We show that the Landauer multi-terminal formula for the conductance of a nanoscale system is incomplete because it does not take into account many-body effects which cannot be treated as contributions to the single-particle transmission probabilities. We show that the physical origin of these effects is related to the viscous nature of the electron liquid, and develop a perturbative formalism, based on the time-dependent current-density-functional theory, for calculating the corrections to the resistance in terms of the ``Kohn-Sham current distribution'' and the exchange-correlation kernel. The difficulties that still remain in calculating the latter are critically discussed.
The interplay of spin-polarized electronic edge states with the dynamics of the host nuclei in quantum Hall systems presents rich and non-trivial transport physics. Here, we develop a Landauer-Büttiker approach to understand various experimental features observed in the integer quantum Hall set ups featuring quantum point contacts. The approach developed here entails a phenomenological description of spin resolved inter-edge scattering induced via hyperfine assisted electron-nuclear spin flip-flop processes. A self-consistent simulation framework between the nuclear spin dynamics and edge stat…
Landauer's formula is the standard theoretical tool to examine ballistic transport in nano- and meso-scale junctions, but it necessitates that any variation of the junction with time must be slow compared to characteristic times of the system, e.g., the relaxation time of local excitations. Transport through structurally dynamic junctions is, however, increasingly of interest for sensing, harnessing fluctuations, and real-time control. Here, we calculate the steady-state current when relaxation of electrons in the reservoirs is present and demonstrate that it gives rise to three regimes of beh…
While the Landauer viewpoint constitutes a modern basis to understand nanoscale electronic transport and to realize first-principles implementations of the non-equilibrium Green's function (NEGF) formalism, seeking an alternative picture could be beneficial for the fundamental understanding and practical calculations of quantum transport processes. Herein, introducing a micro-canonical picture that maps the finite-bias quantum transport process to a drain-to-source or multi-electrode optical excitation, the multi-space constrained-search density functional theory (MS-DFT) formalism for first-p…
Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-elec…
Landauer-Büttiker formula describes the electronic quantum transports in nanostructures and molecules. It will be numerically demanding for simulations of complex or large size systems due to, for example, matrix inversion calculations. Recently, Chebyshev polynomial method has attracted intense interests in numerical simulations of quantum systems due to the high efficiency in parallelization, because the only matrix operation it involves is just the product of sparse matrices and vectors. Many progresses have been made on the Chebyshev polynomial representations of physical quantities for is…
In a recent article, Chiang and Hsu [The Journal of Chemical Physics 153, 044103 (2020)] examine one and two site electronic junctions identically connected to finite reservoirs. For these two examples, they derive analytical solutions, as well as provide asymptotic analyses, for the steady-state current from the driven Liouville-von Neumann (DLvN) equation - an open system approach to transport in non-interacting systems where relaxation maintains a bias. The two site junction they examine has destructive interference, which they show leads to slow convergence of the DLvN to the Landauer limi…
The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient and widely applicable but not suited to transient phenomena and time dependent currents because it assumes that the charge carrier population attains a time independent dynamic equilibrium as soon as the external voltage is turned on. In this article, we construct a very general expression for a time dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian, we propagate the Schrodinger wave function equation to numerically compute the time dependent pop…
Recent electronic transport experiments using metallic contacts attached to proteins identified some 'stylized facts' which contradict conventional wisdom that increasing either the spatial distance between the electrodes or the temperature suppresses conductance exponentially. These include nearly temperature independent conductance over the protein in the 30-300K range, distance independent conductance within a single-protein in the 1-10 nm range and an anomalously large conductance in the 0.1-10 nS range. In this paper we develop a generalization of the low temperature Landauer formula whic…
Understanding the behavior of light in non-equilibrium scenarios underpins much of quantum optics and optical physics. While lasers provide a severe example of a non-equilibrium problem, recent interests in the near-equilibrium physics of so-called photon `gases', such as in Bose condensation of light or in attempts to make photonic quantum simulators, suggest one re-examine some near-equilibrium cases. Here we consider how a sinusoidal parametric coupling between two semi-infinite photonic transmission lines leads to the creation and flow of photons between the two lines. Our approach provide…
Marcus and Landauer-Buttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion (HEOM) results, we demonstrate that our …
Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory, respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled to a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression, and present a series of approximations of this r…
We present a multiprobe recursive Green's function method to compute the transport properties of mesoscopic systems using the Landauer-Büttiker approach. By introducing an adaptive partition scheme, we map the multiprobe problem into the standard two-probe recursive Green's function method. We apply the method to compute the longitudinal and Hall resistances of a disordered graphene sample, a system of current interest. We show that the performance and accuracy of our method compares very well with other state-of-the-art schemes.
