Ballistic Regime Research Articles

Know the enemy: 2D Fermi liquids

We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

A fast synthetic iterative scheme for the stationary phonon Boltzmann transport equation

The heat transfer in solid materials at the micro- and nano-scale can be described by the mesoscopic phonon Boltzmann transport equation (BTE), rather than the macroscopic Fourier’s heat conduction equation that works only in the diffusive regime. The implicit discrete ordinate method (DOM) is efficient to find steady-state solutions to the BTE for highly non-equilibrium heat transfer problems, but converges extremely slowly in the near-diffusive regime. In this paper, a fast synthetic iterative scheme is developed to expedite convergence for the implicit DOM. The key innovative point of the present scheme is the introduction of a macroscopic diffusion-type equation for the temperature variation, which is exactly derived from the phonon BTE and valid for all Knudsen numbers. The synthetic equation, which is asymptomatically preserving to Fourier’s heat conduction equation in the diffusive regime, contains a term related to Fourier’s law and a term determined by the second-order moment of the distribution function that reflects the non-Fourier heat transfer. The mesoscopic kinetic equation and macroscopic diffusion-type equations are tightly coupled, because the macroscopic equation provides the temperature for the BTE, while the BTE provides a high-order moment to the diffusion-type equation. This synthetic iterative scheme strengthens the coupling of phonons with different wave vectors in the phase space to facilitate fast convergence from the diffusive to ballistic regimes. Typical numerical tests in one-, two-, and three-dimensional problems demonstrate that our scheme can describe the multiscale heat transfer problems accurately and efficiently. For all test cases, the present convergence is one to three orders of magnitude faster than the traditional implicit DOM in the near-diffusive regime.

Ballistic Graphene Cooper Pair Splitter.

We report an experimental study of a Cooper pair splitter based on ballistic graphene multiterminal junctions. In a two transverse junction geometry, namely the superconductor-graphene-superconductor and the normal metal-graphene-normal metal, we observe clear signatures of Cooper pair splitting in the local as well as nonlocal electronic transport measurements. Our experimental data can be very well described by our beam splitter model. These results open up possibilities to design new entangled state detection experiments using ballistic Cooper pair splitters.

Klein tunneling through the trapezoidal potential barrier in graphene: conductance and shot noise

When a single-layer graphene sheet is contacted with metallic electrodes, tunnel barriers are formed as a result of the doping of graphene by the metal in the contact region. If the Fermi energy level is modulated by a gate voltage, the phenomenon of Klein tunneling results in specific features in the conductance and noise. Here we obtain analytically exact solutions for the transmission and reflection probability amplitudes using a trapezoidal potential barrier, allowing us to calculate the differential conductance and the Fano factor for a graphene sheet in the ballistic regime. We put in evidence an unexpected global symmetry—the transmission probability is the same for energies symmetric with respect to half of the barrier height. We outline a proposal for the experimental verification of these ideas using realistic sample parameters.

Cosmic ray propagation in the Universe in presence of a random magnetic field

The origin of the ultrahigh energy cosmic ray remains being a mystery. However, aconsiderable progress has been made in the past few years due to the good quality data recordedby current cosmic ray observatories. One of the recent achievements is obtaining firm observationalevidence about the extragalactic origin of the most energetic cosmic rays by the Pierre Augerobservatory. On the other hand, it is believed that there is a non-null turbulent magnetic fieldthat fills the intergalactic medium. Therefore, the presence of the intergalactic magnetic fieldcan play an important role on the propagation of the ultrahigh energy cosmic rays through theUniverse, which in principle can be relevant to interpret the experimental data. In this work wepresent a system of partial differential equations that describes the propagation of the ultrahighenergy cosmic rays through the Universe, in the presence of a turbulent intergalactic magnetic field,that includes the diffusive and the ballistic regime of propagation and also the transition betweenthem. Also, as an example of application, the system of equations is solved numerically in asimplified physical situation.

Anomalous diffusion in nonlinear transformations of the noisy voter model.

Voter models are well known in the interdisciplinary community, yet they have not been studied from the perspective of anomalous diffusion. In this paper, we show that the original voter model exhibits a ballistic regime. Nonlinear transformations of the observation variable and time scale allow us to observe other regimes of anomalous diffusion as well as normal diffusion. We show that numerical simulation results coincide with derived analytical approximations describing the temporal evolution of the raw moments.

Orientational Pair Correlations and Local Structure of Benzonitrile from Molecular Dynamics Simulations with Comparisons to Experiments.

