Phonon Transport

Calculates the phononic transport according to [1].

Requirements

• Python 3.x
• tmoutproc

Calculation of phonon transmission

python3 phonon_transport.py config_file

Preparation

• Build molecule in Avogadro. Save as .xyz file
• Relaxation and hessian:
  • Geometry optimization e.g. using xtb (https://xtb-docs.readthedocs.io/en/latest/optimization.html)
  • Align molecule -> x axis through anchoring atoms (not hydrogen). Important if in_plane option is used
  • Calculate hessian e.g using xtb (https://xtb-docs.readthedocs.io/en/latest/hessian.html)

Config file

[Data Input]
data_path= #path where data is located
hessian_name=hessian #filename of hessian
coord_name=coord.xyz #filename of coord file (.xyz and Turbomole format allowed)

[Calculation]
n_l=5,1,2 #indices of atoms (-> ordering of coord file) connected to left lead
n_r=1,2,3 #indices of atoms (-> ordering of coord file) connected to right lead
M_L=Au # atom type in left/right lead
M_C=Au # atom type in center connected to lead
gamma= #coupling constant from [Phonon interference effects in molecular junctions](https://doi.org/10.1063/1.4849178)
E_D= #Debey energy
N= #number of grid points for transmission calculation
in_plane=False #in_plane option from [Phonon interference effects in molecular junctions](https://doi.org/10.1063/1.4849178)
T_min= #lower bound for thermal conductance integral (avoid zero)
T_max= #upper bound for thermal conductance integral
kappa_grid_points= #number of grid point in thermal conductance integral
T_kappa_c= #temperature at which kumulative thermal conductance is calculated

[Eigenchannel]
eigenchannel=True (True: Eigenchannels are calculated. See comment)
every_nth=1 (for all, -1 for none. Specifies number of plotted eigenchannels in data_path/transport_channels.pdf)
channel_max=3 (number of plotted and stored eigenchannels. All channels are calculated)

[Data Output]
plot_g=True #plot surface green function 

Output

• data_path/phonon_trans.dat
• data_path/kappa.dat
• data_path/transport.pdf
• data_path/g0.pdf (optional, see plot_g)
• data_path/transport_channels.pdf (optional, see Eigenchannel)
• data_path/transport_channels.dat (NOT IMPLEMENTED YET, see Eigenchannel)
• data_path/eigenchannels/*.nmd (optional, see Eigenchannel)

NOTE: transport_channels.dat not implemented yet.

Calculation of Eigenchannels

If eigenchannel=True is set, the transmission eigenchannels according to [2] are calculated. The total transmission is then calculated as sum over all eigenchannels. The first channel_max channels are plotted in data_path/transport_channels.pdf. every_nth specifies which eigenchannels are written to *nmd file.

Calculation of Propagator elements

NOTE: Not implemented yet.

Calculation of Participation Ratio

NOTE: Not implemented yet.

Calculation of thermal conductance (Standalone)

Usage

python3 calculate_kappa.py config_file

Calculates thermal conductance from phonon transmission. Energy must be in Hartrees!

Preperation

Transport calculation for transmission (does not necessarily have to be calculated with this program)

Config file

A reduced config file is sufficient for this

[Data Input]
data_path= #path where data is located
transp_name= #name of file containing phonon transmission
transp_units = [har],[sqrt(har/(bohr**2*u))] # hartree is default

[Calculation]
kappa_int_lower_E=0 #lower integral limit in kappa Energy integral in meV (optional, for further analysis). See commet below
kappa_int_upper_E=5 #upper integral limit in kappa Energy integral in meV (optional, for further analysis). See comment below
T_min= #lower bound for thermal conductance integral (avoid zero)
T_max= #upper bound for thermal conductance integral
kappa_grid_points= #number of grid point in thermal conductance integral

If kappa_int_lower_E and kappa_int_upper_E are set, the cumulative thermal conductance $\kappa^{\mathrm{c}}_{\mathrm{ph}}$ is calculated with this integral limits at 300K.

Output

• data_path/kappa.dat
• data_path/kappa.pdf
• data_path/kappa_c.dat (optional)
• data_path/kappa_c.pdf (optional)

Calculation of Phonon Eigenchannels (Standalone)

NOTE: Not implemented yet.

Planned features

• Eigenchannel

  • .g98 files for Eigenchannels
  • Calculation of Phonon Eigenchannels (Standalone)
  • Writeout of eigenchannel data

• Multiple electrode models

• Database for coupling parameters or more consistent calculation

• Example files

• Writeout of propagator elements

• Writeout of Participation ratio

References

[1] Markussen, T. (2013). Phonon interference effects in molecular junctions. The Journal of chemical physics, 139(24), 244101. https://doi.org/10.1063/1.4849178
[2] Klöckner, J. C., Cuevas, J. C., & Pauly, F. (2018). Transmission eigenchannels for coherent phonon transport. Physical Review B, 97(15), 155432. https://doi.org/10.1103/PhysRevB.97.155432

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Matthias Blaschke [email protected]