Computer Lab

Unix Training

• Getting Started With UNIX/Linux
• Summary of Basic Unix Commands
• UNIX Tutorial
• UD Mills Supercomputer User Guide

MATLAB Training

Hands-on tutorials by Instructor

• Getting started with MATLAB
• Sparse matrices
• GPU accelerated computing with MATLAB

Hands-on Lab tutorials by MathWorks

• Getting Started video
• MATLAB video tutorials for students and faculty
• Code Examples
• MATLAB Student Center
• How to run code sections
• Introduction to GPU computing in MATLAB
• Using GPUs with MATLAB

Reference

• MATLAB Brief List of Commands
• MATLAB Documentation
• Some Common MATLAB Programming Pitfalls and How to Avoid Them

Books and notes

• C. Moler, Numerical Computing with MATLAB (SIAM, Philadelphia, 2004).
• C. Moler, Experiments with MATLAB (MathWorks, Natick, 2011).

Implementation Tools

• Running MATLAB m-files in the background under Linux
• Multithreaded MATLAB performance on multicores

Python training

• Crash course on Python
• Hands-on Python: A tutorial introduction for beginners
• Python programming for physicists

Using Anaconda Python on ulam

• in order to enable the python environment provided by Anaconda you need to add the following to your ~/.bashrc:

export PATH="/opt/anaconda/1.9.2/bin:$PATH"

• if you want to use the Accelerate and NumbaPro add-ons you'll need to request a free academic license from here and once you receive the license put it in the ~/.continuum directory in your home directory

MATLAB Scripts

Electron density in nanowires using equilibrium density matrix

• electron_density.m
• Discretization of 1D Hamiltonian

DOS of 1D disordered nanowire using eigenvalues + visualization of Anderson localization of eigenfunctions

• disordered_nanowire.m

Density of states using equilibrium retarded Green function

• dos_negf_closed.m computes DOS for finite 1D wire
• dos_negf_open.m computes DOS for finite 1D wire attached to one or two macroscopic reservoirs
• graphene_dos.m computes DOS for a supercell of graphene with periodic boundary conditions

Magnetic field on the lattice

• How to put magnetic field into tight-binding Hamiltonian

Subband structure of graphene nanoribbons using tight-binding models

• 8zgnr.m (poor man's script follows literally the lecture slide, so it works only for 8-ZGNR)

Quantum transport in 1D nanowires using NEGF

• How to use NEGF matrix formulas: Step-by-step in pictures
• qt_1d.m (computes conductance, as well as total and local density of states for 1D nanowire modeled as tight-binding chain, with possible potential barriers or impurities, attached to two semi-infinite leads)

Tunneling magnetoresistance in tight-binding models of magnetic tunnel junctions using NEGF

• mtj_1d.m (computes TMR of F/I/F MTJs modeled using 1D tight-binding chain)
• mtj_3d.m (computes TMR of F/I/F MTJs modeled using mixed real space and k-space tight-binding model of 3D junctions

Quantum transport in graphene nanostructures using NEGF

• gnr_cond_recursive.m,bstruct.m, blocktosparse.m, sparsetoblock.m, h_zigzag.m, invnn.m, Invb.m

Self.m, (code to compute the conductance of a finite graphene nanoribbon attached to two semi-infinite graphene electrodes)

• M.-H. Liu and K. Richter, Efficient quantum transport simulation for bulk graphene heterojunctions, Phys. Rev. B 86, 115455 (2012). [PDF].

MATLAB functions

• matrix_exp.m (Exponential, or any other function with small changed in the code, of a Hermitian matrix)
• visual_graphene_H.m (For a given tight-binding Hamiltonian on the honeycomb lattice, function plots position of carbon atoms and draws blue lines to represent hoppings between them; red circles to represent on-site potential between them; and cyan lines to represent the periodic boundary conditions; it can be used to test if the tight-binding Hamiltonian of graphene is set correctly); This function calls another three function which should be placed in the same directory (or in the path): atomCoord.m, atomPosition.m, and constrainView.m
• self_energy.m (Self-energy of the semi-infinite ideal metallic lead modeled on the square tight-binding lattice - the code shows how to convert analytical formulas of the lead surface Green function into a working program)
• transmission.m (Transmission function for 1D tight-binding chain with spin-dependent terms)

Quantum transport simulations using KWANT package

• Kwant Website
• Conductance of ZGNR
• Conductance of ZGNR+adatoms=2D topological insulator

First-principles electronic structure calculations using DFT within GPAW package

• Delta benchmark of DFT codes

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 nickel.py

Getting started 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
• STM simulations
• Band structure of Ni plotted in three steps
• Lattice constant, DOS, and band structure of Si

GPAW Exercises Related to Midterm Project

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

Technical Details

• J. Enkovaara et. al., 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
• How to use ASE (Atomistic Simulation Environment) to define atomic coordinates
• LCAO basis set in GPAW
• Quantum transport with GPAW

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

Zero-bias conductance

• Crash course on NEGF+DFT codes
• Conductance of Pt-$\mathrm {H} _{2}$-Pt nanojunction.
• Conductance of annulene molecule between two graphene nanoribbon electrodes

I-V curve calculations

• I-V curve of annulene molecule between two graphene nanoribbon electrodes
• I-V curve of magnetically ordered zigzag GNR
• D. A. Areshkin and B. K. Nikolić, I-V curve signatures of nonequilibrium-driven band gap collapse in magnetically ordered zigzag graphene nanoribbon two-terminal devices, Phys. Rev. B 79, 205430 (2009). [PDF]
• J. Chen, K. S. Thygesen, and K. W. Jacobsen, Phys. Rev. B 85, 155140 (2012). [PDF]