presence of a magnetic field B in the mesoscopic regime. Non-pertubative expressions in B are given for the magneto-optical effects and optical anisotropy. We then consider the multiple scattering regime and address the fate of the coherent backscattering (CBS) effect. We show that, for atoms with nonzero spin in their ground state, the CBS interference contrast can be increased compared to its value when B=0, a result at variance with classical samples. We validate our theoretical results by a quantitative comparison with experimental data.

A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries

A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge–Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green–Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for isothermal systems. Verification of the SDPD-DV is achieved with simulations of transient, Poiseuille and Couette isothermal flow of liquid water between plates with heights of 10−5 m and 10−3 m. The velocity profiles from the SDPD-DV simulations are in very good agreement with analytical estimates and the field density fluctuation near solid boundaries is shown to be below 5%. Verification of SDPD-DV applied to domains with internal curved solid boundaries is accomplished with the simulation of a body-force driven, low-Reynolds number flow of water over a cylinder of radius R=0.02 m. The SDPD-DV field velocity and pressure compare favorably with those obtained by FLUENT. The results from these benchmark tests show that SDPD-DV is effective in reducing the density fluctuations near solid walls, enforces the no-slip condition, and prevents particle penetration. Scale-effects in SDPD-DV are examined with an extensive set of SDPD-DV isothermal simulations of liquid water and gaseous nitrogen in mesoscopic periodic domains. For the simulations of liquid water the mass of the fluid particles is varied between 1.24 and 3.3×107 real molecular masses and their corresponding size is between 1.08 and 323 physical length scales. For SDPD-DV simulations of gaseous nitrogen the mass of the fluid particles is varied between 6.37×103 and 6.37×106 real molecular masses and their corresponding size is between 2.2×102 and 2.2×103 physical length scales. The equilibrium states are obtained and show that the particle speeds scale inversely with particle mass (or size) and that the translational temperature is scale-free. The self-diffusion coefficient for liquid water is obtained through the mean-square displacement and the velocity auto-correlation methods for the range of fluid particle masses (or sizes) considered. Various analytical expressions for the self-diffusivity of the SDPD fluid are developed in analogy to the real fluid. The numerical results are in very good agreement with the SDPD-fluid analytical expressions. The numerical self-diffusivity is shown to be scale dependent. For fluid particles approaching asymptotically the mass of the real particle the self-diffusivity is shown to approach the experimental value. The Schmidt numbers obtained from the SDPD-DV simulations are within the range expected for liquid water.

Spatially dependent relative diffusion of nanoparticles in polymer melts

We formulate and apply a microscopic statistical-mechanical theory for the non-hydrodynamic relative diffusion coefficient of a pair of spherical nanoparticles in entangled polymer melts based on a combination of Brownian motion, mode-coupling, and polymer physics ideas. The focus is on the mesoscopic regime where particles are larger than the entanglement spacing. The dependence of the non-hydrodynamic friction on interparticle separation, degree of entanglement, and tube diameter is systematically studied. The overall magnitude of the relative diffusivity is controlled by the ratio of the particle to tube diameter and the number of entanglements in a manner reminiscent of single-particle self-diffusion and Stokes-Einstein violations. A rich spatial separation dependence of mobility enhancement relative to the hydrodynamic behavior is predicted even for very large particles, and the asymptotic dependence is derived analytically in the small and large separation limits. Particle separations in excess of 100 nm are sometimes required to recover the hydrodynamic limit. The effects of local polymer-particle packing correlations are found to be weak, and the non-hydrodynamic effects are also small for unentangled melts.

Observation of the Kibble–Zurek scaling law for defect formation in ion crystals

Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble-Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γ(β), where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.