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chernrealspace.f90
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!>>> this method comes from 2010 EPL 92 67004
! Disordered topological insulators via C*-algebras
! http://iopscience.iop.org/0295-5075/92/6/67004)
! T. A. Loring and M. B. Hastings
! this code is written by QuanSheng Wu on 12th Dec 2012
subroutine chern_realspace(Ef, res)
use para
implicit none
!>> inout parameter
real(dp), intent(in) :: Ef
real(dp), intent(out) :: res
!>> local variables
integer :: i
integer :: j
integer :: k
integer :: it
integer :: nfill
real(dp) :: thetax
real(dp) :: thetay
real(dp), allocatable :: Eig(:)
real(dp), allocatable :: xi(:)
real(dp), allocatable :: yi(:)
complex(dp), allocatable :: logy(:)
complex(dp), allocatable :: ham(:, :)
complex(dp), allocatable :: dis(:, :)
complex(dp), allocatable :: PX(:, :)
complex(dp), allocatable :: PY(:, :)
complex(dp), allocatable :: TT(:, :)
complex(dp), allocatable :: P (:, :)
complex(dp), allocatable :: zeig(:)
allocate(ham(ndim, ndim))
allocate(dis(ndim, ndim))
allocate(PX(ndim, ndim))
allocate(PY(ndim, ndim))
allocate(P (ndim, ndim))
allocate(TT(ndim, ndim))
allocate(eig(ndim))
allocate(zeig(ndim))
allocate(logy(ndim))
allocate(xi(Ndim))
allocate(yi(Ndim))
PX= zzero
PY= zzero
P = zzero
it=0
do i=1, Nx
do j=1, Ny
do k=1, Nband*2
it= it+1
Xi(it)= dble(i)-1d0
Yi(it)= dble(j)-1d0
enddo
enddo
enddo
Xi= Xi/dble(Nx)*2d0*pi
Yi= Yi/dble(Ny)*2d0*pi
! PX= exp(i 2 pi X)
! PY= exp(i 2 pi Y)
do i=1, ndim
PX(i, i)= cos(xi(i))+ zi* sin(xi(i))
PY(i, i)= cos(yi(i))+ zi* sin(yi(i))
enddo
thetax = 0d0
thetay = 0d0
! prepare hamiltonian
!call ham_bulk(thetax, thetay, ham)
call ham_haldane(thetax, thetay, ham)
call disorder(dis)
ham= ham+ dis
call eigensystem_c('V', 'U', Ndim, ham, eig)
nfill= 0
do i=1, ndim
if (eig(i).le.Ef) nfill= nfill+1
enddo
call zgemm('N', 'C', Ndim, Ndim, nfill, zone, ham, &
Ndim, ham, Ndim, zzero, P, Ndim)
! P exp(i X 2 pi) P
call mat_mul(Ndim, P, PX, TT)
call mat_mul(Ndim, TT, P, PX)
! P exp(i Y 2 pi) P
call mat_mul(Ndim, P, PY, TT)
call mat_mul(Ndim, TT, P, PY)
! PX*PY*PX'*PY'
call mat_mul (Ndim, PX, PY, TT)
call mat_mul_c(Ndim, TT, PX, ham)
call mat_mul_c(Ndim, ham, PY, TT)
call eigensystem_zge('N', Ndim, TT, zeig)
res= 0d0
do i=1, nfill
res= res+ aimag(log(zeig(i)))/2d0/pi
enddo
return
end subroutine chern_realspace
!>>> this method comes from Ref: 2011 J. Phys. A: Math. Theor. 44 113001
! Disordered topological insulators: a non-commutative geometry perspective
! Emil Prodan
! this code is written by QuanSheng Wu on 17th Dec 2012
subroutine chern_prodan(Ef, res)
use para
implicit none
!>> inout parameter
real(dp), intent(in) :: Ef
real(dp), intent(out) :: res
!>> local variables
integer :: i
integer :: j
integer :: k
integer :: it
integer :: nfill
! this parameter comes from Eq (120, 121, 122) in Ref
integer :: Q
real(dp) :: thetax
real(dp) :: thetay
! Delta= 2*pi/Nx
real(dp) :: Delta
real(dp) :: rt1
real(dp), allocatable :: Eig(:)
real(dp), allocatable :: xi(:)
real(dp), allocatable :: yi(:)
! BB(1)=1/(2*Delta)
complex(dp), allocatable :: BB(:)
! CC=Aij^-1*BB
complex(dp), allocatable :: CC(:)
