English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the zaia usage as premium feature

ZAIA

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the access of premium content as premium feature

Premium Content

Zendy Tools

Zendy Open

The growing need for smaller electronic components has recently sparked theinterest in the breakdown of the classical conductivity theory near the atomicscale, at which quantum effects should dominate. In 2012, experimentalmeasurements of electric resistance of nanowires in Si doped with phosphorusatoms demonstrate that quantum effects on charge transport almost disappear fornanowires of lengths larger than a few nanometers, even at very low temperature(4.2K). We mathematically prove, for non-interacting lattice fermions withdisorder, that quantum uncertainty of microscopic electric current densityaround their (classical) macroscopic values is suppressed, exponentially fastwith respect to the volume of the region of the lattice where an externalelectric field is applied. This is in accordance with the above experimentalobservation. Disorder is modeled by a random external potential along withrandom, complex-valued, hopping amplitudes. The celebrated tight-bindingAnderson model is one particular example of the general case considered here.Our mathematical analysis is based on Combes-Thomas estimates, theAkcoglu-Krengel ergodic theorem, and the large deviation formalism, inparticular the G\"artner-Ellis theorem.

Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media