Jose Luis Mendoza-Cortes

Jose L. Mendoza-Cortes is a theoretical condensed matter physicist and material scientist specializing in computational physics, materials science, chemistry, and engineering. His studies include methods for solving Schrödinger's or Dirac's equation, machine learning equations, among others. These methods include the development of computational algorithms and their mathematical properties.

Because of graduate and post-graduate studies advisors, Dr. Mendoza-Cortes' academic ancestors are Marie Curie and Paul Dirac. His family branch is connected to Spanish Conquistador Hernan Cortes and the first Viceroy of New Spain Antonio de Mendoza.

Dr. 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. He has made several key contributions to a substantial number of subjects (see below) including Relativistic Quantum Mechanics, models for Beyond Standard Model of Physics, Renewable and Sustainable Energy, Future Batteries, Machine Learning and AI, Quantum Computing, Advanced Mathematics, to name a few. From all these contributions on disparate fields, he is considered a Polymath.

Education
Throughout his childhood, he participated in various events such as the National Olympiad for Primary Schools, and the Chemistry, Informatics, Mathematics, and Physics Olympiads. He participated in the 34th International Chemistry Olympiad at Groningen, Netherlands 2002.

Jose L. Mendoza completed his B.Sc. in chemistry and physics from Tec de Monterrey (ITESM), Monterrey, Mexico in 2008. During this time, he had an interchange program in the last two years of his B.Sc. to finish all the master's degree classes at the University of California, Los Angeles. Following this, he moved to Pasadena, California to complete his M.Sc. at California Institute of Technology (CalTech)in 2010. After the completion of his M.Sc., he stayed at Caltech and completed his Ph.D. in physics in 2012. His research advisor was William Goddard III and his dissertation title is “Design of Molecules and Materials for Applications in Clean Energy, Catalysis and Molecular Machines Through Quantum Mechanics, Molecular Dynamics and Monte Carlo Simulations.” He completed his postdoctoral studies at University of California, Berkeley.

Career
During his undergraduate studies, Dr. Mendoza was awarded the Newcomb Cleveland Prize of the American Association for the Advancement of Science (AAAS) is annually awarded to the author(s) of outstanding scientific paper published in the Research Articles or Reports sections of Science. This is AAAS's oldest and most prestigious award. Specifically, Dr. Mendoza-Cortes synthesized and designed the first 3D-Covalent organic framework (COF), ever, COF-103 and COF-108, helping unleash this new field. Besides synthesizing them, Dr. Mendoza-Cortes created the computational models that would simulate their X-ray pattern, thus identifying and characterizing their chemical structures.

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. He started the theory and simulations arm of JCAP at Caltech and then moved to UC Berkeley.

In 2015, he started as a Faculty with Florida State University at the Department of Physics, Scientific Computing, Chemical and Biomedical Engineering, Materials Science and Engineering until 2020. During this time, he was also a scientist at the National High Magnetic Field Laboratory and Condensed Matter group. He is credited with starting and developing the first class in Quantum Computing and Machine Learning at Florida State University.

Mendoza is currently a Faculty at the Department of Physics and Astronomy & Chemical Engineering and Material Science at Michigan State University. He created several courses combining Machine Learning, Physics, Chemistry, Materials Science, and Quantum modeling to create materials starting at the atomic scale.

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. This is a fellowship is for only 50 faculty per year including both the US and Canada. His works on the amphidynamic behavior in oligo-functionalized covalent-organic frameworks were selected as one of the 2018 Emerging Investigators collection from the Royal Society of Chemistry. 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.

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.

Dr. Mendoza's research has been featured in Forbes, CNBC, MRS Bulletin, C&EN News, Public Radio, Laser Focus World magazine, and the DOE Highlights, to name a few. This work has been disseminated across more than 60 national and international invited and keynote lectures at scientific meetings and universities all over the world.

Published Work
As an independent researcher, Dr. Mendoza-Cortes' work has been cited over 8,000 times with an average of over 148 citations/paper, as well as Erdős number = 5, H-index = 27, and i10-index = 40.

Relativistic Quantum Mechanics
The nuclear waste problem can be alleviated if we can understand the heaviest elements, the actinides. Studies of actinide-containing compounds are at the frontier of the applications of current theoretical methods due to the need to consider relativistic effects and approximations to the Dirac equation in them. The Mendoza-Cortes lab contributed to creating new ways to understand relativistic effects by implementing and deploying four-component relativistic quantum calculations and scalar approximations, thus pushing the frontier of what can be done currently.

The Mendoza-Cortes lab has expanded the study of relativistic effects to 2-dimensional materials, which will allow us to design and understand quantum materials, specifically topological insulators. 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.

