Transport In Low-dimensional Systems Research Articles

Analysis of ballistic transport and resonance in the α-Fermi-Pasta-Ulam-Tsingou model.

Ballistic transport and resonance phenomena are elucidated in the one-dimensional α-Fermi-Pasta-Ulam-Tsingou (FPUT) model using an approach of computing thermal response functions. The existence of periodic oscillations in spatially sinusoidal temperature profiles seen in previous studies is confirmed. However, the results obtained using response functions enable a more complete understanding. In particular, it is shown that resonance involves beats between normal modes which tend to reinforce in a one-dimensional chain. Anharmonic scattering acts to destroy phase coherence across the statistical ensemble, and with increasing anharmonicity, transport is driven toward the diffusive regime. These results provide additional insight into anomalous heat transport in low-dimensional systems. Normal-mode scattering is also explored using time correlation functions. Interestingly, these calculations, in addition to demonstrating loss of phase coherence across an ensemble of simulations, appear to show evidence of so-called q-breathers in conditions of strong anharmonicity. Finally, we describe how the approach outlined here could be developed to include quantum statistics and also also first-principles estimates of phonon scattering rates to elucidate second sound and ballistic transport in realistic materials at low temperatures.

Anomalous transport in low-dimensional systems: A pedagogical overview

This manuscript contains the notes of the lectures given in July 2021 at the Summer School “Fundamental Problems in Statistical Physics XV”, Bruneck, Italy. A pedagogical approach has been adopted by first providing the students a summary of the basic concepts of non-equilibrium statistical mechanics associated with transport processes. A detailed account about anomalous heat transport in anharmonic lattices is the first research topic described in these lecture notes. The interest of these results for material science is then highlighted, in order to point out the applicative potentials of anomalous transport in nanostructures, polymers etc. Further details about anomalous transport phenomena are reported in the presence of a magnetic field or of long-range interactions. A large section of these lecture notes is devoted to the theoretical approaches adopted for obtaining a consistent description of anomalous transport phenomena, including recent achievements that point out the crucial importance of finite-size effects on theoretical predictions and, accordingly, on experimental verifications. The final section is devoted to a summary about coupled transport in low-dimensional systems and the consequences of the presence of anomalous diffusion processes in this complex scenario. The appendices provide additional information about transport in basic 1d models (harmonic chains and rotor model), in 2d lattices and about integrable nonlinear models.

Dephasing-enhanced performance in quasiperiodic thermal machines

Understanding and controlling quantum transport in low-dimensional systems is pivotal for heat management at the nanoscale. One promising strategy to obtain the desired transport properties is to engineer particular spectral structures. In this work we are interested in quasiperiodic disorder - incommensurate with the underlying periodicity of the lattice - which induces fractality in the energy spectrum. A well known example is the Fibonacci model which, despite being non-interacting, yields anomalous diffusion with a continuously varying dynamical exponent smoothly crossing over from superdiffusive to subdiffusive regime as a function of potential strength. We study the finite-temperature electric and heat transport of this model in linear response in the absence and in the presence of dephasing noise due to inelastic scattering. The dephasing causes both thermal and electric transport to become diffusive, thereby making thermal and electrical conductivities finite in the thermodynamic limit. Thus, in the subdiffusive regime it leads to enhancement of transport. We find that the thermal and electric conductivities have multiple peaks as a function of dephasing strength. Remarkably, we observe that the thermal and electrical conductivities are not proportional to each other, a clear violation of Wiedemann-Franz law, and the position of their maxima can differ. We argue that this feature can be utilized to enhance performance of quantum thermal machines. In particular, we show that by tuning the strength of the dephasing noise we can enhance the performance of the device in regimes where it acts as an autonomous refrigerator.

Observation of anomalous heat transport in a trapped ion chain

Energy transport in low-dimensional systems or systems with long-range interactions shows unusual properties not observed in conventional three-dimensional materials. Trapped linear ion chains have been proposed as an ideal platform to study such phenomena, but many predicted features have not been demonstrated yet and the existing experiments mainly focus on the weak excitation limit where the dynamics can be described by linearized phonon modes. Here, we study the energy transport in a chain of $^{174}\mathrm{Yb}^{+}$ ions using a focused heating laser beam. Nontrivial effects are observed such as a nonmonotonic energy distribution with reflection symmetry, oscillatory heating dynamics, and a change in the heating pattern due to the competition between the external driving and interion coupling. Our work deepens the understanding about transport in low-dimensional systems and also provides guidelines for the sympathetic cooling of long ion chains, with applications in quantum information processing and precision measurement.

