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units of epmatwe and epmatwp 
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Joined: Thu Jul 26, 2018 8:25 am
Posts: 11
University: Konstanz
Post units of epmatwe and epmatwp
Dear developers and users,

I need the electron phonon coupling matrix elements g for my project. For the beginning it is sufficient to get these on the coarse k,q grids. I have found the relevant variables in the EPW code and added a routine to write them to disk in a user-readable format. Here is what I get for graphene with a 3x3x1 q-mesh and a 6x6x1 k-mesh (low quality calculations, just for understanding the code):

epmatwe:
# nbnd= 5 nrr_k= 43 nmode= 6 nqc= 9
# ibnd, jbnd, irk, imode, iq, epmatwe
1 1 1 1 1 0.00000430+0.00000000i
1 1 1 1 2 0.00001443-0.00000001i
1 1 1 1 3 -0.00000185-0.00000000i
1 1 1 1 4 0.00006872+0.00000000i
1 1 1 1 5 0.00001443-0.00000001i
1 1 1 1 6 -0.00001050-0.00000000i
1 1 1 1 7 -0.00001673+0.00000001i
1 1 1 1 8 0.00008162+0.00000000i
1 1 1 1 9 0.00000430+0.00000000i
1 1 1 2 1 -0.00000248-0.00000000i
1 1 1 2 2 -0.00000837+0.00000004i
1 1 1 2 3 -0.00000141-0.00000000i
1 1 1 2 4 -0.00005459+0.00000000i
1 1 1 2 5 -0.00000837+0.00000004i
...

epmatwp:
# nbnd= 5 nrr_k= 43 nmode= 6 nrr_g= 13
# ibnd, jbnd, irk, imode, irg, epmatwp
1 1 1 1 1 0.00000430+0.00000000i
1 1 1 1 2 0.00001443-0.00000001i
1 1 1 1 3 -0.00000185-0.00000000i
1 1 1 1 4 0.00006872+0.00000000i
1 1 1 1 5 0.00001443-0.00000001i
1 1 1 1 6 -0.00001050-0.00000000i
1 1 1 1 7 -0.00001673+0.00000001i
1 1 1 1 8 0.00008162+0.00000000i
1 1 1 1 9 0.00000430+0.00000000i
1 1 1 1 10 0.00002973-0.00000000i
1 1 1 1 11 0.00000030+0.00000000i
1 1 1 1 12 0.00000430+0.00000000i
1 1 1 1 13 0.00001443-0.00000001i
1 1 1 2 1 -0.00000248-0.00000000i
...

Could somebody please tell me the physical units of these matrix elements in both cases (epmatwe and epmatwp)?

A second question: How are the quantities nrr_k and nrr_g determined? By the spatial decay of the g?


Tue Aug 07, 2018 1:44 pm
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Joined: Thu Jan 14, 2016 10:52 am
Posts: 144
University: University of Oxford
Post Re: units of epmatwe and epmatwp
Hi,

It seems to me that you printed are not the matrix elements for the coarse (k,q) grid but the matrix elements in real space (after Wannier rotations).
If you want the matrix elements on the (k,q) grid the easiest option is to use the 'prtgkk' input variable, and you can choose the fine (k,q) grids to be the same as the coarse one. Then you will get the matrix elements in eV/meV.

Best,
Carla

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Department of Materials | University of Oxford
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Wed Aug 08, 2018 8:41 am
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Joined: Thu Jul 26, 2018 8:25 am
Posts: 11
University: Konstanz
Post Re: units of epmatwe and epmatwp
Hello Carla, thank you for the useful information regarding prtgkk.

I'm sorry, I had a mistake in the formulation of my question. I need the g in Wannier-Wannier and Wannier-Phonon (on coarse q-grid) representations.

To my understanding the varaibles are as follows (please correct me if I'm wrong):

epmatwe: Wannier-Phonon representation, g(Re,q), equation 34 in PRB 76, 165108
epmatwp: Wannier-Wannier representation, g(Re,Rp), equation 24 in PRB 76, 165108

link to publication: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.76.165108

Do the variables epmatwe/epmatwp correspond to the quantities in the mentioned equations and if so, what are the units of these variables within the EPW code?

Many thanks for your help!


