My current research concerns the application of the
AdS/CFT correspondence, or gauge/gravity duality, to condensed matter systems. This duality is considered one of the important breakthroughs in Theoretical Physics of the past decades. It has allowed to map weakly coupled classical gravity systems to certain strongly-interacting quantum field theories. It has found relevant applications in quantum many-body systems.
Though the correspondence is only well-stablished in a few cases where the dual quantum theory has been constructect, in the absence of such theory, like in some Condensed Matter systems, AdS/CFT offers valuable information. For example, transport properties and measures of quantum entanglement.
In particular, thorugh the AdS/CFT correspondence I have studied a certain type of bounds, Mazur-Suzuki bounds, on some transport properties. These bounds are known in Condensed Matter, though they have not been explored in holographic theories, where it is easier to compute properties of the dual quantum theory.
I have also studied strongly coupled superconductors in the limit of large number of dimensions. We have observed that they become more weakly coupled as the number of dimensions increases. I am also investigating the holographic description of the Proximity Effect and a Josephson Junction of strongly coupled superconductors.
My initial research focused on the properties of weakly coupled superconducting thin films with a thickness in the nanoscale. The critical temperature shows oscillations (shape resonances) as the thickness changes. The shape resonances are caused by a change in the spreading of the quantum levels as the thickness changes. This leads to 'jumps' in the density of states and translates into jumps in observables. Shape resonances, and other finite-size-effects, in principle, would allow superconductivity to be enhanced. In order to obtain reallistic predictions, we used a mean-field approach to study the role of the substrate as well as if the number of conduction bands in favours the enhancement of the critical temperature for certain geometries.