Mendoza is a big proponent of renaissance science and engineering, where his lab solves problems, by combining and developing several areas of knowledge, independently of their formal separation by the human mind.
[5] Following his graduation, Mendoza joined the Caltech & Joint Center for Artificial Photosynthesis (JCAP) as a staff scientist until 2013 and then as a postdoctoral fellow at the California Institute of Technology, where he served until 2014.
His work and reputation have already led to significant national attention as he is the only researcher to be named four times in a row to the prestigious Scialog Fellowship (2020–2023) for his contributions to the development of negative emissions technologies.
[7] He was also the recipient of the GAP awards in 2018 from Florida State University for his work on creating the database to reliably predict which compounds will produce materials with the most desirable properties for a given purpose.
[8] He was part of the American Physical Society (APS) national committee on diversity and inclusion (9 persons), which developed the Bridge program; which has now expanded into the Inclusive Graduate Education Network (IGEN) which is made of 30 societies (including ACS, MRS, APS), corporations, and national laboratories, which is considered one of the most influential programs in post-graduate education for minorities in the USA.
[9][10] Dr. Mendoza's research has been featured in Forbes,[11] CNBC,[12] MRS Bulletin,[13] C&EN News, Public Radio, Laser Focus World magazine, and the DOE Highlights, to name a few.
They did this by implementing and developing the spin current density functional theory (SCDFT), which is the generalization of the standard DFT to treat a fermionic system embedded in the effective external field produced by the spin-orbit coupling interaction.
They showed that the explicit account of spin currents in the electron-electron potential of the SCDFT is key to the appearance of a Dirac cone at the onset of the topological phase transition.
[16] In December 2023, Dr. Mendoza-Cortes and co-workers published in the Philosophical Transactions of the Royal Society a design of a diamond material that would detect a non-zero electric dipole moment in a particle, indicating physics beyond the Standard Model.
[17] "Philosophical Transactions is the world's first and longest-running scientific journal", some "Famous and notable contributors" include Isaac Newton, Dorothy Hodgkin, Alan Turing, Charles Darwin, Michael Faraday, James Clerk Maxwell, and Stephen Hawking.
The Mendoza-Cortes lab created a new workflow for designing and predicting semiconductor structures made of abundant elements suitable for applications, especially for solar energy (i.e. photovoltaics) and photocatalytic water splitting.
The study successfully identifies numerous semiconductor candidates made of earth-abundant elements with ideal properties for artificial photosynthesis, highlighting a significant advancement in the conversion of sunlight into chemical fuels.
The findings are considered a step forward in developing high-performance KIBs, offering a method to overcome previous challenges related to K+ intercalation in carbon-based electrodes.
They enumerate chinampas with zero and one profits, offering algorithms for predicting vertex activation and efficiently reconstructing cascades, thereby advancing the understanding of complex signal flow networks and their potential applications in various domains.
One of the these problems is discussed in the paper, titled "A Poset Version of Ramanujan Results on Eulerian Numbers and Zeta Values," authored by Eric R. Dolores-Cuenca and Jose L. Mendoza-Cortes.
It introduces new proofs of some of Ramanujan’s results regarding Eulerian numbers by generalizing a family of zeta value identities and demonstrating their relevance in the context of disjoint unions of points.
The study establishes a significant connection between these findings and the linear independence of zeta values, leveraging the operad of finite posets to achieve a deeper understanding of these mathematical phenomena.