Deeveloped and Optimized Matlab Codes for Tight-Binding Calculations

The following Matlab codes are developed and optimized for tight-binding calculations during my research at Institute of Physics, Academia Sinica before ChatGPT.

Developed Codes:

• Downfolding: use the renormalization method to obtain an effective low-energy Hamiltonian. Similar works has recently been published on arXiv [1][2].

• Basis Rotation: spatially rotate the basis of the tight-binding orbitals (i.e., s-,p-,d-orbitals) to align with the crystal symmetry.

• Spin Moment Rotation: generalized the method of rotating the spin moments to tight-binding models in real space.

• Adaptive Mesh: implement an adaptive mesh refinement technique to improve the calculation speed for accurate Fermi surface.

• Projection Spectrum from Green's Function: calculate the projected spectrum through projection operator obtained by Green's function with an energy-dependent self-energy.

Optimized Codes:

• Linear Conductivities: optimize the integration method on 2D and 3D BZ, substantially improving the computational efficiency.

• Josephson Junction (JJ): optimize and format the codes simulating JJ through NEGF.

• Quasi-Particle Interference (QPI): optimize and format the codes simulating QPI.