We present an experimentally parametrized molecular dynamics study of single-molecule and collective orientational relaxation in neat benzonitrile through the analysis of the reorientational anisotropy and polarizability anisotropy time correlation function (PA-TCF). The simulations show that the PA-TCF is dominated by collective reorientation after 20 ps. Collective reorientation is found to be slower than single-molecule reorientation by a factor of 1.67, consistent with recent experiments. The simulations provide direct evidence of local antiparallel benzonitrile configurations. These structures, which have been the center of some debate, are responsible for the slower rate of collective versus single-molecule reorientation in the liquid. Further structural analysis indicates that significant Coulombic interactions between the nitrile group and hydrogen atoms on adjacent molecules play a role in the formation of the antiparallel structures. The single-molecule dynamics reflected in the anisotropy are complex and consist of a ballistic regime, restricted angular diffusion, and spatially anisotropic free diffusion. The principal components of the rotational diffusion tensor are independently obtained and shown to reproduce the free diffusion regime of the anisotropy for each principal axis according to the predictions of a previous theory.

Coherent Electronic Transport in Periodic Crystals

We consider independent electrons in a periodic crystal in their ground state, and turn on a uniform electric field at some prescribed time. We rigorously define the current per unit volume and study its properties using both linear response and adiabatic theory. Our results provide a unified framework for various phenomena such as the quantification of Hall conductivity of insulators with broken time-reversibility, the ballistic regime of electrons in metals, Bloch oscillations in the long-time response of metals, and the static conductivity of graphene. We identify explicitly the regime in which each holds.

Hydrodynamic and Ballistic Transport over Large Length Scales in GaAs/AlGaAs.

We study hydrodynamic and ballistic transport regimes through nonlocal resistance measurements and high-resolution kinetic simulations in a mesoscopic structure on a high-mobility two-dimensional electron system in a GaAs/AlGaAs heterostructure. We evince the existence of collective transport phenomena in both regimes and demonstrate that negative nonlocal resistances and current vortices are not exclusive to only the hydrodynamic regime. The combined experiments and simulations highlight the importance of device design, measurement schemes, and one-to-one modeling of experimental devices to demarcate various transport regimes.

The worm-LBM, an algorithm for a high number of propagation directions on a lattice Boltzmann grid: The case of phonon transport

The lattice Boltzmann method (LBM) is a numerical approach to tackle problems described by a Boltzmann type-equation, where time, space, and velocities are discretized to describe scattering and advection. Even though the LBM executes advection along a lattice direction without numerical error, its usage in the high Knudsen number regime (ballistic) has been hindered by the ray effect problem (for dimensions greater than 1D). This problem has its origin in the low number of available propagation directions on standard LBM lattices. Here, to overcome this limitation, we propose the worm-lattice Boltzmann method (worm-LBM), which allows a high number of lattice directions by alternating in time the basic directions described within the next neighbor schemes. Additionally, to overcome the velocity anisotropy issue, which otherwise clearly manifests itself in the ballistic regime (e.g. the 2 higher grid velocity of the D2Q8 scheme along the diagonal direction compared to the axial one), the time-adaptive scheme (TAS) is proposed. The TAS method makes use of pausing advection on the grid, allowing to impose not only isotropic propagation but also arbitrary direction-dependent grid velocity. Last but not least, we propose a grid-mean free path (grid-MFP) correction to correctly handle the aforementioned velocity issue in the diffusive limit, without affecting the ballistic one. We provide a detailed description of the TAS method and the worm-LBM algorithm, and verify their numerical accuracy by using several transient diffusive-ballistic phonon transport cases, including different initial and boundary conditions. We demonstrate the accuracy of the new worm-LBM to describe problems where a high angular resolution (i.e. a high number of propagation directions) is required, as the in-plane thermal transport problem under adiabatic-diffusive boundary conditions. In this particular case, we show that schemes with a low number of propagation directions (D2Q8) result in an overestimation of the analytical Fuchs-Sondheimer solution for intermediate and high Knudsen numbers, and that schemes with a higher number of propagation directions are required to correctly describe the problem. Overall, the new, very accurate, and efficient worm-LBM algorithm, free of numerical smearing and false scattering, has the potential to be at the forefront of the numerical solvers to tackle the advective part of different equations in a wide field of applications.

Fluctuation and dissipation within a deformed holographic model with backreaction

In this work we study the fluctuation and dissipation of a string attached to a brane in a deformed and backreacted AdS-Schwarzschild spacetime. This space is a solution of Einstein-dilaton equations and contains a conformal exponential factor exp⁡(k/r2) in the metric. We consider the backreaction contributions coming only from the exponential warp factor on the AdS-Schwarzschild black hole, where the string and brane are in the probe approximation. Within this Lorentz invariant holographic model we have computed the admittance, the diffusion coefficient, the two-point functions and the regularized mean square displacement sreg2. From this quantity we obtain the diffuse and ballistic regimes characteristic of the Brownian motion. From the two-point functions and the admittance, we also have checked the well know fluctuation-dissipation theorem in this set up.