! Aij= j^{2i-1}
complex(dp), allocatable :: Aij(:, :)
complex(dp), allocatable :: ham(:, :)
complex(dp), allocatable :: dis(:, :)
complex(dp), allocatable :: PX(:, :)
complex(dp), allocatable :: PY(:, :)
complex(dp), allocatable :: expx(:)
complex(dp), allocatable :: TT1(:, :)
complex(dp), allocatable :: TT2(:, :)
complex(dp), allocatable :: xppx(:, :)
complex(dp), allocatable :: yppy(:, :)
complex(dp), allocatable :: P (:, :)
! the expansion order
if (Nx.ge.16) then
Q= 8
else
Q= Nx/2
endif
allocate(ham(ndim, ndim))
allocate(dis(ndim, ndim))
allocate(PX(ndim, Q))
allocate(PY(ndim, Q))
allocate(P (ndim, ndim))
allocate(BB (Q))
allocate(CC (Q))
allocate(Aij(Q, Q))
allocate(TT1(ndim, ndim))
allocate(TT2(ndim, ndim))
allocate(xppx(ndim, ndim))
allocate(yppy(ndim, ndim))
allocate(eig(ndim))
allocate(xi(Ndim))
allocate(yi(Ndim))
allocate(expx(ndim))
PX= zzero
PY= zzero
P = zzero
it=0
do i=1, Nx
do j=1, Ny
do k=1, Nband*2
it= it+1
Xi(it)= dble(i)
Yi(it)= dble(j)
enddo
enddo
enddo
! PX= exp(I *i * X*Delta)
! PY= exp(I *i * Y*Delta)
Delta= 2d0*pi/dble(Nx)
do i=1, Q
do j=1, Ndim
rt1= dble(i)*Xi(j)*Delta
PX(j, i)= cos(rt1)+ zi* sin(rt1)
rt1= dble(i)*Yi(j)*Delta
PY(j, i)= cos(rt1)+ zi* sin(rt1)
enddo
enddo
! > Aij
do i=1, Q
do j=1, Q
Aij(i,j)= dble(j)**(2*i-1)
enddo
enddo
BB= zzero
BB(1)= 1d0/2d0/Delta
! > calculate CC= Aij^-1*BB
call inv(Q, Aij)
i=1
j=1
call ZGEMV('N',Q,Q,zone,Aij,Q,BB,i,zzero,CC,j)
thetax = 0d0
thetay = 0d0
! prepare hamiltonian
!call ham_bulk(thetax, thetay, ham)
!call ham_twist(thetax, thetay, ham)
call ham_haldane(thetax, thetay, ham)
call disorder(dis)
ham= ham+ dis
call eigensystem_c('V', 'U', Ndim, ham, eig)
nfill= 0
do i=1, ndim
if (eig(i).le.Ef) nfill= nfill+1
enddo
call zgemm('N', 'C', Ndim, Ndim, nfill, zone, ham, &
Ndim, ham, Ndim, zzero, P, Ndim)
! > Eq.(130)
xppx= zzero
do i=1, Q
expx= conjg(PX(:,i))
call mat_mul_diagA(Ndim, expx, P, TT1)
expx= PX(:,i)
call mat_mul_diagB(Ndim, TT1, expx, TT2)
xppx= xppx+ zi* CC(i)* TT2
expx= PX(:,i)
call mat_mul_diagA(Ndim, expx, P, TT1)
expx= conjg(PX(:,i))
call mat_mul_diagB(Ndim, TT1, expx, TT2)
xppx= xppx- zi* CC(i)* TT2
enddo
yppy= zzero
do i=1, Q
expx= conjg(PY(:,i))
call mat_mul_diagA(Ndim, expx, P, TT1)
expx= PY(:,i)
call mat_mul_diagB(Ndim, TT1, expx, TT2)
yppy= yppy+ zi* CC(i)* TT2
expx= PY(:,i)
call mat_mul_diagA(Ndim, expx, P, TT1)
expx= conjg(PY(:,i))
call mat_mul_diagB(Ndim, TT1, expx, TT2)
yppy= yppy- zi* CC(i)* TT2
enddo
!> P[xppx, yppy], Eq.(129)
call mat_mul(Ndim, xppx, yppy, TT1)
call mat_mul(Ndim, yppy, xppx, TT2)
TT1= TT1- TT2
call mat_mul(Ndim, P, TT1, TT2)
res= 0d0
do i=1, Ndim
res= res+ aimag(TT2(i, i))*2d0*pi/dble(Nx)/dble(Ny)
enddo
return
end subroutine chern_prodan
!>>> this method comes from Ref:
! Journal of the Physical Society of Japan
! Vol. 74, No. 6, June, 2005, pp. 1674–1677
! Chern Numbers in Discretized Brillouin Zone:
! Efficient Method of Computing (Spin) Hall Conductances
! Takahiro FUKUI, Yasuhiro HATSUGAI and Hiroshi SUZUKI
! This code is written by QuanSheng Wu on 18th Dec 2012
! chern number in Discretized Brillouin Zone
! subroutine chern_DBZ(Ef, res)
! use para
! implicit none
! integer :: ik, i, j
!
