[Pw_forum] Left and right going Bloch's states from PWCOND

Alexander Smogunov smogunov at sissa.it
Thu Oct 22 17:47:05 CEST 2009 

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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> > -- 
> > e-mail: smogunov at sissa.it
> > home-page: http://people.sissa.it/~smogunov
> > 
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