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Tight binding models for high temperature superconductors

This page lists a set of tight-binding models that are suitable to describe high temperature superconductors

Some of the models have been compiled from the literature for comparison, others are calculated using first principles calculations or adjusted to match experimental measured quantities.
For each model, the hopping parameters are given in a comma separated file (csv), and basic plots of the band structure and Fermi surface are provided for comparison. The tight-binding file contains lines with the following format:
rx, ry, rz, a, b, Re(t), Im(t)
Here ri is the i-th component of the real space vector that describes the hopping process, a and b are integer numbers labeling the orbitals and the last two entries are the real and imaginary part of the hopping (usually given in eV).
The corresponding Bloch Hamiltonian (in orbital representation) can be obtained by a Fourier transform and summation over all lines to yield the matrix Hab.


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Simple 1 band model with nearest neighbor and next nearest neighbor hopping parameter; note the energy unit is fixed to the nearest neighbor hopping t=1.
Around half filling, this model describes the low-energy electronic structure of Cuprate materials and has been used widely in the literature. Some of my own investigations include
A. T. Rømer, A. Kreisel, I. Eremin, M. A. Malakhov, T. A. Maier, P. J. Hirschfeld, B. M. Andersen
Phys. Rev. B 92, 104505 (2015)
Pairing symmetry of the one-band Hubbard model in the paramagnetic weak-coupling limit: a numerical RPA study
A. Kreisel, A. T. Rømer, P. J. Hirschfeld, B. M. Andersen
J. Supercond. Nov. Magn. 30, 85 (2017)
Superconducting phase diagram of the paramagnetic one-band Hubbard model Publishers version

Download model and figures: 1band_roemer.tar.gz

Fermi surface at filling of 0.45.
Gap symmetry function for leading superconducting instability using spin-fluctuation theory. (Rømer, et al., Phys. Rev. B 92, 104505 (2015))
Non-interacting (green) and RPA susceptibility.
Density of states.
Band structure along high symmetry directions.