! integer :: NN, knv3
! ! number of occupied states
! integer :: nfill
!
! real(dp) :: thetax
! real(dp) :: thetay
! integer, allocatable :: fill(:)
! real(Dp), allocatable :: W(:)
! ! Hamiltonian of bulk system
! complex(Dp), allocatable :: Ham(:, :)
! complex(dp), allocatable :: dis (:,:)
!
! integer , allocatable :: ikpoint(:,:)
! real(dp), allocatable :: kpoint(:,:)
!
! complex(dp), allocatable :: zx(:)
! complex(dp), allocatable :: zx(:)
! complex(dp), allocatable :: U1_mat(:, :)
! complex(dp), allocatable :: U2_mat(:, :)
! complex(dp), allocatable :: detU1(:, :)
! complex(dp), allocatable :: detU2(:, :)
! complex(dp), allocatable :: eigvec(:, :, :)
! NN= 10
! knv3= NN*NN
! allocate( kpoint(knv3, 2))
! allocate(ikpoint(knv3, 2))
! allocate(W(ndim))
! allocate(ham(ndim, ndim))
! allocate(dis(ndim, ndim))
! allocate(zx(ndim))
! allocate(zy(ndim))
! allocate(U1_mat(ndim, ndim))
! allocate(U2_mat(ndim, ndim))
! allocate(eigvec(ndim, ndim, knv3))
! allocate(detU1(NN, NN))
! allocate(detU2(NN, NN))
! allocate(fill(knv3))
!
! ! > asign kpoint in [0, 1)*[0, 1)*4*pi*pi
! ik= 0
! do i=1, NN
! do j=1, NN
! ik= ik+ 1
! kpoint(ik, 1)= dble(i-1)*/dble(NN)
! kpoint(ik, 2)= dble(j-1)*/dble(NN)
! ikpoint(ik, 1)= i
! ikpoint(ik, 2)= j
! enddo
! enddo
! kpoint= kpoint*2d0*pi
!
! call disorder(dis)
! ! >> prepare eigenvectors
! do ik= 1, knv3
!
! thetax = kpoint(ik, 1)
! thetay = kpoint(ik, 2)
!
! ! calculation bulk hamiltonian
! Ham=0d0
! call ham_twist(thetax, thetay, Ham)
! Ham= Ham+ dis
!
