# [Pw_forum] Electron-phonon matrix calculation and elph.#iq.#irr.xml

Jaehong Park ignasio.ssp at gmail.com
Mon May 11 05:15:51 CEST 2015

Dear Quantum-ESPRESSO,

I am trying to calculate phonon related property of 2-dimensional
transition metal dichalcogenide(TMDC) and i have several questions about
electron-phonon matrix calculation;

elphmat(j,i) = <psi_{k+q,j}|dvscf_q*psi_{k,i}>

in code "elphon.f90"

>From developer manual and source code of ph.x, I found that the
electron-phonon matrix is written in the file "elph.#iq.#irr.xml" in
q-point and irrep(irreducible representation) wise manner.

There are three questions.

1)

Since my unitcell(2-D TMDC monolayer slab with vacuum) has one metal atom
and two surfur atoms, there are 9 normal modes in total.

At gamma point(q-point), there are only 6 irreps and thus 6 elph.1.#irr.xml
files where #irr runs from 1 to 6 due to degeneracy,

However, where q-point!=0 without such degeneracy, there are 9 irreps and
corresponding 9  elph.#iq.#irr.xml  files.

So, i cannot figure out how i can get collection of xml files which
correspond to the specific normal mode i concern for all q-points(by
collecting xml files for q=0 and q!=0).

Numbering  each mode or irrep even does not seem to follow magnitude of the
phonon frequency. I also looked into relevant ph.x source codes but i
couldn't understand.

2)

I want to know which physical quantity the values in elph.#iq.#irr.xml
stand for.

The developer manual of ph.x reads;

"elph.#iq.#irr.xml contains the contribution to the electron phonon
coefficients at the q vector #iq of the representation #irr. These files
are written by elphel and contain the quantities g_qν (k, i, j) (see User
Manual)."

and  g_qν (k, i, j) seems to contain factor "sqrt[h/(2*M*w)]" followed by
<psi_{k+q,j}|dvscf_q*psi_{k,i}>

from User Manual.

But, i found that the values of g_qν (k, i, j) in elph.#iq.#irr.xml do not
change with mass of atoms (To check this, i artificially change mass of
surfur atoms to 100000)

I also, wondering the value in elph.#iq.#irr.xml  are whether

<\psi(k+q)|dV_{SCF}/du^q_{i a}|\psi(k)>   (which is written in elphon.f90)

or just,

<psi_{k+q,j}|dvscf_q*psi_{k,i}>

3)

It seems little trivial, I want to know some detail inside the
elph.#iq.#irr.xml.

Following is my elph.1.1.xml

------elph.1.1.xml--------
...

<NUMBER_OF_BANDS type="integer" size="1">
17
</NUMBER_OF_BANDS>
<K_POINT.1>
<COORDINATES_XK type="real" size="3" columns="3">
0.000000000000000E+000  0.000000000000000E+000  0.000000000000000E+000
</COORDINATES_XK>
<PARTIAL_ELPH type="complex" size="289">
-1.145849195795035E-003,-8.341398318595372E-013
8.430451497377110E-012, 1.448582735931787E-011
9.829111482844918E-009,-8.516622246844407E-010
-1.370251344974451E-008,-4.042717328869155E-008
3.014026080010312E-002, 7.108929268140980E-010
4.389283347067152E-011,-1.018558197269840E-010
-3.050731442163088E-002,-6.384100774284654E-009
1.093044270914813E-008,-2.878418099873511E-009
-3.256726063415212E-009,-1.803331763403733E-009

...

------elph.1.1.xml--------

The lines after <PARTIAL_ELPH type="complex" size="289"> would be

the g_qν (k, i, j) for q=gamma, v=1 (first irrep) and k=gamma.

I guess that, since the total number of electronic bands are 17, 17x17
lines after  <PARTIAL_ELPH type="complex" size="289"> are

g values in following order

band-i (initial band), band-j (final band)
1,1
2,1
3,1
...
17,1
1,2
2,2
3,2
...
17,2
...

is it true?

Finally,  the values of second column for each line seem to be imaginary
part of g. I am not good at quantum mechanics but i thought perturbing
hamiltonian by phonon should be also hermitian and 'diagonal' element
should be real number.
But in this case, there are so many indices g(q,v,i,j,k) that i cannot
figure out what is 'diagonal' element of g in this case.

I apologize for ill-organized questions.

Best regards

Jaehong Park

--
==========================================================
Jaehong Park
Ph.D. Candidate
Dielectric Thin Film Laboratory
Department of Materials Science & Engineering , Seoul National University

Electronic Materials Research Center

Post-Si Semiconductor Institute

Korea Institute of Science and Technology (KIST)
Hwarangno 14-gil, Seongbuk-gu, Seoul, 136-791, KOREA

Tel :      +82-2-958-6653

Mobile : +82-10-5481-5143

E-mail : catinabox at snu.ac.kr
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