Nano Electronics

Quantum Transport

Since the introduction of the integrated circuit or chip in the sixties, the power of microprocessors has always grown together with the integration scale, following what is called the Moore's law. If such a miniaturization rate will continue, modern electronics will attain its ultimate limit, the molecular and atomic scale, around the year 2015. As a consequence, Electronics at the Nanoscale, namely Nanoelectronics, represents the next years' technological challenge. A bottom-up process instead of a top-down as followed so far, will allow the realization of Electronic Devices made out of Molecules and Nanostructures. And this is boosted not only by the need for shorter integration scales, and device miniaturization, but also by the expectation that unusual quantum effects are going to be observed due to quantum phenomena effects.

Beside the experimental efforts to synthesize nanoelectronic devices, quantum transport theory has the formidable task to understand and to model the mechanisms behind these phenomena and to predict them from a first principles approach.

Several years ago, important progresses have been accomplished in the theory of quantum transport thank to the setup of two frameworks: the Landauer-Buttiker (LB) and Kubo-Greenwood formalisms. These two formalisms rely on theories able to provide the electronic structure of the nanodevices. And these can be the semi-empirical Tight-Binding (TB); or fully ab initio Density-Functional Theory (DFT).

The Landauer-Buttiker on the top of Density-Functional Theory, today to be considered the state-of-the-art, has demonstrated its ability to describe small bias coherent transport in nanojunctions. These approaches were successful in accounting for the contact resistance and conductance degrading mechanisms induced by impurities, defects and non-commensurability patterns in the conductor region.

The theoretical effort and trend today is to move toward theories able to account for non-coherent and dissipative effects due to electron-phonon and electron-electron scattering mechanisms inside the conductor and for non-linear response, far from equilibrium, finite-bias transport. Along these directions, the two major research lines are Time-Dependent Density-Functional Theory (TDDFT) [Runge, E.K.U. Gross, W. Kohn]; and Non-Equilibrium Green's Function (NEGF) theory [Schwinger, Baym, Kadanoff, Keldysh]. Both NEGF and also TDDFT [G. Stefanucci, C.-O. Almbladh] are in principle correct frameworks to address the above objections.

Researchers at the Rhone-Alpes associated ETSF node have demonstrated [Darancet et al], in the framework of NEGF, that a GW approximation on the Self-Energy can introduce diffusion and loss-of-coherence effects due to the electron-electron scattering and giving rise to reduction of conductance and appearance of resistance inside the conductor.

Gold Monoatomic Nanowire:
Differential conductance vs applied voltage

Together with the result of another theory group in Copenhaguen who introduced electron-phonon scattering effects through a self-consistent Born approximation (SCBA), their calculated conductance characteristics as a function of the applied voltage for a gold monoatomic nanowire fully explains all the features present in the experimental measures of Agrait et al.

P. Darancet, A. Ferretti, D. Mayou and V. Olevano, Phys. Rev. B (2007).
T. Frederiksen, M. Brandbyge, N. Lorente, and A.-P. Jauho, Phys. Rev. Lett., 93, 256601 (2004).
G. Stefanucci and C.-O. Almbladh, Europhysics Letters 67, 14 (2004).
N. Agrait, C. Untiedt, G. Rubio-Bollinger and S. Vieira, Phys. Rev. Lett., 88, 216803 (2002).