Beyond Standard Model of Physics
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. The cover of the paper discusses how we understand the structure of a certain type of defect in diamond and its use in quantum applications, which was featured in the cover. "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.

Renewable Energy and Sustainability
Solar Energy - Artificial Photosynthesis. 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 methodology, named SALSA (Substitution Approximation evoLutionary Search and Ab-initio calculations), involves generating candidate structures from a database of known compounds, filtering them based on desired properties, and then employing algorithms to determine their most stable crystal structures. 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.

Hydrogen Storage. Dr. Mendoza-Cortes and coworkers published a breakthrough paper related to sustainable fuels, more specifically Hydrogen storage. In this paper, they designed porous materials that can achieve the US Department of Energy hydrogen storage targets for 2025. These porous materials incorporated the more affordable and abundant elements often outperformed the precious metals. This promising development brings us one step closer to realizing a Hydrogen economy. This paper was featured on the Journal cover.

Future Batteries
High-voltage lithium batteries. The Mendoza-Cortes lab helped to better understand and design high-voltage lithium batteries. The breakthrough involves using cationic chain transfer agents to prevent the degradation of ether electrolytes by arresting uncontrolled polymer growth at the anode. Additionally, cathode electrolyte interphases (CEIs) composed of preformed anionic polymers and supramolecules are used to extend the high-voltage stability of these electrolytes. This study contributes to the broader field of energy storage technologies, offering methods to overcome challenges related to the stability of polymer electrolytes in high-voltage lithium batteries, thus advancing the development of more sustainable and effective energy storage solutions.

Potassium Batteries. The Mendoza-Cortes lab in collaboration with the Rodriguez-Lopez labs found a way to improve the performance of potassium-ion batteries (KIBs). The research utilizes ultrathin few-layer graphene (FLG) electrodes. The FLG electrodes are preconditioned in a Li+-containing electrolyte to form a solid-electrolyte interphase (SEI). This method is aimed at improving the intercalation performance of K+ in these electrodes. 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. This research contributes to the broader field of energy storage technologies and could have implications for the development of more sustainable and cost-effective battery systems.

Machine Learning and AI
Dr. Mendoza et al lab proved mathematically what could be the limit of conexions and neurons for a neural network, which is the basis for the most popular machine learning and AI algorithms, thus helping paved the way to have a solid understanding of ML/AI. More specifically, the paper "Polychrony as Chinampas" delves into the dynamics of signal flow through nonlinear pathways, emphasizing nodes that emit signals upon receiving stimuli or when two incoming signals surpass a threshold. This process forms polychrony groups, which can lead to cascades, characterized by a net gain in activated nodes termed as 'profit.' Dr. Mendoza et al introduced a novel analogy to graph theory, referring to cascades as 'chinampas' and providing a topological classification for them. 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.

The Mendoza-Cortes lab created a Machine Learning course that includes machine learning methods, quantum computing, and game development: Machine Learning guide for non-Computer Science majors with applications to Art, Engineering, Physics, Medicine, and Chemistry. Some algorithms that are covered include Neural Networks (NN), Support Vector Machines (SVM), Convolutional Neural Networks (CNN), Bayesian methods, Genetic Algorithms, Decision Trees, K-Nearest-Neighbors (KNN), Non-Negative Tensor Factorization to name a few. Some of these algorithms are applied to problems in Physics, Chemistry, Art, and Medicine.

Quantum Computing
The Mendoza-Cortes lab created guides for introduction to Quantum Computing. Quantum computing is one approach to obtaining answers that classical conventional computers cannot easily handle or are intractable at all. Using the power of superposition and entanglement of quantum systems, quantum algorithms have the potential to provide speed-up (exponential or quadratic) over classical algorithms. For now, the existing quantum devices are not identified as universal quantum computers but have their advantages over conventional computers. We can implement certain algorithms with a limited number of qubits in systems such as IBM Q, DWave, and Qiskit.

Advanced Mathematics
Dr. Mendoza has been working on advanced mathematics, specifically on the fundamentals of machine learning and AI as well as problems that can not be solved with classical computers. 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 explores the application of finite posets and their algebras to investigate the combinatorial properties of zeta values. 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.

Random facts
These are some random facts about his life so far:
 * He published a paper in the field of mathematics, and, due to this, he now have an Erdős number number of 5. With this paper, anyone who publishes with him will gain at least Erdős number of 6.
 * He met the president of the country as one of the best students in the national academic Olympiad, which included all the 6th graders.
 * He appeared on the back cover of all the textbooks of a public high school system because he participated in all of the available Science Olympiads at the time (Chemistry, Physics, Informatics, and Mathematics) and represented a country.