Wed Aug 08, 2018 9:15 am
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Joined: Wed Jan 13, 2016 7:25 pm
Posts: 532
University: Oxford
Post Re: units of epmatwe and epmatwp
Dear MaxS,

You are correct for the epmat*

The g in reciprocal space has energy unit (in atomic unit with Ry).
Then its just a real-space Fourier transform.

Best wishes,
Samuel

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Wed Aug 08, 2018 9:41 am
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Joined: Thu Jul 26, 2018 8:25 am
Posts: 11
University: Konstanz
Post Re: units of epmatwe and epmatwp
sponce wrote:
Dear MaxS,

You are correct for the epmat*

The g in reciprocal space has energy unit (in atomic unit with Ry).
Then its just a real-space Fourier transform.

Best wishes,
Samuel


So its unit is Ry (equals 13.6...eV). Great, many thanks! :)

Best regards,
Maxim


Wed Aug 08, 2018 10:56 am
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Joined: Thu Jul 26, 2018 8:25 am
Posts: 11
University: Konstanz
Post Re: units of epmatwe and epmatwp
I have an additonal question regarding the units: What are the units of epmatwef? Or even better, can somebody show me the exact definition of the physical quantity that epmatwef represents, including N_p, N_e (phonon/electron Wigner-Seitz cells)? I know that epmatwef is given in equation 34 of PRB 76, 165108:
Image

But I'm not sure about the units and whether any prefactors are omited.

I tried to trace back the definition of epmatwef through epmatf by starting from the output of prtgkk, which prints ryd2mev*epc (line 223). (epc is derived from epf17 which corresponds to epmatf)
So I suppose epc has units of Rydberg. But if I check how epc is calculated in print_gkk.f90, then its units must be:
Ry = [epc] = [epc_sym] = [sqrt(g2)] = [gamma] = [sqrt(epf17*epf17/omega_q)]
But: From [omega_q]=Ry follows [sqrt(Ry*Ry/Ry)]=sqrt(Ry)=[epc], which is a contradiction.
What am I missing?


Wed Dec 05, 2018 2:25 pm
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Joined: Thu Jan 14, 2016 10:52 am
Posts: 144
University: University of Oxford
Post Re: units of epmatwe and epmatwp
Hi,

Indeed all the matrix element arrays (epmatf etc) do not include the 1/sqrt(omega_q) factors which appear in the definition of the matrix element. This is why, in order to get the matrix elements in [Ry], you always have to multiply by that factor as it’s done in print_gkk.

Hope this helps,
Carla

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Carla Verdi
Department of Materials | University of Oxford
Parks Road | OX1 3PH Oxford


Wed Dec 05, 2018 11:45 pm
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Joined: Thu Jul 26, 2018 8:25 am
Posts: 11
University: Konstanz
Post Re: units of epmatwe and epmatwp
Hi Carla,

I do understand the missing factor sqrt(1/2*omega_q). It comes from eq. 5 of PRB 76, 165108:
Image
Because you are using g^SE in further calculations (like a²F ...), you convert the g on the right side to g^SE.
hbar and m0 are missing. According to comments in superconductivity.f90 I assume that m0 is already included in g (through the eigenmodes) and hbar does not occur because it is simply set to 1 (for whatever reasons). Then, to obtain the g on the left side of the upper equation I need to multiply epmatf with sqrt(hbar)*sqrt(m0). Is that correct? If yes, the units of that g should be energy over distance, as stated in the mentioned publication.
Please help me out with that. I'm already quite close but I'm still missing some details. :)


Thu Dec 06, 2018 11:04 am
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Joined: Thu Jan 14, 2016 10:52 am
Posts: 144
University: University of Oxford
Post Re: units of epmatwe and epmatwp
Hi Max,

The internal units in Quantum Espresso and EPW are always (Rydberg) atomic units, where hbar=1, hence why you don't see it.
It is correct that the 1/sqrt(m) is already included in g through the ph eigenmodes.
To obtain the g on the left side of the equation you need to multiply epmatf with 1/sqrt(2*omega_q). This will give you g (or g^SE as it says in that equation) in Ry. Epmatf is NOT in Ry; epmatf/sqrt(omega_q) is.

Best,
Carla

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Carla Verdi
Department of Materials | University of Oxford
Parks Road | OX1 3PH Oxford


Thu Dec 06, 2018 1:08 pm
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