Energy transport and diffusion in low-dimensional lattices

Scientific studies in many disciplines have entered the low-dimensional mesoscopic world. This creates a valuable chance for not only improving near-equilibrium statistical mechanics, but also investigating the foundations of statistical mechanics, establishing thermodynamics and statistical mechanics for small systems, and developing the theory of nonequilibrium systems far from the equilibrium state. Predicting transport coefficients, as a main task of the near-equilibrium statistical mechanics, was formally fulfilled in the 1960-1970s, Green-Kubo formula which bridges the states of equilibrium and nonequilibrium. The Green-Kubo formula has played a crucial role in understanding nonequilibrium transport processes though so far only qualitatively, as the exact values of a systems transport coefficients cannot be worked out explicitly given the systems Hamiltonian. A quantitative description of transport behavior, therefore, is still required. Specifically, the “last mile” problem remains unsolved, and is still the bottleneck of near-equilibrium theory. Encouragingly, though, achievements in recent years may lead to a breakthrough in the near future. On one hand, the rapid development of computing technology has made it possible to effectively investigate the dynamics of nonlinear lattices, providing an important method of studying transports; on the other hand, various low-dimensional materials have now been synthesized in laboratories. With the help of advanced measurement and testing techniques, it has also become possible to perform experimental studies of transport in low-dimensional systems; theoretical results can be checked directly, which could in turn stimulate new ideas for improving theories. In addition, some theoretical approaches, such as nonlinear fluctuation hydrodynamics and wave turbulence theories, have been successfully applied to transport and diffusion studies—there are more effective theoretical tools available now than ever before. We therefore anticipate a first-principle formula that gives transport coefficients explicitly by solving the Green-Kubo formula based on microscopic dynamics. In the last four decades, thermal transport and diffusion in one-dimensional lattices has been studied intensively and extensively by researchers all over the world, and many insights have been obtained. In this work, we review the advances made by the group in Xiamen University—the most important of which being the discovered relation between heat conduction behavior and symmetry of internal interaction potential. We find that the latter both affects the exponent of the power-law decaying tail of the thermal current correlation function (TCCF) that characterizes hydrodynamic transport and dominates rapid decay behavior due to the kinetic process. When the potential is asymmetric, at certain temperatures and nonlinear interaction strength regions, the TCCF may decay by several orders due to the kinetic process exclusively, resulting in system size-independent heat conductivity such that the Fourier heat conduction law is obeyed formally. In contrast, when the potential is symmetric, though the TCCF still undergoes rapid decay in the kinetic process stage, the rate of decay rate can be much lower than exponential, leading to a system size-dependent heat conductivity. If, besides internal interactions, the system is also subject to any on-site potentials, its heat conductivity will converge to a finite constant, as the total momentum is not conserved in this case, and the TCCF in general only decays exponentially. These findings demonstrate that the kinetic process plays a crucial role not only in a fluid, but also in a lattice, which must be taken into account for calculating transport coefficients; in other words, a complete transport theory must be established on the basis of both kinetics and hydrodynamics. In addition, we review the general laws followed by the energy equipartition process in lattices and their deep connections with the transport behavior, in addition to several novel effects observed in coupled transport.

Characterization of low-resistance ohmic contacts to a two-dimensional electron gas in a GaAs/AlGaAs heterostructure

The study of electron transport in low-dimensional systems is of importance, not only from a fundamental point of view, but also for future electronic and spintronic devices. In this context heterostructures containing a two-dimensional electron gas (2DEG) are a key technology. In particular GaAs/AlGaAs heterostructures, with a 2DEG at typically 100 nm below the surface, are widely studied. In order to explore electron transport in such systems, low-resistance ohmic contacts are required that connect the 2DEG to macroscopic measurement leads at the surface. Here we report on designing and measuring a dedicated device for unraveling the various resistance contributions in such contacts, which include pristine 2DEG series resistance, the 2DEG resistance under a contact, the contact resistance itself, and the influence of pressing a bonding wire onto a contact. We also report here a recipe for contacts with very low resistance values that remain below 10 Ω for annealing times between 20 and 350 s, hence providing the flexibility to use this method for materials with different 2DEG depths. The type of heating, temperature ramp rate and gas forming used for annealing is found to strongly influence the annealing process and hence the quality of the resulting contacts.

