Physicist Sergio Ulloa
Ohio University’s Dr. Sergio Ulloa, a professor in Physics and Astronomy, published a paper, “Conductance and Kondo interference beyond proportional coupling” in the American Physical Society’s Physical Review Letters.
Ulloa collaborated with Brazilian co-authors Luis G. G. V. Dias da Silva of University of São Paulo, Caio H. Lewenkopf of Fluminense Federal University in Rio de Janeiro, Edson Vernek and Gerson J. Ferreira of the Federal University of Uberlandia.
Motivated by recent electronic transport experiments conducted at the Swiss Federal Institute of Technology (ETH) and at the University of Grenoble Alpes, Ulloa and the co-authors undertook the generalization of the Meir-Wingreen formula used to analyze such experiments.
The Meir-Wingreen formula has been used successfully for many years to describe the electrical current and conductance in mesoscopic systems where electronic interactions are important. However, analysis of the latest ETH and Grenoble experiments required an improved formulation.
The work of the collaboration was needed to extend the theory in this formula, as experiments of this nature fall outside its regime of validity.
- After the original ETH work was published, Ulloa was asked to write a “Viewpoint” about it for the American Physical Society.
“For about 25 years, researchers have been able to understand nanoscale electronic conductance of quantum dot systems using the famous Meir-Wingreen formula—or MW formula,” Ulloa says. “MW is valid when there is a similar behavior of the left/right current leads attached to the system, known as ‘the proportional coupling.’ Such is the case when the two current leads are only different by how well they connect to the mesoscopic structure (such as a quantum dot), and are therefore ‘proportional’ to one another.”
The researchers’ generalization includes the possibility of intricate energy structures (strong energy dependence) in one or both of the leads connecting to the dot system, and it goes well beyond the proportional coupling simplification of MW. The co-authors predict it should be possible to describe the transport of many such dot systems, including current leads attached to complex molecules.
As a first example of its application, the Brazil-U.S. authors used this new formula to describe the ETH experiments and found excellent agreement with their results. The ETH experiments also discovered an interesting Kondo effect that appears in their structure, where one of the current leads is cleverly coupled to an “electronic mirror” and causes strong energy dependence in the coupling to that lead.
“Dias and Vernek labored to resolve some of the difficult theory issues, and their work paid off handsomely,” said Ulloa. “We worked together to develop the new formalism and write it in a way that should be very useful in the analysis of future experiments with complex geometries. Further understanding of more complex structures may yield innovative electronic and spintronic devices to be used in future technology.”
(L to R) Luis G. G. V. Dias da Silva of University of São Paulo and Edson Vernek of Federal University of Uberlandia are pleased after solving a particularly difficult mathematics problem which allowed for a compact final form of the transport formula.
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