Transport In Mesoscopic Systems Research Articles

An investigation of the background potential in quantum constrictions using scanning gate microscopy and a swarming algorithm

Scanning gate microscopy (SGM) is a valuable scanning probe technique for characterizing electronic transport in mesoscopic systems. However, the interpretation of the method is often limited by many experimental challenges. In this work, we propose an empirically-constrained optimization approach based on swarm search and Green’s functions to extract more information from SGM measurements. The approach is applied to a quantum point contact fabricated on an InAlAs/InGaAs/InAlAs quantum well, and the results indicate that the corresponding SGM could be generated, in a weak approximation, by a fluctuating background potential with features with radii in the order of 20 to 30 nm and a correlation length of 5.7 nm. Our method represents a data-driven tool for estimating solutions for inverse problems in mesoscopic physics, and can be used to generate estimates for the potential landscape experienced by free electrons in mesoscopic systems.

A hybrid Monte Carlo-discrete ordinates method for phonon transport in micro/nanosystems with rough interfaces

In recent years, the rapid development of micro/nanosystems raises the demand of thermal optimization of the new designs, and thus the accurate and efficient prediction of phonon transport in mesoscopic systems with complex interfaces is required. This work proposes a hybrid Monte Carlo-discrete ordinates method (MC-DOM) for steady-state phonon transport in such systems by developing an algorithm to exchange information between MC and DOM subdomains. Based on the phonon Boltzmann transport equation which is physically compatible with the system scale, our formulation exploits the computational efficiency of DOM in the bulk region with flexibility of MC near complex interfaces. The cross-plane phonon transport through the thin films is considered first as the benchmark for method verification, whose results agree well with those calculated by numerical and analytical solutions. It is noteworthy that compared to MC as a pure particle method, the hybrid method runs faster over a hundred of times for the temperature calculation when high-precision results are needed. The hybrid method is then applied to simulate the in-plane phonon transport through the double-layer thin films with rough interfaces. It is found that for rectangular interfaces with different roughness, the interfaces perpendicular to the heat flux will cause a larger thermal resistance than the parallel ones. Our hybrid method enriches numerical tools for mesoscopic phonon transport simulation, and is helpful to reveal the mechanisms behind and optimize the heat transport in micro/nanosystems with complex geometries.

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

A brief review of thermal transport in mesoscopic systems from nonequilibrium Green’s function approach

With the rapidly increasing integration density and power density in nanoscale electronic devices, the thermal management concerning heat generation and energy harvesting becomes quite crucial. Since phonon is the major heat carrier in semiconductors, thermal transport due to phonons in mesoscopic systems has attracted much attention. In quantum transport studies, the nonequilibrium Green’s function (NEGF) method is a versatile and powerful tool that has been developed for several decades. In this review, we will discuss theoretical investigations of thermal transport using the NEGF approach from two aspects. For the aspect of phonon transport, the phonon NEGF method is briefly introduced and its applications on thermal transport in mesoscopic systems including one-dimensional atomic chains, multi-terminal systems, and transient phonon transport are discussed. For the aspect of thermoelectric transport, the caloritronic effects in which the charge, spin, and valley degrees of freedom are manipulated by the temperature gradient are discussed. The time-dependent thermoelectric behavior is also presented in the transient regime within the partitioned scheme based on the NEGF method.

Brownian thermal transistors and refrigerators in mesoscopic systems

Fluctuations are significant in mesoscopic systems and of particular importance in understanding quantum transport. Here, we show that fluctuations can be considered as a resource for the operations of open quantum systems as functional devices. We derive the statistics of the thermal transistor amplification factor and the cooling-by-heating refrigerator efficiency under the Gaussian fluctuation framework. Statistical properties of the stochastic thermal transistor and the cooling-by-heating efficiency are revealed in the linear-response regime. We clarify the unique role of inelastic processes on thermal transport in mesoscopic systems. We further show that elastic and inelastic processes lead to different bounds based on the linear transport coefficients by establishing a generic theoretical framework for mesoscopic heat transport, which treats electron and bosonic collective excitations in an equal-footing manner. The underlying physics are illustrated concretely using a double-quantum-dot three-terminal system, though the theory applies to more general systems.

Preface to the Special Issue on Quantum Transport in Mesoscopic Systems

Preface to the Special Issue on Quantum Transport in Mesoscopic Systems

Time-dependent thermoelectric transport in mesoscopic systems under a quantum quench

We investigate the transient behavior of the quantum transport in mesoscopic systems under a quantum quench within the Caroli scheme. Using the nonequilibrium Green's function approach, an exact solution of the transient electric current, energy current, and their fluctuations in the presence of both external bias and temperature gradient are presented that goes beyond the wide-band limit. The exact solution of the time-dependent Seebeck coefficient in the linear response regime is also obtained. This formalism is applied to study the transient behavior of a single-level quantum dot with Lorentzian linewidth induced by the temperature gradient. The damped oscillatory behavior is found in the transient electric and energy currents, as well as their fluctuations. The oscillation frequency of electric and energy currents increases with the increasing energy level of quantum dot and the decay rate of oscillation decreases as the bandwidth increases. A significantly enhanced Seebeck coefficient is generated in the transient regime. We find the maximum value of the time-dependent Seebeck coefficient can be enhanced by increasing the energy level of the quantum dot and the reference temperature of leads.

