Deriving an extended one-band Hubbard model for cuprate superconductors
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
The so-called three-band Hubbard model is generally believed to be a good model for fermions on a CuO 2 lattice and to contain key features allowing to understand high-temperature superconductivity in the cuprates. A simpler and more popular model is the one-band Hubbard model. In this thesis,an extended one-band Hubbard model is derived from the three-band model.
First, some mathematical background is given, as well as an introduction to Hubbard-like models. Then, to derive the extended one-band Hubbard model, the CuO 2 lattice is divided into clusters of one Cu and two O sites, and a variant of the Feshbach method is used to replace each such cluster by a single lattice site. To nd a suitable one-band model, all Hamiltonian matrix elements are matched between the two models. Finally, dierent sets of three-band parameters are considered, and it is studied how this aects the parameters in the extended one-band Hubbard model.
Place, publisher, year, edition, pages
2011. , 74 p.
Trita-FYS, ISSN 0280-316X
IdentifiersURN: urn:nbn:se:kth:diva-37895OAI: oai:DiVA.org:kth-37895DiVA: diva2:435555
Subject / course
Master of Science in Engineering -Engineering Physics
UppsokPhysics, Chemistry, Mathematics
Langmann, Edwin, Professor