[Pw_forum] Electron-phonon coupling
Malgorzata Wierzbowska
wierzbom at tcd.ie
Sun Mar 30 11:37:39 CEST 2003
No, it is not not correct. Look to the definition of el-ph
in one of Savrasov's papers and you will see that that there is
double delta on Fermi surface. You can split the integration over
phonon vectors (q-points) and over electron momentum (k-points)
if you first integrate over phonons and later over electrons.
Not the other way around. Just because there is delta_k+q delta_k .
You try to integrate delta_k * delta_q or delta_k+q * delta_q
if I understand correctly your e-mail.
If you start from the integration over k first then at q=0 you meet
the problem of delta_k*delta_k+0 which is mathematically not defined.
Gosia
Eyvaz Isaev wrote:
>Dear all,
>
>Now I am trying to calculate the electron-phonon
>coupling constant. According to the 7-th example the
>code is able to calculate the EPC constant for an
>arbitrary k-point in the BZ (\lambda_{nk}). I
>followed this example and now I am calculating
>\lambda_{nk} for a number of k-points in the 1/48 part
>of the IBZ for FCC lattice (k-points are vertex of
>small tetrahedra). Then I am going to integrate
>\lambda_{nk} using the tetrahedron method.
>
>So, I would like to ask you is this procedure correct?
>If no, what should be done for this kind of
>calculations?
>
>Regards,
>Eyvaz.
>
>
>--- Malgorzata Wierzbowska <wierzbom at tcd.ie> wrote:
>
>>
>>Dear Ma Yanming,
>>
>>Find some of my results and look to attached files
>>with Eliashberg function
>>calculated for Nb with norm conserving PP (KB) and
>>ultrasoft (US).
>>Experimental total lambda is 1.04 or 1.22 (from refs
>>in S.Y. Savrasov
>>PRB, vol 54, p. 16487 (1996)), calculated by
>>Savrasov 1.26.
>>
>>As you can see from attached files KB PP behaves
>>correctly
>>but US gives too big total lambda. The reason is
>>because
>>Eliashberg function, in case of US, doesn't fall
>>down to zero for small
>>frequencies. Small frequencies are for phonon
>>vectors close to Gamma point.
>>However for first sight we calculate different
>>quantities we still can
>>make common
>>conclusions. You integrate only over k, leaving
>>q-dependence (phonon).
>>I integrate over both k and q points, but with
>>frequncy resolution (I
>>see the relations
>>between q-points and frequencies.).
>>
>>The answer for the question whether you can just
>>throw points is NO! It
>>is not so easy,
>>but we will get there. What I suggest is:
>>If you could write a file with q-points you
>>calculated and corresponding
>>frequencies
>>and corresponding calculated el-ph couplings. And if
>>you could send me
>>refs. to experimental
>>values which you refer. Maybe we will see that one
>>needs to work a bit
>>more on generation of PP.
>>Especially concentrating attention to get gamma
>>point very close to zero.
>>
>>I am satisfied with the KB PP attached here (format
>>for old version of
>>PWscf). And I was still
>>working on getting US PP better. But now I don't
>>have enough computer
>>power to continue
>>because I lost an account in my previous place and
>>here I work on a
>>different project.
>>Maybe you can generate better pseudos. If you decide
>>to do this for US
>>PP, there is a parameter
>>called "rinner" in Vanderbilt's input. Phonons at
>>gamma point are very
>>sensitive on that.
>>
>>Good luck!
>>Gosia
>>
>>
>>
>>
>>
>>
>>ma Yanming wrote:
>>
>>>Dear Gosia
>>>
>>>Sorry for replying you so late. I'd already
>>>
>>calculated the E_P
>>
>>>coupling for most of possible q vectors to try to
>>>
>>analyze the results.
>>
>>>So It takes time. I use Norm-Conserving PPs. As
>>>
>>what you said, for
>>
>>>some q vectors with small phonon frequencies, the
>>>
>>calculated E_P
>>
>>>coupling is extremely large. I do not know why?
>>>
>>>I use 16 16 16 Monkshort-Pack K mesh to generate q
>>>
>>points for BCC Nb.