The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscop…
We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General analytical formulas of the conductance in $D=1,2,3$ dimensions are obtained, which recover the Boltzmann-Drude formula and Landauer-Büttiker formula in the diffusive and ballistic limits, respectively. This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport ph…
We investigate the power dissipated by an electronic current flowing through a quantum point contact in a two-dimensional electron gas. Based on the Landauer-Büttiker approach to quantum transport, we evaluate the power that is dissipated on the two sides of the constriction as a function of the Fermi energy, temperature, and applied voltage. We demonstrate that an asymmetry appears in the dissipation, which is most pronounced when the quantum point contact is tuned to a conductance step where the transmission strongly depends on energy. At low temperatures, the asymmetry is enhanced when the …
In this paper, we study the quantum properties of a bilayer graphene with (asymmetry) line defects. The localized states are found around the line defects. Thus, the line defects on one certain layer of the bilayer graphene can lead to an electric transport channel. By adding a bias potential along the direction of the line defects, we calculate the electric conductivity of bilayer graphene with line defects using Landauer-Büttiker theory, and show that the channel affects the electric conductivity remarkably by comparing the results with those in a perfect bilayer graphene. This one-dimension…
We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-Büttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to lo…
We consider the scattering of Dirac particles in graphene due to the superposition of an external magnetic field and mechanical strain. As a model for a graphene nanobubble, we find exact analytical solutions for single-particle states inside and outside a circular region submitted to the fields. Finally, we obtain analytical expressions for the scattering cross-section, as well as for the Landauer current through the circular region. Our results provide a fully-analytical treatment for electronic transport through a graphene nanobubble, showing that a combination of a physical magnetic field …
Two-dimensional material-based field effect transistors (2DM-FETs) are playing a revolutionary role in electronic devices. However, after years of development, no device model can match the Pao-Sah model for standard silicon-based transistors in terms of physical accuracy and computational efficiency to support large-scale integrated circuit design. One remaining critical obstacle is the contacts of 2DM-FETs. In order to self-consistently include the contact effect in the current model, it is necessary to perform self-consistent calculations, which is a fatal flaw for applications that priorit…
We examine the electronic heat transport phenomena in nanoscale junctions composed of organic molecules coupled to two metallic reservoirs of different temperatures. The electronic heat flux and its dynamical noise properties are calculated within the scattering (Landauer) formalism with the transmission probability determined by using non-equilibrium Green's functions (NEGF technique). The method based on Taylor series expansion is used to determine nonlinear corrections to the electronic heat flux and its noise power spectral density with up to the second order terms with respect to the temp…
The accuracy of the noninteracting electron approximation is examined for a model of vibrationally coupled electron transport in single molecule junction. In the absence of electronic-vibrational coupling, steady state transport in this model is described exactly by Landauer theory. Including coupling, both electronic-vibrational and vibrationally induced electron-electron correlation effects may contribute to the real time quantum dynamics. Using the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory to describe nuclear dynamics exactly while maintaining the noninteracting…
The analog of two seminal quantum optics experiments are considered in a condensed matter setting with single electron sources injecting electronic wave packets on edge states coupled through a quantum point contact. When only one electron is injected, the measurement of noise correlations at the output of the quantum point contact corresponds to the Hanbury-Brown and Twiss setup. When two electrons are injected on opposite edges, the equivalent of the Hong-Ou-Mandel collision is achieved, exhibiting a dip as in the coincidence measurements of quantum optics. The Landauer-Buttiker scattering t…
