1D Semiconductor-superconductor nanowire

This repository summarizes all the codes in my Majorana-related works during my Ph.D.

Usage

python Majorana_main.py -mu=1 -L=1 -Delta0=0.2 -cond -LDOS calculates the conductance (-cond) and LDOS (-LDOS) of a nanowire with wire length being 1 micron, chemical potential in the semiconductor being 1 meV, and superconductor gap being 0.2 meV.

To run it in parallel using $N cores, use mpirun -np $N_cores python -m mpi4py.futures Majorana_main.py -mu=1 -L=1 -Delta0=0.2 -cond -LDOS, where $N should be replaced by the number of cores available.

Output

-cond

• -lead_num=1 -lead_pos=L or -lead_pos=R: conductance.
• -lead_num=1 -lead_pos=LR: conductance from the left end and right end, separately.
• -lead_num=2 -lead_pos=LR: nonlocal conductance, topological visibility, thermal conductance (kappa)
• Example: mpirun -np 4 python -m mpi4py.futures Majorana_main.py -L=1 -mu=1 -lead_num=2 -lead_pos=LR -cond

-LDOS

• Local density of states as a function of x and y where y has to be V_bias. The third axis is the spatial position.

• Example: mpirun -np 4 python -m mpi4py.futures Majorana_main.py -L=1 -mu=1 -lead_num=2 -lead_pos=LR -LDOS -barrier_E=0 -dissipation=0

-energy

• Calculate the energy spectrum. If the self-energy SE is not flagged, exact diagonalization is used. Otherwise, the energy spectrum is obtained by first calculating the LDOS, and exacting the peaks.

• Example (No self-energy): mpirun -np 4 python -m mpi4py.futures Majorana_main.py -L=1 -mu=1 -lead_num=2 -lead_pos=LR -energy -barrier_E=0 -dissipation=0

• Example (Self-energy): mpirun -np 4 python -m mpi4py.futures Majorana_main.py -L=1 -mu=1 -lead_num=2 -lead_pos=LR -energy -barrier_E=0 -dissipation=0 -SE

-wavefunction

• Wavefunction is better visualized using jupyter notebook. An example if provided in wavefunction.ipynb.

Help

python Majorana_main.py -h shows the definitions for all parameters.

Imhomogeneous Potential type

NB: Some rare types of inhomogeneous potentials have been removed in the newer branch refactoring-2.

Requirements

kwant, mpi4py, tinyarray, SciPy, NumPy, matplotlib,

To Do:

• Extend y-axis beyond the energy (bias voltage) in calculating the LDOS
• Incorporate the finite temperature (only support when y is v_bias)
• Add the wavefunction
• Energy spectrum