We present a theory of the four--terminal conductance for the multi-channel tunneling barrier, which is based on the self-consistent solution of Shrodinger, Poisson and continuity equations. We derive new results for the case of a barrier embedded in a long wire with and without disorder. We also recover known expressions for the conductance of the barrier placed into a ballistic constriction. Our approach avoids a problematic use of two chemical potentials in the same system.
In this paper, we propose a method to calculate the exact Taylor series of the scattering matrix in general multiterminal tight-binding systems to arbitrary order N, which allows us to find the Taylor expansion of Landauer conductance in mesoscopic systems. The method is based on the recursive scattering matrix method (RSMM) that permits us to find the scattering matrix of a system from the scattering matrices of its subsystems. Following ideas of automatic differentiation, we determine expressions for the sum, product, inverse, and diagonalization of a matrix Taylor expansion, and use them in…
Thermal boundary conductance (TBC) is critical in many thermal and energy applications. A decades-old puzzle has been that many of the measured TBCs, such as those well characterized across Al/Si and ZnO/GaN interfaces, significantly exceed theoretical results or even the absolute upper limit called the ``radiation limit", suggesting the failure of the theory. Here, we identify that for high-transmission interfaces, the commonly assumed phonon local thermal equilibrium adjacent to the interface fails, and the measurable phonon temperatures are not their emission temperature. We hence develop a…
We report on a striking departure from the canonical step sequence of quantized conductance in a ballistic, quasi-one-dimensional metallic channel. Ideally, in such a structure, each sub-band population contributes its Landauer conductance quantum independently of the rest. In a picture based exclusively on coherent single-carrier transmission, unitary back-scattering can lower a conductance step below ideal, but it is absolutely impossible for it to enhance the ideal Landauer conductance of a sub-band. Precisely such an anomalous and robust nonlinear enhancement has already been observed over…
From conductance viewed as transmission to resistance viewed as reflection. An extension of Landauer quantum paradigm to the classical case at finite temperature
The Landauer formula allows us to describe theoretically the conductance in terms of the transmission function in a mesoscopic system. We propose a general method to evaluate the transmission function in the complex domain for systems connected to semi-infinite atomic chains. This reveals the presence of complex-conjugated pairs of simple poles that are responsible for transmission peaks in the real-domain evaluations. This leads us to formulate a closed-form expression for the transmission function.
Over the last decade, interest in one-dimensional charge transport has progressed from the seminal discovery of Landauer quantization of conductance, as a function of carrier density, to finer-scale phenomena at the onset of quantization. This has come to be called the "0.7 anomaly", rather connoting a theoretical mystery of some profundity and universality, which remains open to date. Its somewhat imaginative appellation may tend to mislead, since the anomaly manifests itself over a range of conductance values: anywhere between 0.25 to 0.95 Landauer quanta. In this paper we offer a critique o…
We generalize the Landauer formula to describe the dissipative electron transport through a superconducting point contact. The finite-temperature, linear-in-bias, dissipative DC conductance is expressed in terms of the phase- and energy-dependent scattering matrix of the Bogoliubov quasiparticles in the quantum point contact. The derived formula is also applicable to hybrid superconducting-normal structures and normal contacts, where it agrees with the known limits of Andreev reflection and normal-state conductance, respectively.
Within the Landauer transport formalism we demonstrate that conductance zeroes are possible in bipartite systems at half-filling when leads are contacted to different sublattice sites. In particular, we investigate the application of this theory to graphene quantum dots with leads in the armchair configuration. The obtained conductance cancellation is robust in the presence of any single-site impurity.
We study the radiative heat transfer between two semi-infinite half-spaces, bounded by conductive surfaces in contact with vacuum. This setup is interpreted as a four-terminal mesoscopic transport problem. The slabs and interfaces are viewed as bosonic reservoirs, coupled perfectly to a scattering center consisting of the two interfaces and vacuum. Using Rytov's fluctuational electrodynamics and assuming Kirchhoff's circuital law, we calculate the heat flow in each bath. This allows for explicit evaluation of a conductance matrix, from which one readily verifies Büttiker symmetry. Thus, radiat…
Using the non-equilibrium Keldysh formalism, we investigate the spatial relation between the electro-chemical potential measured in scanning tunneling spectroscopy, and local current patterns over the entire range from the quantum to the classical transport regime. These quantities show similar spatial patterns near the quantum limit, but are related by Ohm's law only in the classical regime. We demonstrate that defects induce a Landauer residual resistivity dipole in the electro-chemical potential with the concomitant spatial current pattern representing the field lines of the dipole.
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…
The largest eigenvalue distribution of the Wishart-Laguerre ensemble, indexed by Dyson parameter $β$ and Laguerre parameter $a$, is fundamental in multivariate statistics and finds applications in diverse areas. Based on a generalization of the Selberg integral, we provide an effective recursion scheme to compute this distribution explicitly in both the original model, and a fixed-trace variant, for $a,β$ non-negative integers and finite matrix size. For $β= 2$ this circumvents known symbolic evaluation based on determinants which become impractical for large dimensions. Our exact results have…
Quantized thermal conductance of dielectric quantum wires
利用输运理论的Landauer公式，我们预测介电量子线在低温下应该表现出量子化的热导，在弹道声子制度。热传导的量子是通用的，与材料的特性无关，并且等于$π^2 k^2_B T /3h$，其中$k_B$是玻耳兹曼常量，h是普朗克常数，T是温度。量子化的热导应该是实验上可观察到的悬浮纳米结构，磁耦合到水库，设备，可以实现在目前的时间。
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…
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…
We report a thorough theoretical investigation on the quantum transport of a disordered four terminal device in the presence of Rashba spin orbit coupling (RSOC) in two dimensions. Specifically we compute the behaviour of the longitudinal (charge) conductance, spin Hall conductance and spin Hall conductance fluctuation as a function of the strength of disorder and Rashba spin orbit interaction using the Landauer Buttiker formalism via Green's function technique. Our numerical calculations reveal that both the conductances diminish with disorder. At smaller values of the RSOC parameter, the lon…
The longitudinal conductance of mesoscopic Hall samples with arbitrary disorder and periodic modulations
本文利用Kubo-Landauer方法计算了置于强垂直磁场中的二维电子系统在周期调制和无序势作用下的纵向（两端）电导。散射问题被改写为一组非均匀的，耦合的线性方程组，使我们能够找到从有限大小的系统计算的传输概率;结果是准确的非相互作用的电子。我们的方法充分考虑了无序和周期调制的影响，无论它们的相对强度如何，只要朗道能级混合可以忽略不计。特别是，我们专注于周期性调制和那些无序的影响之间的相互作用。这似乎是理解最近实验的相关机制[S。Melinte { \em et al}，Phys. Rev. Lett. { \bf 92}，036802（2004）]，我们的数值结果与这些实验结果定性一致。我们开发的数值技术可以直接推广到多终端的几何形状，以及其他多通道散射问题。
An expression for the transmission matrix based conductance is provided for the propagation of scalar waves in certain bifurcated discrete waveguides using the paradigm of a three-terminal Landauer-Buttiker junction. It is found that the conductance across the terminals of bifurcated branches forming a sharp corner, interpreted as a controller of `leakage' flux, can be tuned by manipulating the number of channels and the type of lateral confinement. Natural applications in engineering and science arise in the context of nanoscale transport involving elastic, phononic, or electronic waves. In p…
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…