>>
>>>At q point (0 -0.0625 0.1875) the E_P coupling is
>>>
>>worst. For q points
>>
>>>as the following, the results are also bad
>>>(0 -0.0625 0.4375)
>>>(0 -0.125 0.5)
>>>(0 -0.0625 0.3125)
>>>(0 -0.125 0.375)
>>>(0 -0.125 0.25)
>>>(0 -0.1875 0.3125)
>>>(-0.0625 -0.1875 0.25)
>>>(-0.0625 -0.1875 0.375)
>>>(-0.125 -0.1875 0.3125)
>>>So Can I just pick out these unusual q vectors and
>>>
>>then make average
>>
>>>over the left q points to get the E_P Coupling
>>>
>>lambda. Or ...?
>>
>>>>It would help to check from which
>>>>region at frequency axis it comes.
>>>>
>>>
>>>I do not quite understand the above sentence.Can
>>>
>>you give me more
>>
>>>explanation?
>>>Thanks in advance.
>>>
>>>Best Wishes!
>>>
>>>Yanming Ma PhD
>>>Steacie Institute for Molecular Sciences,
>>>National Research Councils of Canada.
>>>100 Sussex
>>>K1A 0R6
>>>
>>>
>>>
>>>
>>>
>>>>From: Malgorzata Wierzbowska <wierzbom at tcd.ie>
>>>>Reply-To: pw_forum at pwscf.org
>>>>To: pw_forum at pwscf.org
>>>>Subject: Re: [Pw_forum] Electron-phonon coupling
>>>>Date: Sat, 22 Mar 2003 13:03:41 +0000
>>>>
>>>>
>>>>Which version of the program and what
>>>>
>>pseudopotentials do you use?
>>
>>>>If this is ultrasoft pseudopotetial then do as
>>>>
>>follows:
>>
>>>>Edit the file phonon.F (or phonon.f90) in phlib
>>>>
>>(or PH).
>>
>>>>Go to the end and you see the place when
>>>>
>>elph=.true..
>>
>>>>Write "call dvanqq" as it is below and recompile
>>>>
>>the program.
>>
>>>>if (elph) then
>>>>call dvanqq
>>>>if (.not.trans) call elphon
>>>>call elphsum
>>>>endif
>>>>
>>>>If pseudo is normconserving and you have too big
>>>>
>>el-ph couplings
>>
>>>>(with good phonon spectra) probably it happens at
>>>>
>>phonon vectors
>>
>>>>which have small frequencies.
>>>>What exactly are the numbers? It would help to
>>>>
>>check from which
>>
>>>>region at frequency axis it comes.
>>>>Which q-points are particularly bad?
>>>>
>>>>Gosia
>>>>
>>>>
>>>>
>>>>ma Yanming wrote:
>>>>
>>>>>Dear Paolo,
>>>>>
>>>>>Thanks for your reply.I do choose q points
>>>>>
>>using Monkhorst-Pack K
>>
>>>>>mesh. But I am still upset. I already increased
>>>>>
>>the K mesh to 48 48 48
>>
>>>>>when I calculated the EP coupling. To test the
>>>>>
>>performance in several
>>
>>>>>high symmetry q if (elph) then points, I still
>>>>>
>>got the results for
>>
>>>>>phonon linewidth far away from the experimental
>>>>>
>>data, despite I
>>
>>>>>obtained the good results for phonon. :-(
>>>>>Any comments?
>>>>>
>>>>>Best Wishes!
>>>>>
>>>>>Yanming Ma
>>>>>
>>>>>
>>>>>>>I have been puzzled by the calculation of
>>>>>>>
>>the electron-phonon (EP)
>>
>>>>>>>coupling coefficient lambda using PWSCF
>>>>>>>
>>>>>>me too...
>>>>>>
>>>>>>The calculation of the electron-phonon
>>>>>>
>>coupling coefficients
>>
>>>>>>is presently done using a simple but
>>>>>>
>>not-so-smart algorithm:
>>
>>>>>>for each phonon q one calculates \lambda(q),
>>>>>>
>>performing a
>>
>>>>>>(slowly convergent) sum over k of electronic
>>>>>>
>>states.