Electromagnetically induced transparency and bound in continuum states in double Aharonov-Bohm coupled rings

Abstract We investigated electromagnetic induced transparency (EIT) resonances and bound in continuum (BIC) states in a simple mesoscopic structure made of double Aharonov-Bohm rings of lengths d1 and d2 threaded by a magnetic flux and coupled by a wire of length d0. These investigations are accomplished through an analysis of the amplitude of the transmission coefficient obtained using the Green’s function method. This structure may exhibit a large band gap and an EIT resonance in the transmission spectrum without introducing any impurity in one arm of the loop. In addition, we show that the shape of the EIT resonances and the width of the band gaps can be tuned by means of the magnetic flux and the geometry of the structure. These results may have important applications for electronic transport in mesoscopic systems.

Reconciliation of quantum local master equations with thermodynamics

The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.

Geometrically induced broadening for phonon blocking at low temperatures

Because of the presence of robust massless modes with no excitation gap, the heat current carried by phonons tends to survive at low temperatures even when scattering mechanisms are incorporated into the system. This becomes a fundamental obstacle to thermoelectric applications at low temperatures. In this study, we investigate the effect of energy broadening on phonon transport in mesoscopic systems coupled to leads or probes in various geometries using a nonequilibrium Green's function formalism. An analytic theory derived from a minimal model consisting of a harmonic chain shows that geometrically induced broadening sizably suppresses low-temperature phonon transport. It is also demonstrated from numerical calculations that this scheme for phonon blocking is viable for realistic systems in higher dimensions.

Transmission gaps, trapped modes and Fano resonances in Aharonov–Bohm connected mesoscopic loops

A simple mesoscopic structure consisting of a double symmetric loops coupled by a segment of length d0 in the presence of an Aharonov–Bohm flux is designed to obtain transmission band gaps and Fano resonances. A general analytical expression for the transmission coefficient and the density of states (DOS) are obtained for various systems of this kind within the framework of the Green's function method in the presence of the magnetic flux. In this work, the amplitude of the transmission and DOS are discussed as a function of the wave vector. We show that the transmission spectrum of the whole structure may exhibit a band gap and a resonance of Fano type without introducing any impurity in one arm of the loop. In particular, we show that for specific values of the magnetic flux and the lengths of the arms constituting the loops, the Fano resonance collapses giving rise to the so-called trapped states or bound in continuum (BIC) states. These states appear when the width of the Fano resonance vanishes in the transmission coefficient as well as in the density of states. Also, we show that the shape of the Fano resonances and the width of the band gaps are very sensitive to the value of the magnetic flux and the geometry of the structure. These results may have important applications for electronic transport in mesoscopic systems.

Fast thermometry with a proximity Josephson junction

We couple a proximity Josephson junction to a Joule-heated normal metal film and measure its electron temperature under steady state and nonequilibrium conditions. With a timed sequence of heating and temperature probing pulses, we are able to monitor its electron temperature in nonequilibrium with effectively zero back-action from the temperature measurement in the form of additional dissipation or thermal conductance. The experiments demonstrate the possibility of using a fast proximity Josephson junction thermometer for studying thermal transport in mesoscopic systems and for calorimetry.

Resolvent expansions for the Schrödinger operator on the discrete half-line

Simplified models of transport in mesoscopic systems are often based on a small sample connected to a finite number of leads. The leads are often modelled using the Laplacian on the discrete half-line ℕ. Detailed studies of the transport near thresholds require detailed information on the resolvent of the Laplacian on the discrete half-line. This paper presents a complete study of threshold resonance states and resolvent expansions at a threshold for the Schrodinger operator on the discrete half-line ℕ with a general boundary condition. A precise description of the expansion coefficients reveals their exact correspondence to the generalized eigenspaces, or the threshold types. The presentation of the paper is adapted from that of Ito-Jensen [Rev. Math. Phys. 27, 1550002 (2015)], implementing the expansion scheme of Jensen-Nenciu [Rev. Math. Phys. 13(6), 717–754 (2001) and Rev. Math. Phys. 16(5), 675–677 (2004)] in its full generality.

Conceptual density functional theory for electron transfer and transport in mesoscopic systems.

Molecular and supramolecular systems are essentially mesoscopic in character. The electron self-exchange, in the case of energy fluctuations, or electron transfer/transport, in the case of the presence of an externally driven electrochemical potential, between mesoscopic sites is energetically driven in such a manner where the electrochemical capacitance (C[small mu, Greek, macron]) is fundamental. Thus, the electron transfer/transport through channels connecting two distinct energetic (ΔE[small mu, Greek, macron]) and spatially separated mesoscopic sites is capacitively modulated. Remarkably, the relationship between the quantum conductance (G) and the standard electrochemical rate constant (kr), which is indispensable to understanding the physical and chemical characteristics governing electron exchange in molecular scale systems, was revealed to be related to C[small mu, Greek, macron], that is, C[small mu, Greek, macron] = G/kr. Accordingly, C[small mu, Greek, macron] is the proportional missing term that controls the electron transfer/transport in mesoscopic systems in a wide-range, and equally it can be understood from first principles density functional quantum mechanical approaches. Indeed the differences in energy between states is calculated (or experimentally accessed) throughout the electrochemical capacitance as ΔE[small mu, Greek, macron] = β/C[small mu, Greek, macron], and thus constitutes the driving force for G and/or kr, where β is only a proportional constant that includes the square of the unit electron charge times the square of the number of electron particles interchanged.

