Transport durch einen p-n Übergang in Graphene

#include "tqt.h"

using namespace TQT;

//Define a Fermi function used for potential steps
REAL pot(REAL x, REAL x0, REAL a0)
{
  return 1. / (1. + exp((x - x0) / a0));
}

int main()
{

  //Run through all different bands
  for (INDEX wp_id = 0; wp_id < 20; wp_id++)
  {

    //Define a graphene nanoribbon (length=500 unit cells, with=6*2 unit cells)
    Grid grid(500, 6, 2.46 * SI_ANGS, 2.46 * SI_ANGS);

    //Define atomistic graphene Hamiltonian and corresponding state to propagate
    GrapheneZZ2 hamiltonian(grid);
    Timestate state(hamiltonian);

    //Define a time discretization and split it every 50 time steps
    Timeline timeline(500.0e-15, .1e-15);
    timeline.add_equalsplit(50);

    //Define global parameters (split multiple valleys, energy bounds) of the leads
    LeadParam leadparam(timeline, hamiltonian);
    leadparam.set(LeadParam::SPLIT);
    leadparam.set_Emin(-7.*SI_CHARGE_ELECTRON);
    leadparam.set_Emax(5*SI_CHARGE_ELECTRON);
    leadparam.info();

    //Initialize two leads at -9nm and +9nm of the p-n junction and write bands
    LeadWavePacket lead1(leadparam, -9. * SI_NM, grid.get_y0(), -9. * SI_NM,
        grid.get_y1(), "lead1");
    LeadWavePacket lead2(leadparam, 9. * SI_NM, grid.get_y1() - 1.e-10, 9. * SI_NM,
        grid.get_y0(), "lead2");
    lead1.write_band("band_lead1.plt");
    lead2.write_band("band_lead2.plt");

    //Add potential and left/right absorber to the Hamiltonian 
    {
      REAL border = 40 * SI_NM;
      REAL border_width = grid.get_x1()-border;
      REAL x;
      for (INDEX ix = 0; ix < grid.get_NX(); ix++)
        for (INDEX iy = 0; iy < grid.get_NY(); iy++)
        {
          x = grid.get_x0() + ix * grid.get_dx();
          hamiltonian.V(ix, iy) = .6 * pot(-x, 0., 1.492 * SI_NM) *
              SI_CHARGE_ELECTRON;
          hamiltonian.M(ix, iy) += .000001 * SI_CHARGE_ELECTRON;
          hamiltonian.Vat(ix, iy) -= 0.15 * pot(x, -border-0.5*border_width,
              border_width*0.3) * SI_CHARGE_ELECTRON;
          hamiltonian.Vat(ix, iy) -= 0.15 * pot(-x, -border-0.5*border_width,
              border_width*0.3) * SI_CHARGE_ELECTRON;
        }
    }

    //Initialize a propagator using Faber polynomials with DeltaE=20, E0=0, d=0.4
    FaberPropagator prop(timeline, state, 20. * SI_CHARGE_ELECTRON, 0., 0.4);
    prop.set_Hamiltonian(hamiltonian);

    //Define the norm observable and add it to the propagator
    Norm norm(timeline, state);
    prop.add(norm);

    //Define the transmission observable for the band wp_id and analyze all
    //amplitudes through lead1 and lead2 between -2.5eV and 1.8eV
    Transmission transmission(timeline, state, lead1, wp_id, -2.5 *
        SI_CHARGE_ELECTRON, 1.8* SI_CHARGE_ELECTRON);
    transmission.add(lead2);
    //Add the transmission to the propagator
    prop.add(transmission);

    //Calculate the time evolution
    prop.runall();

    //Write the time evolution of the norm
    std::stringstream filename;
    filename << "norm" << wp_id << ".nc";
    norm.write_t(filename.str().c_str());

    //Write the energy dependent transmission into all modes
    filename.str("");
    filename << "all_transmissions" << wp_id << ".dat";
    transmission.write_E(filename.str().c_str());

    //Write the energy dependent transmission into different leads
    filename.str("");
    filename << "sum_transmissions" << wp_id << ".dat";
    transmission.write_E_sum(filename.str().c_str());

  }//End loop through all different bands

  return 0;
}