BdG equation

What is BdG equation,first time I encounter this is in quantum menchanies,I just known that we can write a Hamilitonian in matrix form,just filling numeric value in definite position,we can diagonalization this matrix,we can get eigenvalue and eigenvector,all problem is solved.

Sometimes the general formation about BdG equation just like this: $$ \begin{gathered} \begin{bmatrix} H(\vec{r}) & \Delta \\\ \Delta^* & -H(\vec{r}) \end{bmatrix} \begin{bmatrix} u\\\ v \end{bmatrix} =E \begin{bmatrix} u\\\ v \end{bmatrix} \end{gathered} $$ The final aim is obtain the eigenvalue *E* and eigrnvector $[u,v]$. My project is repeat this particle Vortex pinning by the point potential in topological superconductors:A scheme for braiding Majorana bound states,this is my first project in Master studying,teacher asked me read it and use fortran or other program language to solve it.

Solving this problem really made me in trouble,I have a litte experience in program but doesn’t have enough help in this project.At first I have no idea about BdG I review my courses like ,.

I don’t want to talk about many about my project,I finish my project under help of my teacher and senior,I really thanks to them. I upload my whole project in github,you can view this project in that and use it,but this code doesn’t have more value unless you would like to learn BdG equation application and how to convert Hamiltonian to code maybe helpfull.

Result

These are some result images about my calculation which attract you in some meanning.