Surface Diffusion by Means of Stochastic Wave Functions. The Ballistic Regime

Stochastic wave function formalism is briefly introduced and applied to study the dynamics of open quantum systems; in particular, the diffusion of Xe atoms adsorbed on a Pt(111) surface. By starting from a Lindblad functional and within the microscopic Caldeira–Leggett model for linear dissipation, a stochastic differential equation (Ito^-type differential equation) is straightforwardly obtained. The so-called intermediate scattering function within the ballistic regime is obtained, which is observable in Helium spin echo experiments. An ideal two-dimensional gas has been observed in this regime, leading to this function behaving as a Gaussian function. The influence of surface–adsorbate interaction is also analyzed by using the potential of two interactions describing flat and corrugated surfaces. Very low surface coverages are considered and, therefore, the adsorbate–adsorbate interaction is safely neglected. Good agreement is observed when our numerical results are compared with the corresponding experimental results and previous standard Langevin simulations.

Collision dominated, ballistic, and viscous regimes of terahertz plasmonic detection by graphene

The terahertz detection performance and operating regimes of graphene plasmonic field-effect transistors (FETs) were investigated by a hydrodynamic model. Continuous wave detection simulations showed that the graphene response sensitivity is similar to that of other materials including Si, InGaAs, GaN, and diamond-based FETs. However, the pulse detection results indicated a very short response time, which favors rapid/high-sensitively detection. The analysis on the mobility dependence of the response time revealed the same detection regimes as the traditional semiconductor materials, i.e., the non-resonant (collision dominated) regime, the resonant ballistic regime, and the viscous regime. When the kinematic viscosity (ν) is above a certain critical viscosity value, νNR, the plasmonic FETs always operates in the viscous non-resonant regime, regardless of channel length (L). In this regime, the response time rises monotonically with the increase of L. When ν < νNR, the plasmonic resonance can be reached in a certain range of L (i.e., the resonant window). Within this window, the carrier transport is ballistic. For a sufficiently short channel, the graphene devices would always operate in the non-resonant regime, regardless of the field-effect mobility, corresponding to another viscous regime. The above work mapped the operating regimes of graphene plasmonic FETs and demonstrated the significance of the viscous effects for the graphene plasmonic detection. These results could be used for the extraction of the temperature dependences of viscosity in graphene.

Non-Destructive Label-Free Biomaterials Detection Using Tunneling Carbon Nanotube-Based Biosensor

Label-free monitoring of biomaterials has become spotlight topic for the advanced nano-biosensing fields. In this regard, a non-destructive doping-less tunneling carbon nanotube field effect transistor (DL-TCNTFET) -based biosensor using the charge plasma concept is introduced. In doping-less structures, source and drain are created using the concept of charge plasma and by selecting appropriate work function of source and drain metals. The sensitivity of DL-TCNTFET is investigated in terms of dielectric constant variations at different bias conditions. The simulation is carried out in the ballistic regime by simultaneously solving the Poisson and Schrodinger equations in a self-consistent way using the non-equilibrium Green's function in the form of state space approach. Simulations show that the DL-TCNTFET has better ambipolar behavior and also lower OFF current by reducing the dielectric constant of biomolecules. In addition, the ON current and biosensor sensitivity are significantly improved by increasing the dielectric constant.

Mapping current profiles of point-contacted graphene devices using single-spin scanning magnetometer

We demonstrate two-dimensional mapping of current flow in graphene devices by using a single-spin scanning magnetometer based on a nitrogen-vacancy defect center in diamond. We first image the stray magnetic field generated by the current and then reconstruct the current density map from the field data. We focus on the visualization of current flow around a small sized current source of ∼500 nm diameter, which works as an effective point contact. In this paper, we study two types of point-contacted graphene devices and find that the overall current profiles agree with the expected behavior of electron flow in the diffusive transport regime. This work could offer a route to explore interesting carrier dynamics of graphene including ballistic and hydrodynamic transport regimes.

Diffusion Transitions in a 2D Periodic Lattice

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional ``soft'' billiard, classically modeled from an optical lattice hamiltonian system, is used to study diffusion transitions with the control parameters variation. Sudden transitions between normal and ballistic regimes are found and characterized by inspection of the topological changes in phase-space. Transitions correlated with increases in global stability area are shown to occur for energy levels where local maxima points become accessible, deviating trajectories approaching it. These instabilities promote a slowing down of the dynamics and an island myriad bifurcation phenomenon, along with the suppression of long flights within the lattice. Other diffusion regime variations occurring during small intervals of control parameters are shown to be related to the emergence of a set of orbits with long flights, thus altering the total average displacement for long integration times but without global changes in phase-space.

