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The behavior of electrons in a material depend on the material. Crystals and sheets of graphene are special because of their periodicity, i.e. the inability to

The behavior of electrons in a material depend on the material. Crystals and sheets of graphene are special because of their periodicity, i.e. the inability to distinguish one location in the lattice from another over long distances. The wavefuntions of electrons are to first order due to this periodic potential. Crystals are also interesting mathematically because there is a finite number of possible lattices that can exist, and it isn't even that many. All the useful and interesting effects of doping semiconductors is the result of throwing some contaminants in to disrupt the perfect periodicity of the silicon crystal and therebey make junctions that can ultimately be used for computation etc. "Holes" are sort of emergent quasiparticles with charge +1. I think a key term in the article is "moire". When two regular patterns are overlayed and then twisted or offset, they interfere to produce a new emergent pattern, sometimes with radically different periodicity than the original. The electrons must now inhabit this very artificial pattern of pottentials that is neither a crystal or a doped crystal and may not occur in nature at all. Plus there are probably effects caused by the material being nearly 2d. Very exciting stuff, emergent complexity seems to be a major theme in physics so far this century.

westurner 2y ago
"Catalog of topological phonon materials" (2024) https://www.science.org/doi/10.1126/science.adf8458 https://www.science.org/doi/10.1126/science.adf8458 "Non-trivial quantum geometry and the strength of electron–phonon coupling" (2024) https://www.nature.com/articles/s41567-024-02486-0 https://www.nature.com/articles/s41567-024-02486-0 : > Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron–phonon coupling, demonstrating the crucial contributions of the Fubini–Study metric or its orbital selective version to the dimensionless electron–phonon coupling constant. We apply the theory to two materials, that is, graphene and MgB2, where the geometric contributions account for approximately 50% and 90% of the total electron–phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions > Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron–phonon coupling, demonstrating the crucial contributions of the Fubini–Study metric or its orbital selective version to the dimensionless electron–phonon coupling constant. We apply the theory to two materials, that is, graphene and MgB2, where the geometric contributions account for approximately 50% and 90% of the total electron–phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions There is emergence in complex fluid attractor systems. Superhydrodynamics models fluid attractor systems; for example with vorticity in "Gravity as a fluid dynamic phenomenon in a superfluid quantum space. Fluid quantum gravity and relativity." (2015) https://hal.science/hal-01248015/ https://hal.science/hal-01248015/ .. https://news.ycombinator.com/item?id=38871054 https://news.ycombinator.com/item?id=38871054 Vorticity in Electron-Electron interactions: https://news.ycombinator.com/item?id=40360691 https://news.ycombinator.com/item?id=40360691 Is there emergence from just vorticity?

westurner 2y ago

"Catalog of topological phonon materials" (2024) https://www.science.org/doi/10.1126/science.adf8458 https://www.science.org/doi/10.1126/science.adf8458 "Non-trivial quantum geometry and the strength of electron–phonon coupling" (2024) https://www.nature.com/articles/s41567-024-02486-0 https://www.nature.com/articles/s41567-024-02486-0 : > Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron–phonon coupling, demonstrating the crucial contributions of the Fubini–Study metric or its orbital selective version to the dimensionless electron–phonon coupling constant. We apply the theory to two materials, that is, graphene and MgB2, where the geometric contributions account for approximately 50% and 90% of the total electron–phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions > Here, we devise a theory that incorporates the quantum geometry of the electron bands into the electron–phonon coupling, demonstrating the crucial contributions of the Fubini–Study metric or its orbital selective version to the dimensionless electron–phonon coupling constant. We apply the theory to two materials, that is, graphene and MgB2, where the geometric contributions account for approximately 50% and 90% of the total electron–phonon coupling constant, respectively. The quantum geometric contributions in the two systems are further bounded from below by topological contributions There is emergence in complex fluid attractor systems. Superhydrodynamics models fluid attractor systems; for example with vorticity in "Gravity as a fluid dynamic phenomenon in a superfluid quantum space. Fluid quantum gravity and relativity." (2015) https://hal.science/hal-01248015/ https://hal.science/hal-01248015/ .. https://news.ycombinator.com/item?id=38871054 https://news.ycombinator.com/item?id=38871054 Vorticity in Electron-Electron interactions: https://news.ycombinator.com/item?id=40360691 https://news.ycombinator.com/item?id=40360691 Is there emergence from just vorticity?