! W=0d0
! call eigensystem_c( 'N', 'U', ndim ,Ham, W)
! eigvec(:, :, ik)= ham
! nfill= 0
! do i=1, ndim
! if (W(i).le.Ef)nfill= nfill+ 1
! enddo
! fill(ik)= nfill
! enddo
! ! >> calculate U1(k)
! do ik= 1, knv3
! nfill= fill(ik)
! do i= 1, nfill
! do j= 1, nfill
! zx= ham(:, i)
! zy= ham(:, j)
! U_mat(i, j)= ZDOTC(ndim, ZX, INCX, ZY, INCY)
! enddo
! enddo
! ! det{U}
! call det(ndim, nfill, U_mat, det1)
! i= ikpoint(ik, 1)
! j= ikpoint(ik, 1)
! detU(i, j)= det1/abs(det1)
! enddo
! return
! end subroutine chern_DBZ
!>>> this method comes from
! Ref:
! 1. PRB 59 8144(1999)
! 2. JOURNAL OF APPLIED PHYSICS 112, 044306 (2012)
! construct on 18th Dec 2012
subroutine chern_kubo(Ef, res)
use para
implicit none
!>> inout variables
real(dp), intent(in) :: Ef
real(dp), intent(out) :: res
integer :: ik, i, j
integer :: NN, knv3
! number of occupied states
integer :: nfill
real(dp) :: thetax
real(dp) :: thetay
real(dp) :: En
real(dp) :: Em
complex(dp) :: z1
complex(dp) :: z2
complex(dp) :: z3
real(Dp), allocatable :: W(:)
real(dp), allocatable :: sigma(:)
! Hamiltonian of bulk system
complex(Dp), allocatable :: Ham(:, :)
complex(dp), allocatable :: dis (:,:)
real(dp), allocatable :: kpoint(:,:)
complex(dp), allocatable :: zn(:)
complex(dp), allocatable :: zm(:)
complex(dp), allocatable :: vec1(:)
complex(dp), allocatable :: vx(:, :)
complex(dp), allocatable :: vy(:, :)
complex(dp), allocatable :: vx0(:, :)
complex(dp), allocatable :: vy0(:, :)
complex(dp), allocatable :: H01x(:, :)
complex(dp), allocatable :: H01y(:, :)
! vector multiply vector v1*v2
complex(dp), external :: zdotc
allocate(H01x(nband*2, nband*2))
allocate(H01y(nband*2, nband*2))
NN= 10
knv3= NN*NN
allocate( kpoint(knv3, 2))
allocate(W(ndim))
allocate(ham(ndim, ndim))
allocate(dis(ndim, ndim))
allocate(zn(ndim))
allocate(zm(ndim))
allocate(vec1(ndim))
allocate(vx(ndim, ndim))
allocate(vy(ndim, ndim))
allocate(vx0(ndim, ndim))
allocate(vy0(ndim, ndim))
allocate(sigma(ndim))
! > asign kpoint in [0, 1)*[0, 1)*4*pi*pi
ik= 0
do i=1, NN
do j=1, NN
ik= ik+ 1
kpoint(ik, 1)= dble(i-1)/dble(NN)
kpoint(ik, 2)= dble(j-1)/dble(NN)
enddo
enddo
kpoint= kpoint*2d0*pi
call disorder(dis)
! > calculate H01x, H01y
do ik=1, nrpts
i = irvec(1, ik)
j = irvec(2, ik)
if (i .eq. 1 .and. j .eq. 0)H01x= Hmnr(:, :, ik)
if (i .eq. 0 .and. j .eq. 1)H01y= Hmnr(:, :, ik)
enddo
call velocity2(ndim, vx0, vy0)
! >> prepare eigenvectors
do ik= 1, knv3
thetax = kpoint(ik, 1)
thetay = kpoint(ik, 2)
! calculation bulk hamiltonian
Ham=0d0
call ham_twist(thetax, thetay, Ham)
Ham= Ham+ dis
W= 0d0
call eigensystem_c( 'V', 'U', ndim, Ham, W)
nfill= 0
do i=1, ndim
if (W(i).le.Ef)nfill= nfill+ 1
enddo
! > prepare velocity operator
call velocity(ndim, thetax, thetay, H01x, H01y, vx, vy)
vx= vx0 + vx
vy= vy0 + vy
sigma= zzero
do i= 1, nfill
zn= ham(:, i)
En= w(i)
do j= nfill+1, Ndim
zm= ham(:, j)
Em= w(j)
call zgemv('N', ndim, ndim, zone, vy, ndim, zm,1, zzero, vec1,1)
z1= zdotc(ndim, zn, 1, vec1, 1)
call zgemv('N', ndim, ndim, zone, vx, ndim, zn,1, zzero, vec1,1)
