palful wrote: ↑Tue Jun 13, 2023 8:28 pm
Dear Sitangshu,

The electron phonon matrix element <nk| dV_lq |mk-q> is saved by yambopy in an array with dimension [Nq,Nk,Nl,Nm,Nn].

It is read from the Yambo ndb.elph_*_fragment_* databases, where each fragment corresponds to a value of q.

Here k is the electron momentum, q=k-k' is the momentum transfer (phonon momentum), n and m are electronic band indices and l is the phonon mode index.

Therefore, you have access to all intraband and interband matrix elements. For example, keeping n=m and q=1 gives the intraband value at vanishing momentum transfer. If you want the coupling between K and K' points in MoS2, you have to work with the indices of k and q. For example, you can take the k-index corresponding to K and the q-index such as K-Q=K'.

In order to find out which indices to correspond to which cartesian coordinates, you can plot the annotated k and q grids using yambopy (as seen in the tutorial).

Cheers,

Fulvio

Hello,

I tried to use elph_plot.py code of yambopy to calculate both intra- and intervalley deformation potentials. As per the code attached (for monolayer MoS2), I use i_n = i_m = 26 as intraband value (CBM occurs at 27th band); i_nu = 1 to choose LA mode of phonon; i_k = 142 (i.e. 'K' point in the BZ plot attached, generated using bz_plot.py) as CBM occurs at the 'K' point. It gives the expanded gkkp matrix elements in q-space (i.e. g_of_q) and it seems that g_of_q is centered at i_k = 142 (i.e. 'K' point in the BZ for electrons). Is it right?

Next using this g_of_q matrix elements I tried to calculate intra- and intervalley deformation potentials for selected phonon modes using the equation that I have attached. Say, for 'Gamma' to 'K' direction (along expanded points 0, 34, 88, 124, 142 in BZ), I calculate M and its slope w.r.t. |q|. This slope near 'Gamma' gives intravalley deformation potentials. Is it right? If yes how to get the intervalley deformation potentials, as in elph_plot.py code I cannot set a particular i_q value, as g_of_q is a complete q-space matrix?

Code: Select all

```
"""
Tutorial for YamboElectronPhononDB.
Electron-phonon matrix element reading and plotting
EDIT the path below to point to the yambo SAVE_expnd_new folder.
"""
save_path='yambo-with-elph/MoS2'
from yambopy import *
import numpy as np
import matplotlib.pyplot as plt
import math
if __name__ == "__main__":
"""
Main part of the script
"""
Kspace_Plot = False
Qspace_Plot = True
# Customly chosen matrix elements
i_n, i_m = [26,26] #i_n =3 -> valence band, i_n = 4 -> conduction band in 2D-hBN
i_nu = 1 # LA phonon mode in 2D-hBN at K (ZO mode at Gamma); LO, TO modes are i_nu=4,5
i_q = 142 # This is the K-point in the hexagonal BZ
i_k = 142
# #
# Start Yambopy part #
# #
# Create "lattice" object by reading the ns.db1 database inside the yambo SAVE_expnd_new
ylat = YamboLatticeDB.from_db_file(filename=save_path+'/SAVE_expnd_new/ns.db1')
#print(ylat)
qx = ylat.car_kpoints[:,0]
qy = ylat.car_kpoints[:,1]
alat = 5.97229044*(0.528e-10) # in m
n = (2*math.pi)/alat
q = (1e-10)*np.sqrt((n*qx)**2+(n*qy)**2) # in 1/Ang
# Create "elphon" object by reading the ndb.elph_gkkp* databases inside the yambo SAVE_expnd_new
yelph = YamboElectronPhononDB(ylat,folder_gkkp=save_path+'/SAVE_expnd_new',save=save_path+'/SAVE_expnd_new')
#print(yelph)
# Print info on how to use this class
#print(yelph.__doc__)
# We select a specific K-point to plot |g(Q)| in qspace
g_of_q = np.abs(yelph.gkkp[:,i_k,i_nu,i_n,i_m])
hbar = (6.62607015e-34)/(2*math.pi) # in (kg m^2/sec) J-sec
m_0= (173.29518e-30)*(1.53381e3) # in kg
omega = np.zeros(5) # in 1/sec
omega[0] = (1e12)*1.088872 # LA
omega[1] = (1e12)*3.399453 # LA
omega[2] = (1e12)*5.585689 # LA
omega[3] = (1e12)*6.443713 # LA
omega[4] = (1e12)*7.042009 # LA
M = np.zeros(5) # in eV/Ang
M[0] = (1e-10)*27.2114*g_of_q[0]/math.sqrt(hbar/(2*m_0*omega[0]))
M[1] = (1e-10)*27.2114*g_of_q[34]/math.sqrt(hbar/(2*m_0*omega[1]))
M[2] = (1e-10)*27.2114*g_of_q[88]/math.sqrt(hbar/(2*m_0*omega[2]))
M[3] = (1e-10)*27.2114*g_of_q[124]/math.sqrt(hbar/(2*m_0*omega[3]))
M[4] = (1e-10)*27.2114*g_of_q[142]/math.sqrt(hbar/(2*m_0*omega[4]))
print('D0 (eV/cm)=',M*(1e8))
q1 = np.zeros(5)
q1[0] = q[0]
q1[1] = q[34]
q1[2] = q[88]
q1[3] = q[124]
q1[4] = q[142]
fit = np.polyfit(q1[0:2+1], M[0:2+1], 1)
coeff = fit[0]
intercept = fit[1]
fit_eq = coeff*q1[0:2+1] + intercept
plt.plot(q1[0:2+1], fit_eq, color='r')
plt.plot(q1, M)
plt.xlabel('q (1/Ang)')
plt.ylabel('M (eV/Ang)')
print('D1 (eV)=', coeff)
if Qspace_Plot:
yelph.plot_elph(g_of_q,s=100,plt_cbar=False,marker='H',cmap='jet')
yelph.ax.set_title('|g(q)| (Hartree)')
yelph.ax.set_xlabel('q_x')
yelph.ax.set_ylabel('q_y')
plt.show()
# We select a specific Q-point to plot |g(K)| in kspace
g_of_k = np.abs(yelph.gkkp[i_q,:,i_nu,i_n,i_m])
if Kspace_Plot:
yelph.plot_elph(g_of_k,s=100,plt_cbar=False,marker='H',cmap='jet')
yelph.ax.set_title('|g(k)| (Hartree)')
yelph.ax.set_xlabel('k_x')
yelph.ax.set_ylabel('k_y')
plt.show()
# #
# End Yambopy part. #
# #
```

Thanks and regards,

Sirsha

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