>>
>=== message truncated ===>
>
>> freq au freq. THz
>> a2F(freq)
>>
>> 1 1.0198717373890380E-003
>>3.355202476562948 2.237529515947500
>> 2 1.0596152121671143E-003
>>3.485951667970094 1.499468581009689
>> 3 1.0993586869451901E-003
>>3.616700859377241 1.350706089637660
>> 4 1.1391021617232664E-003
>>3.747450050784387 1.787859730300818
>> 5 1.1788456365013427E-003
>>3.878199242191533 1.633521655247258
>> 6 1.2185891112794187E-003
>>4.008948433598680 2.422545868169372
>> 7 1.2583325860574948E-003
>>4.139697625005826 3.181579657060079
>> 8 1.2980760608355710E-003
>>4.270446816412972 4.775643794216762
>> 9 1.3378195356136473E-003
>>4.401196007820118 3.455151971299109
>> 10 1.3775630103917234E-003
>>4.531945199227264 3.660159841903176
>> 11 1.4173064851697994E-003
>>4.662694390634410 3.331080505617703
>> 12 1.4570499599478756E-003
>>4.793443582041556 2.385202990990981
>> 13 1.4967934347259517E-003
>>4.924192773448703 1.500343357387741
>> 14 1.5365369095040275E-003
>>5.054941964855849 1.361790472536797
>> 15 1.5762803842821040E-003
>>5.185691156262996 1.169814309637568
>> 16 1.6160238590601801E-003
>>5.316440347670142 0.9833931057291112
>> 17 1.6557673338382564E-003
>>5.447189539077288 0.9990683722507322
>> 18 1.6955108086163322E-003
>>5.577938730484434 1.020410393873696
>> 19 1.7352542833944085E-003
>>5.708687921891580 1.048469785644035
>> 20 1.7749977581724847E-003
>>5.839437113298726 2.040019807863810
>> 21 1.8147412329505608E-003
>>5.970186304705873 3.944271859907947
>> 22 1.8544847077286368E-003
>>6.100935496113019 3.898784584719331
>> 23 1.8942281825067131E-003
>>6.231684687520165 2.593718329665633
>> 24 1.9339716572847889E-003
>>6.362433878927312 1.059836321559148
>> 25 1.9737151320628655E-003
>>6.493183070334458 0.3946383516817085
>> 26 2.0134586068409415E-003
>>6.623932261741603 0.2963668772225613
>> 27 2.0532020816190180E-003
>>6.754681453148750 0.1797051121084532
>> 28 2.0929455563970940E-003
>>6.885430644555897 8.5976271291996138E-002
>> 29 2.1326890311751696E-003
>>7.016179835963042 6.8222080457730936E-002
>> 30 2.1724325059532461E-003
>>7.146929027370189 0.0000000000000000E+000
>>
>> Total lambda 2.98
>>
>>
>> freq au freq. THz
>> a2F(freq)
>>
>> 1 1.2438515240158456E-004
>>0.4092057423356754 2.8869733143880708E-002
>> 2 1.7315545720475367E-004
>>0.5696516508351509 2.3385781074569358E-002
>> 3 2.2192576200792278E-004
>>0.7300975593346266 3.1993707502021920E-002
>> 4 2.7069606681109186E-004
>>0.8905434678341022 3.5713934152708573E-002
>> 5 3.1946637161426099E-004
>>1.050989376333578 6.1944858809984709E-002
>> 6 3.6823667641743008E-004
>>1.211435284833054 5.2590079578703453E-002
>> 7 4.1700698122059920E-004
>>1.371881193332529 7.4231431621878619E-002
>> 8 4.6577728602376833E-004
>>1.532327101832005 9.1897992378171267E-002
>> 9 5.1454759082693746E-004
>>1.692773010331480 9.6819575939830322E-002
>> 10 5.6331789563010650E-004
