[Pw_forum] Left and right going Bloch's states from PWCOND
Manoj Srivastava
manoj at phys.ufl.edu
Fri Oct 30 19:04:16 CET 2009
Just to add one more question.
what is 'lorb' switch. I get following-
lorb, & ! if .t. calculate the scattering (or Bloch) states
so, i guess for transmission calculation i will have to set it to
't'. now-
IF (lorb.and.ikind.eq.2) call errore('do_cond','lorb not working with
ikind = 2',1)
so, it seems that calculation for r and t for right and left going
state, when left and right leads are different doesnot work. Is that
correct? A possible work around may be rotating the whole system by 180
degree, which would be like treating left lead as right lead and
scattering region rotated. Can I do that?
Regards,
Manoj
On Fri, 30 Oct 2009, Manoj Srivastava wrote:
> Dear Alexander,
> Thank you very much! I read the code, it seems that there are
> quiet a few changes in 4.1.1 compared to 4.0.4 :) .So, just to make sure,
> if I want to calculate r and t for left going Bloch's state as well as
> right going Bloch's state, I need to run the code two times, one time with
> 'left_to_right' switch true, and another time false. I dont need to change
> scattering region or interchange left and right leads.
>
> Regards,
> Manoj Srivastava
> On Thu, 29 Oct 2009, Alexander
> Smogunov wrote:
>
> > Dear Manoj
> >
> > On Wed, 2009-10-28 at 01:49 -0400, Manoj Srivastava wrote:
> > > 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?
> >
> > in the 4.1 version there is output of both t and r.
> >
> >
> > >
> > > 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.
> > >
> >
> > again in the 4.1 version you have possibility to calculate t and r for
> > both directions, in the do_cond.f90 the transmit routine is called with
> > an extra parameter which is true (false) if you want to calculate
> > scattering states propagating from the left (from the right).
> >
> > > 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.
> >
> > in the case when |R + T - 1| > 1.d-4 for some band, it should print out
> > the value of R+T but continues to run anyway.
> >
> > All the best,
> > Alexander
> >
> >
> >
> > >
> > > 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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