Single-electron approach for time-dependent electron transport

We developed a new approach to electron transport in mesoscopic systems by using a particular single-particle basis. Although this basis generates redundant many-particle amplitudes, it greatly simplifies the treatment. By using our method for transport of non-interacting electrons, we generalize the Landauer formula for transient currents and time-dependent potentials. The result has a very simple form and clear physical interpretation. As an example, we apply it to resonant tunneling through a quantum dot where the tunneling barriers are oscillating in time. We obtain an analytical expression for the time-dependent (ac) resonant current. However, in the adiabatic limit this expression displays the dc current for zero bias (electron pumping).

Ballistic Transport in Mesoscopic Systems

Ballistic Transport in Mesoscopic Systems

Many-Channel Landauer-Like Conductance Formula in a Uniform Magnetic Field

For long time, it has been well recognized that transport in mesoscopic systems may relate to their scattering properties as it was originally proposed by Landauer [1, 2]. The single-channel conductance formula has been rst obtained heuristically as proportional to the ratio between transmission and re ection coe cients G = 2e 2 h T R [1]. Main attempts to derive this formula from linear-response theory (LRT) are known in the literature (see Ref. [3] and references therein). However, for long time, the generalization to a multichannel formula has been a great challenge for the physicists. The major di culty is that, in the LRT, the currentow in a sample is obtained as a response to an applied external perturbation inside the reservoirs in accordance to the Kubo viewpoint (KVP), whereas in the Landauer viewpoint (LVP) the current itself is considered as responsible for the induction of a position-dependent potential inside the sample. At this level, one has to note that it has been established heuristically that contacts between the reservoirs and the sample are at the origin of the di erence between the two points of view [4]. In recent works [5], a theory of transport that combines the LVP with the LRT and which does not consider the e ect of the contacts (called thereafter a self-consistent LRT) in order to calculate the relevant part of the density-operator for mesoscopic samples in the absence of an external magnetic eld, has been proposed. The obtained density-operator, necessary to evaluate all physical quantities, was used to derive a new and more plausible four-lead multichannel conductance formula that does not endure any of the inconsistencies cited in the literature for the other known formulae [3, 6]. This self-consistent LRT was recently extended to take into account the existence of a uniform magnetic eld [7, 8]. It has been shown that the density-operator may be written as a sum of two terms [7]: the rst represents the Kubo density-operator ρ [7 9] and the second denes the contribution of self-consistent e ects ρ [7, 8]: ρ = ρ + ρ. (1) Our aim in this work is the use of Eq. (1) to determine quantitatively the magnetoconductance of a four-lead mesoscopic measurement in terms of the scattering matrix elements whenever self-consistent e ects are relevant; that is, whenever the e ect of the contacts is neglected and the induced potential inside the sample is considered.

The effective spin concept to analyze coherent charge transport in mesoscopic systems

The concept of effective spin is introduced to underpin the fundamental isomorphism between two apparently disparate fields of physics—phase coherent charge transport in mesoscopic systems and qubit operations in a spin-based quantum logic gate. Together with the Bloch sphere concept, this isomorphism allows transport problems to be formulated in a language more familiar to workers in spintronics and quantum computing. We exemplify the application of the effective spin concept by formulating several charge transport problems in terms of specific unitary operations (rotations) of a spinor on the Bloch sphere.

Mesoscopic nature of the electron transport in electroformed metal-insulator-metal switches

The reversible diode- to resistorlike transition occurring in electroformed metal-insulator-metal structures caused by the application of successive voltage/current sweeps or pulses is ascribed to the modulation of the quantum transmission properties of atomic-sized filamentary paths. Closed-form expressions for the high resistance state (HRS) and low resistance state (LRS) I-V characteristic based on the Landauer formula for electron transport in mesoscopic systems are reported. From the simulation viewpoint, the switch from the exponential (HRS) to the linear (LRS) I-V characteristic and back is achieved by simply changing a model parameter related to the size of the constriction’s bottleneck. It is shown that the proposed model exhibits two limiting cases that are consistent with the experimental observations reported in literature.

Quantum transport in mesoscopic systems

A short introduction to the quantum transport in mesoscopic systems is given, and various regimes of quantum transport such as diffusive, ballistic, and adiabatic are explained. The effect of interactions and inelastic scattering along with the characteristic coherent effects of mesoscopic systems give interesting new mesoscopic effects, such as CoulombBlockade and Kondo Resonance. The basic physics of these phenomena is explained in simple language. In the end, some current research problems in this field are discussed.