Based on the investigation of the multi-terminal conductance of a system composed of two graphene nanoribbons, in which one is on top of the other and rotated by 60 degrees, we propose a setup for a 50/50 electronic beam splitter that neither requires large magnetic fields nor ultra low temperatures. Our findings are based on an atomistic tight-binding description of the system and on the Green's function method to compute the Landauer conductance. We demonstrate that this system acts as a perfect 50/50 electronic beam splitter, in which its operation can be switched on and off by varying the …
Electronic transport in nanodevices is commonly studied theoretically and numerically within the Landauer-Büttiker formalism: a device is characterized by its scattering properties to and from reservoirs connected by perfect semi-infinite leads, and transport quantities are derived from the scattering matrix. In some respects, however, the device becomes a "black box" as one only analyses what goes in and out. Here we use the Husimi function as a complementary tool for quantitatively understanding transport in graphene nanodevices. It is a phase space representation of the scattering wavefunct…
Interference effects in finite sections of one-dimensional moiré crystals are investigated using a Landauer-Büttiker formalism within the tight-binding approximation. We explain interlayer transport in double-wall carbon nanotubes and design a predictive model. Wave function interference is visible at the mesoscale: in the strong coupling regime, as a periodic modulation of quantum conductance and emergent localized states; in the localized-insulating regime, as a suppression of interlayer transport, and oscillations of the density of states. These results could be exploited to design quantum …
Quantum transport has far-reaching applications in modern electronics as it enables the control of currents in nanoscale systems such as quantum dots. In this paper we introduce tinie: a state-of-the-art quantum transport simulation framework, which can efficiently perform first-principle calculations based on the Landauer-Büttiker formalism. The computational repertoire of tinie includes calculations of transmission, conductivity, and currents running through arbitrary multi-terminal two-dimensional transport devices, with additional tools that enable the computation of the local density of s…
Wavepacket basis for time-dependent processes and its application to relaxation in resonant electronic transport
频闪波包基组[P.Bokes，F.科尔塞蒂河W. Godby，Phys. Rev. Lett. 101，046402（2008）]是专门为描述扩展系统中的时间依赖性过程而定制的，如由固体和分子组成的各种接触的非周期性几何形状。解释两个简单的有限系统的建设这样的基础是由一个审查的一般理论扩展系统与连续谱。后者进一步阐述了相互作用表示的引入，充分利用了时间动态内置的基础。的形式主义是适用于一个半解析的例子，通过共振隧穿势垒在1D的电子输运。通过时间依赖性的推广的Landauer公式中给出的传输振幅的傅立叶展开，我们分析的稳态的发病的时间特性。在这个过程中的各种时间尺度被证明是直接相关的能量结构的共振势垒。
Entropy Production in Mesoscopic Electronic Transport Beyond Weak-Coupling
Instituto de Física Teórica, Universidade Estadual Paulista (UNESP)（圣保罗州立大学理论物理研究所）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）；Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）
We investigate charge transport in C$_{60}$-based single-molecule junctions with graphene electrodes employing a combination of density functional theory (DFT) electronic structure calculations and Landauer transport theory. In particular, the dependence of the transport properties on the conformation of the molecular bridge and the type of termination of the graphene electrodes is investigated. Furthermore, electron pathways through the junctions are analyzed using the theory of local currents. The results reveal, in agreement with previous experiments, a pronounced dependence of the transpor…
The function of nano-scale devices critically depends on the choice of materials. For electron transport junctions it is natural to characterize the materials by their conductance length dependence, $β$. Theoretical estimations of $β$ are made employing two primary theories: complex band structure and DFT-NEGF Landauer transport. Both reveal information on $β$ of individual states; i.e. complex Bloch waves and transmission eigenchannels, respectively. However, it is unclear how the $β$-values of the two approaches compare. Here, we present calculations of decay constants for the two most condu…