z2= zdotc(ndim, zm, 1, vec1, 1)
z3= z1*z2
call zgemv('N', ndim, ndim, zone, vx, ndim, zm,1, zzero, vec1,1)
z1= zdotc(ndim, zn, 1, vec1, 1)
call zgemv('N', ndim, ndim, zone, vy, ndim, zn,1, zzero, vec1,1)
z2= zdotc(ndim, zm, 1, vec1, 1)
z3= z3- z1*z2
z3= z3/(En-Em)**2
sigma(i)= sigma(i)+ aimag(z3)
enddo ! j unoccupied
enddo ! i occupied
res= res+ sum(sigma(1:nfill))
print *, ik, res
write(10, '(100f16.8)')kpoint(ik,:), sum(sigma(1:nfill))
if (mod(ik,NN).eq.0)write(10, *)''
enddo ! ik
res= res/dble(NN*NN)*2d0*pi/dble(Nx*Ny)
return
end subroutine chern_kubo
!>>> this method comes from
! Ref: Journal of the Physical Society of Japan
! Vol. 73, No. 10, October, 2004, pp. 2624–2627
! Anomalous Hall Effect and Skyrmion Number in Real and Momentum Spaces
! Masaru ONODA1, Gen TATARA2 and Naoto NAGAOSA1;3
! Eq.(3)
! construct on 20th Dec 2012
subroutine chern_streda(Ef, res)
use para
implicit none
!>> inout variables
real(dp), intent(in) :: Ef
real(dp), intent(out) :: res
integer :: ik, i, j
! number of occupied states
integer :: nfill
integer :: nnzx
integer :: nnzy
integer :: nnzmax
real(dp) :: thetax
real(dp) :: thetay
real(dp) :: En
real(dp) :: Em
real(dp) :: tau
complex(dp) :: z1
complex(dp) :: z2
complex(dp) :: z3
character :: matdescra(6)
integer, allocatable :: iax_coo(:)
integer, allocatable :: jax_coo(:)
integer, allocatable :: iay_coo(:)
integer, allocatable :: jay_coo(:)
complex(dp), allocatable :: vx_coo(:)
complex(dp), allocatable :: vy_coo(:)
real(Dp), allocatable :: W(:)
real(dp), allocatable :: sigma(:)
! Hamiltonian of bulk system
complex(Dp), allocatable :: Ham(:, :)
complex(Dp), allocatable :: dis (:,:)
complex(dp), allocatable :: zn(:)
complex(dp), allocatable :: zm(:)
complex(dp), allocatable :: vec1(:)
complex(dp), allocatable :: X(:, :)
complex(dp), allocatable :: Y(:, :)
complex(dp), allocatable :: vx(:, :)
complex(dp), allocatable :: vy(:, :)
complex(dp), allocatable :: vx1(:, :)
complex(dp), allocatable :: vy1(:, :)
complex(dp), allocatable :: vx2(:, :)
complex(dp), allocatable :: vy2(:, :)
complex(dp), allocatable :: vx0(:, :)
complex(dp), allocatable :: vy0(:, :)
complex(dp), allocatable :: H01x(:, :)
complex(dp), allocatable :: H01y(:, :)
! vector multiply vector v1*v2
complex(dp), external :: zdotc
allocate(H01x(nband*2, nband*2))
allocate(H01y(nband*2, nband*2))
allocate(W(ndim))
allocate(ham(ndim, ndim))
allocate(dis(ndim, ndim))
allocate(zn(ndim))
allocate(zm(ndim))
allocate(vec1(ndim))
allocate(vx(ndim, ndim))
allocate(vy(ndim, ndim))
allocate(vx1(ndim, ndim))
allocate(vy1(ndim, ndim))
allocate(vx2(ndim, ndim))
allocate(vy2(ndim, ndim))
allocate( X(ndim, ndim))
allocate( Y(ndim, ndim))
allocate(vx0(ndim, ndim))
allocate(vy0(ndim, ndim))
allocate(sigma(ndim))
nnzmax= 10*ndim
allocate(iax_coo(nnzmax))
allocate(iay_coo(nnzmax))
allocate(jax_coo(nnzmax))
allocate(jay_coo(nnzmax))
allocate(vx_coo(nnzmax))
allocate(vy_coo(nnzmax))
call disorder(dis)
! > calculate H01x, H01y
do ik=1, nrpts
i = irvec(1, ik)
j = irvec(2, ik)
