[Pw_forum] Left and right going Bloch's states from PWCOND
Manoj Srivastava
manoj at phys.ufl.edu
Wed Oct 28 06:49:34 CET 2009
Dear Alexander,
You are correct, left and right moving states are in general not
related. I was wrong about trying to create a pair. Thanks for
clarification.
I have a few more questions.
1. I want to find out the reflection coefficient in the code. In
transmit.f90, transmission coefficient is |tmat(ig,n)|^2, where tmat is
vec1(ntran-n2d-npol*nocrosr+ig,n). (line 206, of version 4.0.5).
Reflection is not explicitly calculated in the code, but it should be
modulus square of vec1(2*n2d+npol*norbs+ig,n) (line 234). Am I correct?
2. In the code reflection and transmission coefficients are calculated
for one direction lets say t++ and t+-, which is transmission and
reflection coefficient for Bloch' state moving from - to + , or in other
words, left to right. To calculate transmission and reflection for Bloch's
state going from right to left, what should I do? Should i just rotate my
system 180 degree, that way leads get interchanged and also scattering
area has orientation 180 different from before.
3. In the subroutine sunitary.f90, is raux measure of conservation of
flux? If I sum all the transmission and reflecion coefficient for
a particular Bloch's state, I should get 1, and computationally a number
close to 1. How large could it be for S matrix not to be unitary, i m
getting raux more than one e.g. 1.0011 but code still considers smatrix
to be unitary.
Regards,
Manoj Srivastava
University of Florida, Gainesville, FL
<pw_forum at pwscf.org>
On Thu, 22
Oct 2009, Alexander Smogunov wrote:
> On Thu, 2009-10-22 at 11:34 -0400, Manoj Srivastava wrote:
> > Dear Alexander,
> > Thanks for your answer. I just want to make sure. Imagine we have total
> > number of channels in the left lead 2, so total number of Bloch's state
> > are 4. 2 of them left going say a and b, and 2 right going say c and d.
> > So, are you saying that for left going state a, the corresponding right
> > going state is c? Are they ordered this way?
>
> what do you mean by corresponding? Left and right moving Bloch
> states are in general not related one to another, you can even have
> different number of them ... Only if you have some symmetry S which
> brings kz to -kz conserving k_parallel, then the state with
> \psi_{-kz} will be S \psi{kz}. This is true for example at 2D G point
> when you have time reversal operation.
>
> Now the code simply arranges the propagating states in the order of
> increasing |k_z|...
>
> Regards, Alexander
>
>
> >
> > Regards,
> > Manoj
> >
> >
> > On Thu, 22 Oct 2009, Alexander
> > Smogunov wrote:
> >
> > > Dear Manoj.
> > >
> > > The output of complex k vectors is performed in
> > > summary_band.f90 routine. If you want to see all
> > > the complex k vectors, not only propagating ones,
> > > you can change at the end of this routine:
> > >
> > > -------------------
> > > do i = 1, nchanl
> > > WRITE( stdout,'(3f12.7)') DBLE(kvall(i)), AIMAG(kvall(i)), eev
> > > enddo
> > > -------------------
> > >
> > > to
> > > -------------------
> > >
> > > do i = 1, 2*nstl
> > > WRITE( stdout,'(3f12.7)') DBLE(kvall(i)), AIMAG(kvall(i)), eev
> > > enddo
> > > -------------------
> > >
> > > Altogether there are 2*nstl (or 2*nstr) Bloch states in the left
> > > (or right) lead. First half, [1,nstl], are propagating or decaying to
> > > the right states, another half, [nstl+1,2*nstl], - propagating or
> > > decaying to the left. In each group, first nchanl states are propagating
> > > states.
> > >
> > > The propagating states are normalized by the current and are arranged in
> > > the above order at the end of jbloch.f90 routine, after the following
> > > lines:
> > >
> > > !
> > > ! Right ordering (+, >, -, <)
> > > !