>>1.853218918830956 0.1076133627499602
>> 11 6.1208820043327572E-004
>>2.013664827330432 0.1174886803214625
>> 12 6.6085850523644476E-004
>>2.174110735829907 0.1334868819605516
>> 13 7.0962881003961398E-004
>>2.334556644329383 0.1172762277885431
>> 14 7.5839911484278293E-004
>>2.495002552828858 0.1601624697992450
>> 15 8.0716941964595197E-004
>>2.655448461328334 0.1496093643983267
>> 16 8.5593972444912119E-004
>>2.815894369827810 0.1926870865091957
>> 17 9.0471002925229040E-004
>>2.976340278327286 0.2265583611652895
>> 18 9.5348033405545944E-004
>>3.136786186826761 0.2342125536731038
>> 19 1.0022506388586285E-003
>>3.297232095326236 0.2536025477932173
>> 20 1.0510209436617977E-003
>>3.457678003825713 0.2969967638092281
>> 21 1.0997912484649668E-003
>>3.618123912325188 0.3988061602289276
>> 22 1.1485615532681359E-003
>>3.778569820824664 0.7690110504535764
>> 23 1.1973318580713050E-003
>>3.939015729324139 0.8837328494542188
>> 24 1.2461021628744742E-003
>>4.099461637823615 1.071354565294684
>> 25 1.2948724676776433E-003
>>4.259907546323091 0.7903395888522454
>> 26 1.3436427724808127E-003
>>4.420353454822566 0.5783290412553221
>> 27 1.3924130772839816E-003
>>4.580799363322042 0.5451969602494918
>> 28 1.4411833820871505E-003
>>4.741245271821517 0.6573407717215089
>> 29 1.4899536868903196E-003
>>4.901691180320993 0.4927796721997354
>> 30 1.5387239916934887E-003
>>5.062137088820468 0.4898505017287321
>> 31 1.5874942964966579E-003
>>5.222582997319944 0.4815007364165790
>> 32 1.6362646012998272E-003
>>5.383028905819420 0.4951156582318729
>> 33 1.6850349061029959E-003
>>5.543474814318896 0.6488168419863590
>> 34 1.7338052109061652E-003
>>5.703920722818371 0.9696502950376715
>> 35 1.7825755157093339E-003
>>5.864366631317846 0.9959555280125480
>> 36 1.8313458205125034E-003
>>6.024812539817323 1.016992835820577
>> 37 1.8801161253156726E-003
>>6.185258448316798 0.4001474208086026
>> 38 1.9288864301188418E-003
>>6.345704356816274 0.1898949853003984
>> 39 1.9776567349220107E-003
>>6.506150265315750 9.8287516753835096E-002
>> 40 2.0264270397251796E-003
>>6.666596173815225 0.0000000000000000E+000
>>
>> total lambda 1.178
>>
>>
>>
>>>PZ
>>>
>>'Nb' 5.0 2 2 3 .F. 0 .T. ! ** 41.0 Niobio
>>transformed from BHS
>> 2.410000 0.820000 3.741900 -2.741900
>> 0.830000 1.690000 2.010000
>> -0.721060000000000E+01 -0.373700000000000E+00
>>-0.185600000000000E+00
>> 0.776000000000000E-01 0.762000000000000E-01
>>0.198000000000000E-01
>> 0.680000 1.030000 1.350000
>> -0.660260000000000E+01 -0.864000000000000E+00
>>-0.545200000000000E+00
>> 0.161000000000000E-01 0.149000000000000E-01
>>0.212000000000000E-01
>> 3.620000 4.740000 5.570000
>> -0.238090000000000E+01 0.260200000000000E+00
>>0.288000000000000E-01
>> -0.238000000000000E-01 -0.757000000000000E-01
>>-0.479000000000000E-01
>> 41.00 -4.00000 0.06250 189 3
>> Wavefunction 5s
>> 0 2.00
>> 0.26558108E-04 0.28270959E-04 0.30094279E-04
>>0.32035194E-04