if (i .eq. 1 .and. j .eq. 0)H01x= Hmnr(:, :, ik)
if (i .eq. 0 .and. j .eq. 1)H01y= Hmnr(:, :, ik)
enddo
!call velocity2(ndim, vx0, vy0)
! >> prepare eigenvectors
thetax = 0d0
thetay = 0d0
tau = 40d0
! > prepare velocity operator
Ham=0d0
!call ham_twist(thetax, thetay, Ham)
!call ham_bulk(thetax, thetay, Ham)
call ham_haldane2(thetax, thetay, Ham)
call ham_xy(X, Y)
! vx= -i[X, H]
call mat_mul(ndim, X, Ham, vx)
call mat_mul(ndim, Ham, X, vy)
vx= -zi*(vx- vy)
! vy= -i[Y, H]
call mat_mul(ndim, Y, Ham, vy)
call mat_mul(ndim, Ham, Y, X)
vy= -zi*(vy- X)
! calculation bulk hamiltonian with twist boundary
!call ham_twist(thetax, thetay, Ham)
call ham_haldane(thetax, thetay, Ham)
Ham= Ham+ dis
W= 0d0
call eigensystem_c( 'V', 'U', ndim, Ham, W)
nfill= 0
do i=1, ndim
if (W(i).le.Ef)nfill= nfill+ 1
enddo
ik= 0
do i=1, ndim
do j=1, ndim
if (abs(vx(i,j)).ge.1e-3)then
ik=ik+ 1
iax_coo(ik)= i
jax_coo(ik)= j
vx_coo(ik)= vx(i,j)
endif
enddo
enddo
nnzx= ik
ik= 0
do i=1, ndim
do j=1, ndim
if (abs(vy(i,j)).ge.1e-3)then
ik=ik+ 1
iay_coo(ik)= i
jay_coo(ik)= j
vy_coo(ik)= vy(i,j)
endif
enddo
enddo
nnzy= ik
matdescra(1)= 'H'
matdescra(2)= 'U'
matdescra(3)= 'U'
matdescra(4)= 'F'
sigma= zzero
do i= 1, nfill
zn= ham(:, i)
En= w(i)
do j= nfill+1, Ndim
zm= ham(:, j)
Em= w(j)
!<n|vx|m><m|vy|n>
!call zgemv('N', ndim, ndim, zone, vy, ndim, zm,1, zzero, vec1,1)
call mkl_zcoomv('N', ndim, ndim, zone, matdescra, &
vy_coo, iay_coo, jay_coo, nnzy, zm, zzero, vec1)
z1= zdotc(ndim, zn, 1, vec1, 1)
!call zgemv('N', ndim, ndim, zone, vx, ndim, zn,1, zzero, vec1,1)
call mkl_zcoomv('N', ndim, ndim, zone, matdescra, &
vx_coo, iax_coo, jax_coo, nnzx, zn, zzero, vec1)
z2= zdotc(ndim, zm, 1, vec1, 1)
z3= z1*z2
!<n|vy|m><m|vx|n> is equal to conjugate(<n|vx|m><m|vy|n>)
!<n|vy|m><m|vx|n>
!call zgemv('N', ndim, ndim, zone, vx, ndim, zm,1, zzero, vec1,1)
!call mkl_zcoomv('N', ndim, ndim, zone, matdescra, &
! vx_coo, iax_coo, jax_coo, nnzx, zm, zzero, vec1)
!z1= zdotc(ndim, zn, 1, vec1, 1)
!call zgemv('N', ndim, ndim, zone, vy, ndim, zn,1, zzero, vec1,1)
!call mkl_zcoomv('N', ndim, ndim, zone, matdescra, &
! vy_coo, iay_coo, jay_coo, nnzy, zn, zzero, vec1)
!z2= zdotc(ndim, zm, 1, vec1, 1)
!<n|vx|m><m|vy|n>-<n|vy|m><m|vx|n>
!z3= z3- z1*z2
z3= z3*tau*tau/(1d0+(En-Em)**2*tau*tau)
sigma(i)= sigma(i)+ aimag(z3)
enddo ! j unoccupied
enddo ! i occupied
res= res+ sum(sigma(1:nfill))*2
res= res/dble(Nx*Ny)*2d0*pi
return
end subroutine chern_streda
! this subroutine is wrong
! if H= Cn^+ C1+ C1^+ Cn
! then vx= -i [X, H]= (1-n)C1^+ Cn -(1-n)Cn^+C1
! but we need not this subroutine any more
! for comparasion, we keep this
! Dec 25th 2012, the first Christmas day after the end of the world
subroutine velocity(ndim, thetax, thetay, H01x, H01y, vx, vy)
use para,only : dp, Nband, zzero, zi, Nx, Ny
implicit none
!>> inout variables
integer, intent(in) :: ndim
real(dp), intent(in) :: thetax
real(dp), intent(in) :: thetay
complex(dp), intent(in) :: H01x(Nband*2, Nband*2)
complex(dp), intent(in) :: H01y(Nband*2, Nband*2)
