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

• MATLAB: Getting Started
• MATLAB: Sparse Matrices

Hands-on Lab tutorials by MathWorks

• MATLAB Student Center
• Rapid code iteration using cells in the Editor

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). [PDF]
• UD Crash Course on Matlab

Implementation Tools

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

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 (script to compute the conductance and total and local density of states of a 1D nanowire, with possible potential barriers or impurities, attached to two semi-infinite electrodes)

Tunneling magnetoresistance in tight-binding models of magnetic tunnel junctions

• 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 assumed to be periodic in the transverse-to-transport direction)

Quantum transport in graphene nanostructures using NEGF

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

DFT calculations using GPAW

GPAW 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
• Crash course on Python

GPAW Exercises Related to Midterm Project

• How to submit GPAW jobs on mills
• Band structure of bulk graphene
• Subband structure of graphene nanoribbons
• Subband structure of carbon nanotubes

Additional GPAW Exercises

• Getting started with GPAW (structure and binding energies of simple molecules)
• Basics of GPAW calculations
• Band structure of Fe
• DOS of Fe

NEGF-DFT electronic transport calculations using GPAW

Linear response calculations at vanishingly small voltage bias

• Crash course on NEGF+DFT codes
• Conductance of single-molecule Pt-$\mathrm {H} _{2}$-Pt nanojunction.

Finite voltage bias calculations

• 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]