>> 0.34101287E-04 0.36300632E-04 0.38641823E-04
>>0.41134008E-04
>> 0.43786926E-04 0.46610943E-04 0.49617094E-04
>>0.52817125E-04
>> 0.56223542E-04 0.59849655E-04 0.63709632E-04
>>0.67818559E-04
>> 0.72192490E-04 0.76848517E-04 0.81804835E-04
>>0.87080810E-04
>> 0.92697060E-04 0.98675532E-04 0.10503959E-03
>>0.11181409E-03
>> 0.11902552E-03 0.12670206E-03 0.13487370E-03
>>0.14357238E-03
>> 0.15283209E-03 0.16268902E-03 0.17318169E-03
>>0.18435110E-03
>> 0.19624091E-03 0.20889758E-03 0.22237058E-03
>>0.23671257E-03
>> 0.25197961E-03 0.26823136E-03 0.28553136E-03
>>0.30394722E-03
>> 0.32355095E-03 0.34441917E-03 0.36663348E-03
>>0.39028073E-03
>> 0.41545339E-03 0.44224990E-03 0.47077506E-03
>>0.50114045E-03
>> 0.53346486E-03 0.56787476E-03 0.60450480E-03
>>0.64349837E-03
>> 0.68500811E-03 0.72919658E-03 0.77623687E-03
>>0.82631328E-03
>> 0.87962213E-03 0.93637243E-03 0.99678685E-03
>>0.10611025E-02
>> 0.11295721E-02 0.12024646E-02 0.12800668E-02
>>0.13626842E-02
>> 0.14506424E-02 0.15442884E-02 0.16439921E-02
>>0.17501479E-02
>> 0.18631765E-02 0.19835265E-02 0.21116766E-02
>>0.22481379E-02
>> 0.23934558E-02 0.25482131E-02 0.27130324E-02
>>0.28885793E-02
>> 0.30755660E-02 0.32747545E-02 0.34869613E-02
>>0.37130613E-02
>> 0.39539934E-02 0.42107658E-02 0.44844624E-02
>>0.47762501E-02
>> 0.50873863E-02 0.54192285E-02 0.57732446E-02
>>0.61510242E-02
>> 0.65542930E-02 0.69849276E-02 0.74449743E-02
>>0.79366695E-02
>> 0.84624643E-02 0.90250533E-02 0.96274074E-02
>>0.10272813E-01
>> 0.10964920E-01 0.11707793E-01 0.12505979E-01
>>0.13364582E-01
>> 0.14289356E-01 0.15286815E-01 0.16364359E-01
>>0.17530436E-01
>> 0.18794730E-01 0.20168383E-01 0.21664278E-01
>>0.23297367E-01
>> 0.25085075E-01 0.27047797E-01 0.29209494E-01
>>0.31598425E-01
>> 0.34248048E-01 0.37198109E-01 0.40495979E-01
>>0.44198285E-01
>> 0.48372884E-01 0.53101244E-01 0.58481297E-01
>>0.64630783E-01
>> 0.71691119E-01 0.79831726E-01 0.89254641E-01
>>0.10019903E+00
>> 0.11294490E+00 0.12781473E+00 0.14517091E+00
>>0.16540587E+00
>> 0.18892001E+00 0.21608170E+00 0.24716264E+00
>>0.28224441E+00
>> 0.32109894E+00 0.36305988E+00 0.40692163E+00
>>0.45091914E+00
>> 0.49283953E+00 0.53027893E+00 0.56099250E+00
>>0.58322637E+00
>> 0.59591709E+00 0.59871013E+00 0.59183987E+00
>>0.57596317E+00
>> 0.55202083E+00 0.52114959E+00 0.48462794E+00
>>0.44383131E+00
>> 0.40018329E+00 0.35510151E+00 0.30994084E+00
>>0.26593959E+00
>> 0.22417154E+00 0.18550756E+00 0.15058983E+00
>>0.11982118E+00
>> 0.93370566E-01 0.71193969E-01 0.53068182E-01
>>0.38633497E-01
>> 0.27440353E-01 0.18994996E-01 0.12799866E-01
>>0.83857028E-02
>> 0.53338812E-02 0.32889959E-02 0.19627937E-02
>>0.11316214E-02
>> 0.62882186E-03 0.33603430E-03 0.17237553E-03
>>0.84683462E-04
>> 0.39729852E-04 0.17746346E-04 0.75224748E-05
>>0.30155030E-05
>> 0.11389082E-05 0.40366301E-06 0.13369256E-06
>>0.41189222E-07
>> 0.11748275E-07 0.30861089E-08 0.74291650E-09
