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Calculate eigenstates
The subroutine
calculate_eigenstates calculates the new eigenstates for the given
potential phiV [given on Stefan's grid
on input].
DO num_qr=1,num_qr_regions
! loops through all quantum regions
call
get_which_kp(num_qr,kpL,kind_kpC,chargeC)
! checks, if kp is done
!------------------------
! electrons
!------------------------
!---- kp - el ------------
if ((kpL).and.((chargeC=='el').or.(chargeC=='bo')))
then ! if kp is done for electrons,
! update kp states
call
update_kp(num_qr,phiV,'el')
end if
!-- sg - 1b --------------
num_sg_el=sgChargeV(1)%qcV(num_qr)%num_sg_diff_en !
now check single band Schrödinger
! equation
if (num_sg_el>0) then
dim_qr=dim_qrV(num_qr)
do num_sg=1,num_sg_el !
loop through all Schrödinger equations
call
prepare_det_edge('el',num_sg) ! get band edge
corresponding to
!
num_sg --> pot_condM for edge model
num_deg=sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%num_deg
chargeC='el'
num_ev=sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%number_of_ev
num_k_z=sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%num_K_z
allocate(eigenvaluesV(num_ev),eigenfunctionsM(num_ev,dim_qr), &
STAT=istatus)
if (istatus/=0) stop 'error calculate_eigenstates:
alloc. failed'
do n_deg=1,num_deg
! loop through all degeneracies
! and (only 1D)superlattice-vectors
do n_K_z=1,num_K_z
K_z=sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%K_zV(n_K_z)
call
calculate_sg1D(num_qr,num_sg,n_deg,chargeC,phiV,K_z, &
num_ev,dim_qr,eigenvaluesV,eigenfunctionsM)
! calculate Schrödinger equation
sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%
&
eigenvaluesV(n_deg,n_K_z,1:num_ev)=eigenvaluesV
sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%
&
eigenfunctionsM(n_deg,n_K_z,1:num_ev,1:dim_qr)=eigenfunctionsM
SeparationModelC=sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%SeparationModelC
! determine new energy edge according to edge model
call
prepare_det_edge('el',num_sg)
! get band edge corresponding to num_sg
SeparationEnergyEdgeV =
sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%energy_edge_input
! get SeparationEnergyEdgeV from input
call
determine_edge_qm(dim_qr,pot_condM,hV,num_ev,
&
eigenvaluesV,'el',SeparationEnergyEdgeV,SeparationModelC)
! returns new energy edge
if ((n_deg==1).and.(n_K_z==1))
then
sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%energy_edge=minval(SeparationEnergyEdgeV)
! note: only energy edge different for different
num_sg
else
sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%energy_edge=
&
min(minval(SeparationEnergyEdgeV),sgChargeV(1)%qcV(num_qr)%data_deg_sgM(num_sg)%energy_edge)
! so take minimum for different degenerate bands
end if
end do
end do
deallocate(eigenvaluesV,eigenfunctionsM)
deallocate(pot_condM,hV,SeparationEnergyEdgeV)
end do
end if
!============================================================================
NOTE: The
separation energy is
determined in subroutine determine_edge_qm. This subroutine needs
the band edges in the quantum region, which are calculated in subroutine
prepare_det_edge in pot_condM and pot_valM.
subroutine prepare_det_edge(chargeC,num_sg) !
calculates bandedge for edge-model
!------------------------------------------------------------------------
! in pot_condM and pot_valM
! sets up pot_condM,pot_valM in [eV]
! in [eV]
!------------------------------------------------------------------------
...............
select case(chargeC)
case('hl')
..............
case('el')
DO i=1,dim_qr
i_phys=inv_quantumreg_num1DV(num_qr,i)
call extract_octants1D(octV,i_phys)
mat1=mat_numberV(octV(1))
mat2=mat_numberV(octV(2))
mat_ind1=map_qr_to_materialV(mat1,num_qr)
mat_ind2=map_qr_to_materialV(mat2,num_qr)
ind_l=def_quantum_modelsM(num_qr)%data_sg_elM(num_sg)%bandnumV(mat_ind1)
ind_r=def_quantum_modelsM(num_qr)%data_sg_elM(num_sg)%bandnumV(mat_ind2)
pot_l=E_cM(ind_l,octV(1))/abs(electron_charge)
-phiV(octV(1))
pot_r=E_cM(ind_r,octV(2))/abs(electron_charge)
-phiV(octV(2))
if (octV(1)/=octV(2)) then
!--- multiple point ----
! note: on boundaries of quantum region
call
octants_in_qr(num_qr,i_phys,inVL) !
the only bandedges of octants which
! lie within quantum region are taken.
! Mind the general hints on
!
Schrödinger equation.
if (all(inVL)) then
pot_condM(i,1)=pot_l
pot_condM(i,2)=pot_r
else if (inVL(1)) then
pot_condM(i,1)=pot_l
pot_condM(i,2)=pot_l
else if (inVL(2)) then
pot_condM(i,1)=pot_r
pot_condM(i,2)=pot_r
end if
else
pot_condM(i,1)=pot_l
pot_condM(i,2)=pot_r
end if
END DO
end select
end subroutine prepare_det_edge
subroutine octants_in_qr(num_qr,i_phys,inVL)
!----------------------------------------------------------------------
! decides on basis of quantum_gridM
! which octants are in quantum region num_qr
! if so, inVL(xx) =.true.
!----------------------------------------------------------------------
USE gitter1D,only:quantum_gridM
implicit none
integer,intent(in) :: num_qr,i_phys
logical,dimension(2),intent(out) :: inVL
integer :: i_min,i_and
!--------------------------------------------
if (quantum_gridM(i_phys,1,1)/=num_qr) &
stop 'error calculate_sg1D: internal inconsistency'
i_min=i_phys-1
i_and=i_phys+1
inVL=.true.
if (quantum_gridM(i_min,1,1)/=num_qr) inVL(1)=.false.
if (quantum_gridM(i_and,1,1)/=num_qr) inVL(2)=.false.
end subroutine octants_in_qr
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