Excitation of Propagating Plasmons in a Periodic Graphene Structure by Incident Terahertz Waves

Plasmonic transport is considered as a replacement for electronic transport in low-dimensional systems like field-effect transistors, as plasmons are faster than electrons. Plasmons in graphene are promising for use at THz frequencies, but this research is held back by the primitive state of circuitry for plasmonic devices. This study employs an asymmetric periodic grating to solve the problem of effective excitation of propagating plasmons in graphene. The important role of ``dark'' (weakly radiative) plasmon modes in efficient excitation is revealed. The approach outlined here could help to fill the need for THz plasmon sources, for tomorrow's devices.

Advances in Quantum Transport in Low Dimensional Systems

PrefaceThe conference titled, “Advances in Quantum Transport in Low Dimensional Systems (AQT2017)” was held at University College London, during September 4-5, 2017. The conference was organised by the Institute of Physics (IOP) Nanoscale Physics and Technology Group, and was sponsored by the Oxford Instruments (primary sponsor), National Instruments, Nanomagnetics Instruments, Zurich Instruments, University College London, Specs, IOP Nanoscale Physics and Technology Group and IOP Quantum Electronics and Photonics Group.The idea of organising a conference dedicated to advances in the transport in low dimensional systems came from the fact that advances in fabrication of solid state systems have reached the limit in which quantum effects cannot be ignored anymore. This has opened new perspectives for the development of new fundamental physics and products for commercial applications. Due to the rapid development of quantum technologies active collaboration between theory, experiment and industry is essential to meet the future demands. In solid state quantum technologies, there are a number of challenges, at the level of both theory and experiments, which need to be discussed openly in a platform shared by theorists, experimentalists and industry people.

Spin current induced by a charged tip in a quantum point contact

We show that the charged tip of the probe microscope, which is widely used in studying the electron transport in low-dimensional systems, induces a spin current. The effect is caused by the spin–orbit interaction arising due to an electric field produced by the charged tip. The tip acts as a spin-flip scatterer giving rise to the spin polarization of the net current and the occurrence of a spin density in the system.

Interplay between Mechanical and Electronic Degrees of Freedom in π-Stacked Molecular Junctions: From Single Molecules to Mesoscopic Nanoparticle Networks

Functionalized nanoparticle networks offer a model system for the study of charge transport in low-dimensional systems as well as a potential platform to implement and test electronic functionalities. The electrical response of a nanoparticle network is expected to sensitively depend on the molecular interconnects, i.e., on the linker chemistry. If these linkers have complex charge transport properties, then phenomenological models addressing the large-scale properties of the network need to be complemented with microscopic calculations of the network building blocks. In this study we focus on the interplay between conformational fluctuations and electronic π-stacking in single-molecule junctions and use the obtained microscopic information on their electrical transport properties to parametrize transition rates describing charge diffusion in mesoscopic nanoparticle networks. Our results point out the strong influence of mechanical degrees of freedom on the electronic transport signatures of the studied molecules. This is then reflected in the varying charge diffusion at the network level. The modeling studies are complemented with first charge transport measurements at the single-molecule level of π-stacked molecular dimers using state-of-the-art mechanically controllable break junction techniques in a liquid environment.

Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory

Heat transport in low-dimensional systems has attracted enormous attention from both theoretical and experimental aspects due to its significance to the perception of fundamental energy transport theory and its potential applications in the emerging field of phononics: manipulating heat flow with electronic anologs. We consider the heat conduction of one-dimensional nonlinear lattice models. The energy carriers responsible for the heat transport have been identified as the renormalized phonons. Within the framework of renormalized phonons, a phenomenological theory, effective phonon theory, has been developed to explain the heat transport in general one-dimensional nonlinear lattices. With the help of numerical simulations, it has been verified that this effective phonon theory is able to predict the scaling exponents of temperature-dependent thermal conductivities quantitatively and consistently.

