Computer Lab

Python and package installation

• 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

JUPYTER notebooks for hands-on computer lab sessions

• Jupyter Notebook: First steps with Python
• Jupyter Notebook: Functions and Objects in Python
• Jupyter Notebook: Kwant Introduction
• PDF: Kwant Introduction
• Jupyter Notebook: Kwant Honeycomb Lattice
• PDF: Kwant Honeycomb Lattice
• Jupyter Notebook: Kwant Solvers
• PDF: Kwant Solvers

Python references

• J. M. Stewart, Python for Scientists (Cambridge University Press, Cambridge, 2014). (PDF from UD library)
• Scipy lecture notes
• NumPy for Matlab users
• Timing Python script performance

KWANT references

• KWANT documentation
• Selecting matrix solvers in KWANT
• KWANT tools
• VIDEO: Introduction to KWANT
• Learning KWANT through examples
• Interactive tutorials using Jupyter Notebooks
• Discretization of continuous Hamiltonians
• Conductance of graphene nanoribbons
• Conductance of topological insulators built from graphene nanoribbons
• Spin Hall effect in four terminal devices
• Topological Hall effect in four terminal devices

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: 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