complex(dp), intent(out) :: vx(ndim, ndim)
complex(dp), intent(out) :: vy(ndim, ndim)
!>> local variables
integer :: ix1
integer :: ix2
integer :: iy
integer :: idx1
integer :: idx2
complex(dp) :: ratio
vx= zzero
vy= zzero
!> vx
ix1= Nx
ix2= 1
ratio= cos(thetax)+ zi*sin(thetax)
do iy=1, Ny
idx1= (ix1-1)*Ny*Nband*2+(iy-1)*Nband*2
idx2= (ix2-1)*Ny*Nband*2+(iy-1)*Nband*2
vx(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)= &
vx(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)+ &
zi*ratio*H01x
enddo
ix1= 1
ix2= Nx
do iy=1, Ny
idx1= (ix1-1)*Ny*Nband*2+(iy-1)*Nband*2
idx2= (ix2-1)*Ny*Nband*2+(iy-1)*Nband*2
vx(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)= &
vx(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)- &
zi*conjg(ratio)*conjg(transpose(H01x))
enddo
!> vy
ix1= Ny
ix2= 1
ratio= cos(thetay)+ zi*sin(thetay)
do iy=1, Nx
idx1= (iy-1)*Ny*Nband*2+(ix1-1)*Nband*2
idx2= (iy-1)*Ny*Nband*2+(ix2-1)*Nband*2
vy(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)= &
vy(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)+ &
zi*ratio*H01y
enddo
ix1= 1
ix2= Ny
do iy=1, Nx
idx1= (iy-1)*Ny*Nband*2+(ix1-1)*Nband*2
idx2= (iy-1)*Ny*Nband*2+(ix2-1)*Nband*2
vy(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)= &
vy(idx1+1: idx1+Nband*2, idx2+1: idx2+Nband*2)- &
zi*conjg(ratio)*conjg(transpose(H01y))
enddo
return
end subroutine velocity
subroutine velocity2(ndim, vx, vy)
use para,only : dp, Nband, zzero, zi, Nx, Ny, ijmax
implicit none
!>> inout variables
integer, intent(in) :: ndim
complex(dp), intent(out) :: vx(ndim, ndim)
complex(dp), intent(out) :: vy(ndim, ndim)
!>> local variables
! loop index
integer :: i1
integer :: i2
integer :: j1
integer :: j2
complex(Dp), allocatable :: Hij(:, :, :, :)
allocate(Hij(-ijmax:ijmax, -ijmax:ijmax, nband*2, nband*2))
call ham_qlayer2qlayer3(Hij)
vx=0.0d0
do i1= 1, Nx
do j1= 1, Ny
do i2= 1, Nx
if (i2.gt.i1.and.(i2-i1).le.ijmax) then
vx((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j1*Nband*2 ) &
= zi*Hij(i2-i1, 0, 1:nband*2, 1:nband*2)
endif
if (i1.gt.i2.and.(i1-i2).le.ijmax) then
vx((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j1*Nband*2 ) &
= -zi*Hij(i2-i1, 0, 1:nband*2, 1:nband*2)
endif
enddo
enddo
enddo
vy=0.0d0
do i1= 1, Nx
do j1= 1, Ny
do j2= 1, Ny
if (j2.gt.j1.and.(j2-j1).le.ijmax) then
vy((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i1-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j2*Nband*2 ) &
= zi*Hij(0, j2-j1, 1:nband*2, 1:nband*2)
endif
if (j1.gt.j2.and.(j1-j2).le.ijmax) then
vy((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i1-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j2*Nband*2 ) &
= -zi*Hij(0, j2-j1, 1:nband*2, 1:nband*2)
endif
enddo
enddo
enddo
! check hermitcity
!do i1=1, Ndim
!do i2=i1+1, Ndim
! if(abs(vx(i1,i2)-conjg(vx(i2,i1))).ge.1e-6)then
! write(*,*)'there are something wrong with vx'
! stop
! endif
! if(abs(vy(i1,i2)-conjg(vy(i2,i1))).ge.1e-6)then
! write(*,*)'there are something wrong with vy'
! stop
! endif
!enddo
!enddo
return
end subroutine velocity2