Anomalous heat conduction and anomalous diffusion in low dimensional nanoscale systems

Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental rule of heat transfer in solids. It states that the thermal conductivity is independent of sample scale and geometry. Although Fourier's law has received great success in describing macroscopic thermal transport in the past two hundreds years, its validity in low dimensional systems is still an open question. Here we give a brief review of the recent developments in experimental, theoretical and numerical studies of heat transport in low dimensional systems, include lattice models, nanowires, nanotubes and graphenes. We will demonstrate that the phonon transports in low dimensional systems super-diffusively, which leads to a size dependent thermal conductivity. In other words, Fourier's law is breakdown in low dimensional structures.

Tuning thermal transport in nanotubes with topological defects

Using the atomistic nonequilibrium Green’s function, we find that thermal conductance of carbon nanotubes with presence of topological lattice imperfects is remarkably reduced, due to the strong Rayleigh scattering of high-frequency phonons. Phonon transmission across multiple defects behaves as a cascade scattering based with the random phase approximation. We elucidate that phonon scattering by structural defects is related to the spatial fluctuations of local vibrational density of states (LVDOS). An effective method of tuning thermal transport in low-dimensional systems through the modulation of LVDOS has been proposed. Our findings provide insights into experimentally controlling thermal transport in nanoscale devices.

Few-photon transport in low-dimensional systems

We analyze the role of quantum interference effects induced by an embedded two-level system on the photon transport properties in waveguiding structures that exhibit cutoffs (band edges) in their dispersion relation. In particular, we demonstrate that these systems invariably exhibit single-particle photon-atom bound states and strong effective nonlinear responses on the few-photon level. Based on this, we find that the properties of these photon-atom bound states may be tuned via the underlying dispersion relation and that their occupation can be controlled via multiparticle scattering processes. This opens an interesting route for controlling photon transport properties in a number of solid-state-based quantum optical systems and the realization of corresponding functional elements and devices.

Scattering matrix approach to multichannel transport in many lead graphenenanoribbons

Multichannel analysis of graphene nanoribbons (GNR), often required for describingapplications to practical devices, constitutes a heavy computational task, even in asimplified framework like that provided by discrete or nearest neighbour models. Scattering(S) matrix techniques, widely used for quantum transport in low dimensional systems andfor the computation of electromagnetic fields, is shown here to provide a powerful formalplatform for the analysis, and, in principle, the synthesis, of GNR multiport circuits.Periodic modes, solutions of GNR waveguides, are demonstrated to obey chargeconservation and reciprocity constraints corresponding to unitary and symmetryproperties of the S-matrix, under proper normalization conditions. We propose asystematic use of this approach to deal with problems such as scattering by latticedefects, the presence of external applied fields, crossing GNRs and T-junctions.

Few-Photon Transport in Low-Dimensional Systems: Interaction-Induced Radiation Trapping

We present a detailed analysis of the dynamics of photon transport in waveguiding systems in the presence of a two-level system. In these systems, quantum interference effects generate a strong effective optical nonlinearity on the few-photon level. We clarify the relevant physical mechanisms through an appropriate quantum many-body approach. Based on this, we demonstrate that a single-particle photon-atom bound state with an energy outside the band can be excited via multiparticle scattering processes. We further show that these trapping effects are robust and, therefore, will be useful for the control of photon entanglement in solid-state based quantum-optical systems.

Heat transport in low-dimensional systems

Recent results on theoretical studies of heat conduction in low-dimensional systems are presented. These studies are on simple, yet nontrivial, models. Most of these are classical systems, but some quantum-mechanical work is also reported. Much of the work has been on lattice models corresponding to phononic systems, and some on hard particle and hard disc systems. A recently developed approach, using generalized Langevin equations and phonon Green's functions, is explained and several applications to harmonic systems are given. For interacting systems, various analytic approaches based on the Green-Kubo formula are described, and their predictions are compared with the latest results from simulation. These results indicate that for momentum-conserving systems, transport is anomalous in one and two dimensions, and the thermal conductivity kappa, diverges with system size L, as kappa ~ L^alpha. For one dimensional interacting systems there is strong numerical evidence for a universal exponent alpha =1/3, but there is no exact proof for this so far. A brief discussion of some of the experiments on heat conduction in nanowires and nanotubes is also given.