> > >
> > >
> > >
> > > Notice, that in the last versions the code gives in output
> > > both propagating to the right and to the left states.
> > >
> > > Hope this helps,
> > > Alexander
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > > On Wed, 2009-10-21 at 14:13 -0400, Manoj Srivastava wrote:
> > > > Dear All,
> > > > I am trying to figure out the left and right going Bloch's states in the
> > > > lead from PWCOND. For a given (kx,ky)and energy we get kz. The code only
> > > > prints out Bloch's state moving in one direction. eg. in one of the
> > > > calculation-
> > > > k//=(0.375,-0.375)
> > > > Nchannels of the left tip = 1
> > > > k1(2pi/a) k2(2pi/a) E-Ef (eV)
> > > >
> > > > 0.3157801 0.0000000 0.0000000
> > > >
> > > > Now if I want Bloch's state moving in right as well as left direction, I
> > > > can go to kbloch.f90 subroutine, and print out all the eigen values of
> > > > AX=exp(ikd)BX, and out of those the ones with real solution would be our
> > > > Bloch's state, so I get for each channel two solutions-
> > > > kval (-0.275409421993275,1.823688001395235E-010)
> > > > kval (0.315780119742506,-3.611201785292708E-012)
> > > >
> > > > To figure out the direction, I can calculate current associated with these
> > > > Bloch's sate and if the current is +ive it is right moving , and if '-'ive
> > > > its left moving Bloch's state. I can print out current from jbloch.f90
> > > > subroutine which are -
> > > > current eigenvalue -1.86502143831863 1.59149029314457
> > > >
> > > > So, clearly the first state with kval=-0.2754094 is left moving and the
> > > > other one right moving. Upto here its clear to me how to identify left and
> > > > right moving states.
> > > >
> > > > I get confused when for a given (kx,ky,E), I have more than one Bloch'
> > > > state. In another calculation where i get multiple Bloch's state-
> > > > Nchannels of the left tip = 5
> > > > k1(2pi/a) k2(2pi/a) E-Ef (eV)
> > > >
> > > > -0.0746301 0.0000000 0.0000000
> > > > 0.1205527 0.0000000 0.0000000
> > > > 0.3112908 0.0000000 0.0000000
> > > > 0.4200218 0.0000000 0.0000000
> > > > -0.4935150 0.0000000 0.0000000
> > > >
> > > > so i did the same trick i did above to first print out kz and then
> > > > current, which gives me -
> > > > kval (-0.420023481074359,1.979595081419732E-010) (call it a)
> > > > kval (0.420023367986768,2.500979698670295E-011) (b)
> > > > kval (-0.306507431678779,-1.236804629184431E-011) (c)
> > > > kval (-0.125376071175573,-6.134512510438736E-011) (d)
> > > > kval (-7.945001124706894E-002,6.683546930037856E-011)(e)
> > > > kval (0.106554601758169,-6.427946951285107E-011) (f)
> > > > kval (8.866867725358024E-002,8.342250371574646E-011) (g)
> > > > kval (0.325333314672671,1.260810749228185E-011) (h)
> > > > kval (-0.488725859521576,1.769197678346003E-010) (i)
> > > > kval (0.479509832763231,1.765499400037283E-010) (j)
> > > >
> > > > current eigenvalue -9.31389492882581 -1.24296522993488
> > > > -1.21324078359658 -1.11950286753963 -1.08166842367443
> > > > 1.08187482164864 1.11973146584263 1.21295295042188
> > > > 1.24280031534940 9.313897787790
> > > >
> > > > So, the first 5 are left moving and rest are right moving. But I dont know
> > > > the pairs. for example for left moving state a, what is the corresponding
> > > > right moving state whether its f or g ... j ?
> > > >
> > > > Any help would be appreciated.
> > > >
> > > > Regards,
> > > > Manoj Srivastava
> > > > University of Florida, Gainesville.
> > > >
> > > > _______________________________________________
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> > > home-page: http://people.sissa.it/~smogunov
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