lsqt-matlab

A 200-line MATLAB code for a linear-scaling quantum transport method

• This code can be used to obtain intrinsic electronic transport properties of large systems described by a real-space tight-binding Hamiltonian. It differs from the GPUQT code (https://github.com/brucefan1983/gpuqt) in two ways:

  • GPUQT is more than two orders of magnitude faster.
  • GPUQT accepts inputs for a general Hamiltonian, but the current code is only for the square lattice model with Anderson disorder.

• Purposes of this code

  • Help the readers who are interested in this linear-scaling quantum transport method to better understand it.
  • The students in my course are asked to use the code to reproduce the results in sections 5.1 of Ref. [2] below. This is an optional course project.

• The major references for the implementation are (check the references cited in the papers below for original works on this method):

  • [1] Z. Fan, A. Uppstu, T. Siro, and A. Harju, Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene, Comput. Phys. Commun. 185, 28 (2014).
  • [2] Z. Fan, V. Vierimaa, and Ari Harju, GPUQT: An efficient linear-scaling quantum transport code fully implemented on graphics processing units, arXiv:1705.01387 [physics.comp-ph], to be published in Comput. Phys. Commun.

File organizations

• This package consists of the following MATLAB functions (the file names are the same as the function names):

  • lsqt (calls find_H, create_state, find_dos, find_vac, and find_msd)
  • find_dos (calls find_moments and chebyshev_summation)
  • find_vac (calls evolve, find_moments and chebyshev_summation)
  • find_msd (calls evolve, evolvex, find_moments and chebyshev_summation)
  • find_H (calls nothing)
  • create_state (calls nothing)
  • evolve (calls nothing)
  • evolvex (calls nothing)
  • chebyshev_summation (calls nothing)
  • find_moments (calls nothing)

• lsqt is the driver function which the user will call.

Inputs and outputs of the driver function (Nt is the number of time points; Ne is the number of energy points)

• Inputs of the driver function
  • Nx: number of lattice points in the x direction
  • Ny: number of lattice points in the y direction
  • W: Anderson disorder strength
  • E: energy points (1*Ne matrix)
  • E_max: energy scaling factor
  • dt: time steps (Nt*1 matrix)
  • M: order of Chebyshev polynomial expansion
  • flag_vac: if this is 1, calculate the VAC and related quantities
  • flag_msd: if this is 1, calculate the MSD and related quantities
• Outputs of the driver function
  • dos: the density of states (DOS), 1*Ne matrix
  • vac: the velocity autocorrelation (VAC), Nt*Ne matrix
  • msd: the mean square displacement (MSD), Nt*Ne matrix
  • sigma_vac: conductivity from the VAC, Nt*Ne matrix
  • sigma_msd: conductivity from the MSD, Nt*Ne matrix
• Unit system
  • basic units:
    • reduced Planck constant hbar = 1
    • elementary charge e = 1
    • energy unit gamma is choosen by the user
    • length unit a is choosen by the user
  • derived units:
    • time: hbar/gamma
    • DOS: 1/gamma/a^2
    • VAC: a^2*gamma^2/hbar^2
    • MSD: a^2
    • electrical conductivity: e^2/hbar

Contact

• Zheyong Fan: brucenju(at)gmail.com