Computer Lab

Installing Python and course related packages

• Install Anaconda
• Install KWANT package:

conda install -c conda-forge kwant

• Install PythTB package:

pip install pythtb --upgrade

• Install and test ASE package:

pip install --upgrade --user ase
python -m ase test

• GPAW package can be easily installed using Anaconda on Linux or MacOS
• If you want to add RISE package for Jupyter notebooks, execute:

conda install -c conda-forge rise

JUPYTER notebooks for hands-on practice

• Getting started with Python
• Getting started with NumPy and SciPy
• Getting started with Matplotlib
• Nanostructures in equilibrium with Python
• Nanostructures in equilibrium with PythTB
• Nanostructures out of equilibrium with Python
• Nanostructures in equilibrium with KWANT
• Nanostructures out of equilibrium with KWANT
• Superconducting nanostructures with KWANT

JUPYTER notebooks tips and tricks

• Force Jupyter notebook to display all outputs of a give cell (and not just the last one as default):

from IPython.core.interactiveshell import InteractiveShell
InteractiveShell.ast_node_interactivity = "all"

• How do you know that Jupyter notebook is running:
  • Cell Number Indicator: When a cell is actively executing, the input prompt on the left side of the cell will display an asterisk In [*] instead of a number. Once the execution is complete, the asterisk will be replaced by a sequential number In [1], In [2], etc.
  • Kernel Status Indicator: In the top-right corner of the Jupyter Notebook interface, there is a small circle. This circle indicates the kernel's status:
    • Solid/Grey: The kernel is busy, meaning a cell is currently executing.
    • Empty/White: The kernel is idle, meaning no cells are currently executing.
  • Executing this command will display a list of all running Jupyter Notebook servers, including their URLs and the ports they are using.

jupyter notebook list

Python references

• J. M. Stewart and M. Mommert, Python for Scientists (Cambridge University Press, Cambridge, 2023). [PDF] + Jupyter notebooks for each Chapter
• Scipy lecture notes
• NumPy: Absolute Beginners Tutorial
• NumPy: Quickstart tutorial
• NumPy for Matlab users
• Timing Python script performance:

 
def fibonacci(n):
    """Calculate the n-th Fibonacci number using recursion."""
    if n <= 0:
        return 0
    elif n == 1:
        return 1
    else:
        return fibonacci(n - 1) + fibonacci(n - 2)
import time
start = time.perf_counter()
result = fibonacci(40)
end = time.perf_counter()
elapsed = end - start
print(f'Time taken: {elapsed:.6f} seconds')

KWANT references

• KWANT documentation
• VIDEO: Introduction to KWANT
• Learning KWANT through examples
• Selecting matrix solvers in KWANT
• KWANT tools

Density functional theory with GPAW package

How to run GPAW on ulam

GPAW has been installed on ulam with the OS installed python 2.6.

• in order to use the serial version of GPAW type:

 python your_gpaw_program.py

• in order to use the parallel version of gpaw use the following syntax (replace 8 with the number of cores you want to use):

 mpirun -np 8 gpaw-python_openmpi your_gpaw_program.py

Getting started with GPAW

• VIDEO Tutorial: Electronic structure calculations with GPAW
• VIDEO Tutorial: Short overview of GPAW
• VIDEO Longer overview of GPAW
• VIDEO Tutorial: CO molecule
  • Plotting CO wavefunction
  • relax.py used in VIDEO Tutorial:

from ase import Atoms
from ase.io import write
from ase.optimize import QuasiNewton
from gpaw import GPAW

d = 1.10  # Starting guess for the bond length
atoms = Atoms('CO', positions=((0, 0, 0),
                               (0, 0, d)), pbc=False)
atoms.center(vacuum=4.0)
write('CO.cif', atoms)
calc = GPAW(h=0.20, xc='PBE', txt='CO_relax.txt')
atoms.set_calculator(calc)

relax = QuasiNewton(atoms, trajectory='CO.traj', logfile='qn.log')
relax.run(fmax=0.05)

• ASE tutorials
• Basics of GPAW calculations
• Band structure of Ni plotted in three steps
• Lattice constant, DOS, and band structure of Si
• STM simulations

GPAW Exercises Related to Midterm Project

• Band structure of bulk graphene
• Subband structure of graphene nanoribbons
• Subband structure of carbon nanotubes

References

• Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method, J. Phys.: Condens. Matter 22, 253202 (2010). [PDF]
• Parameters selection in GPAW scripts
• LCAO basis set in GPAW
• Parameters selection in ASE to define atomic coordinates
• Density of States in GPAW
• About k-point sampling

First-principles quantum transport calculations using NEGF+DFT within GPAW package

Theory Background

• Crash course on NEGF+DFT codes
• NEGF+DFT within GPAW - see also J. Chen, K. S. Thygesen, and K. W. Jacobsen, Ab initio nonequilibrium quantum transport and forces with the real-space projector augmented wave method, Phys. Rev. B 85, 155140 (2012). [PDF]
• M. Strange, I. S. Kristensen, K. S. Thygesen, and K. W. Jacobsen, Benchmark density functional theory calculations for nanoscale conductance, J. Chem. Phys. 128, 114714 (2008). [PDF]
• D. A. Areshkin and B. K. Nikolić, Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing a large number of atoms, Phys. Rev. B 81, 155450 (2010). [PDF]

GPAW Exercises

• Pt-${\mathrm{H}}_2$-Pt nanojunction.
• Annulene molecule between two graphene nanoribbon electrodes nanojunction