>>0.16221986E-09
>> 0.31184030E-10 0.00000000E+00 0.00000000E+00
>>0.00000000E+00
>> 0.00000000E+00
>> Wavefunction 5p
>> 1 0.00
>> 0.80423491E-08 0.91131754E-08 0.10326581E-07
>>0.11701549E-07
>> 0.13259602E-07 0.15025108E-07 0.17025690E-07
>>0.19292649E-07
>> 0.21861451E-07 0.24772288E-07 0.28070700E-07
>>0.31808294E-07
>> 0.36043545E-07 0.40842718E-07 0.46280897E-07
>>0.52443165E-07
>> 0.59425936E-07 0.67338458E-07 0.76304528E-07
>>0.86464423E-07
>> 0.97977103E-07 0.11102269E-06 0.12580529E-06
>>0.14255618E-06
>> 0.16153745E-06 0.18304606E-06 0.20741853E-06
>>0.23503618E-06
>> 0.26633112E-06 0.30179296E-06 0.34197654E-06
>>0.38751055E-06
>> 0.43910741E-06 0.49757438E-06 0.56382622E-06
>>0.63889950E-06
>> 0.72396880E-06 0.82036511E-06 0.92959661E-06
>>0.10533724E-05
>> 0.11936289E-05 0.13525608E-05 0.15326546E-05
>>0.17367282E-05
>> 0.19679746E-05 0.22300118E-05 0.25269399E-05
>>0.28634049E-05
>> 0.32446712E-05 0.36767046E-05 0.41662652E-05
>>0.47210133E-05
>> 0.53496293E-05 0.60619498E-05 0.68691213E-05
>>0.77837749E-05
>> 0.88202239E-05 0.99946882E-05 0.11325548E-04
>>0.12833632E-04
>> 0.14542543E-04 0.16479030E-04 0.18673403E-04
>>0.21160012E-04
>> 0.23977786E-04 0.27170839E-04 0.30789166E-04
>>0.34889427E-04
>> 0.39535836E-04 0.44801168E-04 0.50767906E-04
>>0.57529536E-04
>> 0.65192018E-04 0.73875454E-04 0.83715984E-04
>>0.94867930E-04
>> 0.10750623E-03 0.12182922E-03 0.13806176E-03
>>0.15645879E-03
>> 0.17730942E-03 0.20094148E-03 0.22772679E-03
>>0.25808712E-03
>> 0.29250090E-03 0.33151098E-03 0.37573338E-03
>>0.42586727E-03
>> 0.48270641E-03 0.54715211E-03 0.62022814E-03
>>0.70309766E-03
>> 0.79708271E-03 0.90368648E-03 0.10246188E-02
>>0.11618257E-02
>> 0.13175229E-02 0.14942348E-02 0.16948397E-02
>>0.19226214E-02
>> 0.21813295E-02 0.24752495E-02 0.28092839E-02
>>0.31890472E-02
>> 0.36209773E-02 0.41124651E-02 0.46720082E-02
>>0.53093911E-02
>> 0.60358981E-02 0.68645666E-02 0.78104858E-02
>>0.88911540E-02
>> 0.10126902E-01 0.11541398E-01 0.13162250E-01
>>0.15021723E-01
>> 0.17157585E-01 0.19614118E-01 0.22443298E-01
>>0.25706184E-01
>> 0.29474520E-01 0.33832571E-01 0.38879185E-01
>>0.44730046E-01
>> 0.51520032E-01 0.59405487E-01 0.68566075E-01
>>0.79205661E-01
>> 0.91551344E-01 0.10584939E+00 0.12235633E+00
>>0.14132302E+00
>> 0.16296880E+00 0.18744332E+00 0.21477410E+00
>>0.24480202E+00
>> 0.27711315E+00 0.31098503E+00 0.34537397E+00
>>0.37896943E+00
>> 0.41032452E+00 0.43803812E+00 0.46093204E+00
>>0.47816152E+00
>> 0.48923152E+00 0.49394180E+00 0.49231313E+00
>>0.48453536E+00
>> 0.47094573E+00 0.45202351E+00 0.42838471E+00
>>0.40076901E+00
>> 0.37001725E+00 0.33704027E+00 0.30278093E+00
>>0.26817164E+00
>> 0.23409069E+00 0.20132254E+00 0.17052492E+00
>>0.14220639E+00
>> 0.11671571E+00 0.94243430E-01 0.74834207E-01
>>0.58407430E-01
>>
>=== message truncated ===
>
>
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