Phonon transport in graphene based materials.

Graphene, due to its atomic layer structure, has the highest room temperature thermal conductivity k for all known materials. Thus, it is expected that graphene based materials are the best candidates for thermal management in next generation electronic devices. In this perspective, we first review the in-plane k of monolayer graphene and multilayer graphene obtained using experimental measurements, theoretical calculations and molecular dynamics (MD) simulations. Considering the importance of four-phonon scattering in graphene, we also compare the effects of three-phonon and four-phonon scattering on phonon transport in graphene. Then, we review phonon transport along the cross-plane direction of multilayer graphene and highlight that the cross-plane phonon mean free path is several hundreds of nanometers instead of a few nanometers as predicted using classical kinetic theory. Recently, hydrodynamic phonon transport has been observed experimentally in graphitic materials. The criteria for distinguishing the hydrodynamic from ballistic and diffusive regimes are discussed, from which we conclude that graphene based materials with a high Debye temperature and high anharmonicity (due to ZA modes) are excellent candidates to observe the hydrodynamic phonon transport. In the fourth part, we review how to actively control phonon transport in graphene. Graphene and graphite are often adopted as additives in thermal management materials such as polymer nanocomposites and thermal interface materials due to their high k. However, the enhancement of the composite's k is not so high as expected because of the large thermal resistance between graphene sheets as well as between the graphene sheet and matrix. In the fifth part, we discuss the interfacial thermal resistance and analyze its effect on the thermal conductivity of graphene based materials. In the sixth part, we give a brief introduction to the applications of graphene based materials in thermal management. Finally, we conclude our review with some perspectives for future research.

Photoacoustic Imaging.

Photoacoustic imaging (PAI) is an emerging imaging modality that shows great potential for preclinical research and clinical practice. As a hybrid technique, PAI uniquely combines the advantages of optical excitation and of acoustic detection. Optical excitation provides a rich contrast mechanism from either endogenous or exogenous chromophores, allowing PAI to perform biochemical, functional, and molecular imaging. Acoustic detection benefits from the low scattering of ultrasound in biological tissue, enabling PAI to generate high-resolution images in both the optical ballistic and diffusive regimes. Accordingly, this hybrid imaging modality features high sensitivity to optical absorption and wide scalability of spatial resolution with the desired imaging depth. Over the past two decades, the photoacoustic technique has led to a variety of exciting discoveries and applications from laboratory research to clinical patient care. In biological research, PAI has become an irreplaceable tool, providing functional optical contrast with high spatiotemporal resolution. Translational PAI also attracted growing interest in clinical applications including tumor margin examination, internal organ imaging, breast cancer screening, and sentinel lymph node mapping, among others.

Баллистическое течение двумерных электронов в магнитном поле

In conductors with a very small density of defects, electrons at low temperatures collide predominantly with a sample edges. Therefore, the ballistic regime of charge and heat transport is realized. The application of a perpendicular magnetic field substantially modifies the character of ballistic transport. For the case of two-dimensional (2D) electrons in the magnetic fields corresponding to the diameter of the cyclotron trajectories smaller than the sample width a hydrodynamic transport regime is formed. In the latter regime, the flow is mainly controlled by rare electron–electron collisions, which determine the viscosity effect. In this work, we study the ballistic flow of 2D electrons in long samples in magnetic fields up to the critical field of the transition to the hydrodynamic regime. From solution of the kinetic equation, we obtain analytical formulas for the profiles of the current density and the Hall electric field far and near the ballistic-hydrodynamic transition as well as for the longitudinal and Hall resistances in these ranges. Our theoretical results, apparently, describe the observed longitudinal resistance of pure graphene samples in the diapason of magnetic fields below the ballistic-hydrodynamic transition.

Non-Fourier heat transport across 1D nano film between thermal reservoirs with different boundary resistances

We describe the nonlocal heat transport across a thin film in contact with two thermal baths using discrete variable model. The effective thermal conductivities , the boundary temperature jumps, the steady-state heat flux, and the internal temperature gradient are calculated analytically as functions of the film size and the boundary resistances. As the system size decreases, all the parameters demonstrate the transition from diffusive (Fourier) heat conduction when the scattering occurs mainly inside the film to ballistic transport when scattering occurs at the boundaries, while inside the film there is no scattering and the temperature profile is flat. We show that when the boundary resistance increases, the temperature profile inside the film also tends to be flat, but in this case the scattering, though small, occurs inside the film. The predicted effective thermal conductivity is consistent with classical continuous theories and available experimental data. • We consider heat transport across 1D nano film. • Discrete variable model has been used. • Effective thermal conductivity is size and resistance dependent. • Transition to ballistic regime is described.