Landauer formula

About: Landauer formula is a research topic. Over the lifetime, 362 publications have been published within this topic receiving 20205 citations. The topic is also known as: Laundauer formula.

Electronic transport in mesoscopic systems

Abstract: 1. Preliminary concepts 2. Conductance from transmission 3. Transmission function, S-matrix and Green's functions 4. Quantum Hall effect 5. Localisation and fluctuations 6. Double-barrier tunnelling 7. Optical analogies 8. Non-equilibrium Green's function formalism.

Generalized many-channel conductance formula with application to small rings.

Abstract: The conductance of a sample scattering elastically and coupled to leads with many channels is derived. We assume that all the incident channels on one side of the sample are fed from the same chemical potential. The transmitted and reflected streams are determined by the incident streams through the multichannel scattering properties of the sample. We do not assume that the channels equilibrate with each other. Our result differs from those given earlier by other authors, except for that of Azbel [J. Phys. C 14, L225 (1981)], which is confirmed. We point out that a similar result is obtained for the conductance in a single channel at a temperature above zero. As an application, we obtain the dependence on channel number N of the contributions to the conductance of a small ring, periodic in the Aharonov-Bohm flux through it. Terms whose period is h/e as well as those with period h/2e vary with N as 1/N.

Landauer formula for the current through an interacting electron region.

Abstract: A Landauer formula for the current through a region of interacting electrons is derived using the nonequilibrium Keldysh formalism. The case of proportionate coupling to the left and right leads, where the formula takes an especially simple form, is studied in more detail. Two particular examples where interactions give rise to novel effects in the current are discussed: In the Kondo regime, an enhanced conductance is predicted, while a suppressed conductance is predicted for tunneling through a quantum dot in the fractional quantum Hall regime.

Relation between conductivity and transmission matrix

Abstract: The dc conductance 1 of a finite system with static disorder is related to its transmission matrix t by the simple relation 1 = (e /2nt) Tr(t t). This relation is derived from the Kubo formula and is valid for any number of scattering channels with or without time-reversal symmetry. Differences between various definitions of the conductance of a finite system are discussed. Some time ago Landauer' proposed that the dc conductance I' of noninteracting (spinless) electrons in a disordered medium in strictly one dimension is given by I' = (e'/2vrh) ~ r ~'/~ r (' where t and r are the transmission and reflection amplitudes. A relation of this kind, especially if it can be generalized to higher dimensions, is of great interest for at least two reasons. First, the cost of numerical computation may be greatly reduced compared with the conventional use of the Kubo formula. '~ Second, such a relation emphasizes the fundamental role of the conductance which is assumed to be the only relevant variable in a recent scaling theory treatment of the localization problem. " This point of view was discussed in a recent analysis of the conductivity of a one-dimensional (ID) chain9 in which Landauer's expression was used. The argument given by Landauer is a heuristic one and not easily generalized to higher dimensions.

Quantum thermal transport in nanostructures

Abstract: In this colloquia review we discuss methods for thermal transport calculations for nanojunctions connected to two semi-infinite leads served as heat-baths. Our emphases are on fundamental quantum theory and atomistic models. We begin with an introduction of the Landauer formula for ballistic thermal transport and give its derivation from scattering wave point of view. Several methods (scattering boundary condition, mode-matching, Piccard and Caroli formulas) of calculating the phonon transmission coefficients are given. The nonequilibrium Green's function (NEGF) method is reviewed and the Caroli formula is derived. We also give iterative methods and an algorithm based on a generalized eigenvalue problem for the calculation of surface Green's functions, which are starting point for an NEGF calculation. A systematic exposition for the NEGF method is presented, starting from the fundamental definitions of the Green's functions, and ending with equations of motion for the contour ordered Green's functions and Feynman diagrammatic expansion. In the later part, we discuss the treatments of nonlinear effects in heat conduction, including a phenomenological expression for the transmission, NEGF for phonon-phonon interactions, molecular dynamics (generalized Langevin) with quantum heat-baths, and electron-phonon interactions. Some new results are also shown. We briefly review the experimental status of the thermal transport measurements in nanostructures.