Superlattice Nanowire Pattern Transfer (SNAP)

During the past 15 years or so, nanowires (NWs) have emerged as a new and distinct class of materials. Their novel structural and physical properties separate them from wires that can be prepared using the standard methods for manufacturing electronics. NW-based applications that range from traditional electronic devices (logic and memory) to novel biomolecular and chemical sensors, thermoelectric materials, and optoelectronic devices, all have appeared during the past few years. From a fundamental perspective, NWs provide a route toward the investigation of new physics in confined dimensions. Perhaps the most familiar fabrication method is the vapor-liquid-solid (VLS) growth technique, which produces semiconductor nanowires as bulk materials. However, other fabrication methods exist and have their own advantages. In this Account, I review a particular class of NWs produced by an alternative method called superlattice nanowire pattern transfer (SNAP). The SNAP method is distinct from other nanowire preparation methods in several ways. It can produce large NW arrays from virtually any thin-film material, including metals, insulators, and semiconductors. The dimensions of the NWs can be controlled with near-atomic precision, and NW widths and spacings can be as small as a few nanometers. In addition, SNAP is almost fully compatible with more traditional methods for manufacturing electronics. The motivation behind the development of SNAP was to have a general nanofabrication method for preparing electronics-grade circuitry, but one that would operate at macromolecular dimensions and with access to a broad materials set. Thus, electronics applications, including novel demultiplexing architectures; large-scale, ultrahigh-density memory circuits; and complementary symmetry nanowire logic circuits, have served as drivers for developing various aspects of the SNAP method. Some of that work is reviewed here. As the SNAP method has evolved into a robust nanofabrication method, it has become an enabling tool for the investigation of new physics. In particular, the application of SNAP toward understanding heat transport in low-dimensional systems is discussed. This work has led to the surprising discovery that Si NWs can serve as highly efficient thermoelectric materials. Finally, we turn toward the application of SNAP to the investigation of quasi-one-dimensional (quasi-1D) superconducting physics in extremely high aspect ratio Nb NWs.

Electronic properties of carbon nanotubes investigated by means of standard electromagnetic simulators

Due to the formal analogy between Maxwell and Schr\"odinger equations, electromagnetic (e.m.) simulators may become a powerful numerical tool for the analysis of carrier transport in low-dimensional systems. In the following, we exploit this analogy in order to investigate the electronic properties of carbon nanotubes (CNTs). As a matter of fact, e.m. commercial solvers have reached a high degree of efficiency due to the demand of the high-speed and microwave circuit market. In this paper, we suggest applying e.m. numerical solvers to CNTs with a view to derive their main properties, such as dispersion curves and effective masses. In particular, we have used the ``CST Microwave Studio,'' implementing a finite element method (FEM). However, many other e.m. solvers are available, exploiting different approaches (FDTD, Method of Moment, TLM, etc.). In order to assess the validity of the approach, we have investigated an important example of band-gap distortion and splitting of degenerate states with respect to the angular momentum, due to an external electric field. The model can also be applied in order to better explain the behavior of metal-CNT contacts, representing a critical point for analysis and synthesis of nanotransistor devices.

Time-Dependent Transport in Low-Dimensional Systems—A Numerical Solution Using the Nonequilibrium Green's Functions

In this paper, we present a novel numerical solution to analyze time-dependent transport in low-dimensional systems, such as one-dimensional (1-D) quantum dot and quasi-one-dimensional (Q1D) carbon nanotube systems, by using the nonequilibrium Green's functions (NEGF). The novelty of proposed approach is to jointly handle the NEGF in both the time-domain and the real-space-domain in a recursive fashion. The time-domain recursive approach is a straightforward approach to solve time-dependent transport problems, while the real-space recursive approach makes the calculations feasible for arbitrary-length 1-D and Q1D systems. To verify our proposed algorithm, we apply this method to explore the transient and ac transport properties of a sample 1-D quantum-dot array system. We will present in this paper the simulated electrical current curves, J (t), in response to various pulses and sinusoid waveforms. From these simulation results, we can obtain the delay and distortion information. We will then discuss how the length of a quantum-dot array and the hopping energy affect the transport behavior. The knowledge we gain from this project will help researchers to evaluate the electrical properties of 1-D and Q1D materials. The knowledge can also benefit the making of time-dependent 1-D and Q1D nanoelectronic devices