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ham_twist.f90
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ham_twist.f90
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! This subroutine is used to caculate Hamiltonian for
! slab system with twist boundary
! History
! Dec/11th/2012 by Quansheng Wu
subroutine ham_twist(thetax, thetay, hamk_twist)
use para
implicit none
! wave vector in 2d
real(Dp), intent(in) :: thetax
real(Dp), intent(in) :: thetay
! Hamiltonian of slab system
complex(Dp),intent(out) ::hamk_twist(ndim, ndim)
! loop index
integer :: i1
integer :: i2
integer :: j1
integer :: j2
complex(Dp) :: ratiox
complex(Dp) :: ratioy
complex(Dp), allocatable :: Hij(:, :, :, :)
allocate(Hij(-ijmax:ijmax, -ijmax:ijmax, nband*2, nband*2))
call ham_qlayer2qlayer3(Hij)
hamk_twist=0.0d0
do i1= 1, Nx
do j1= 1, Ny
do i2= 1, Nx
do j2= 1, Ny
if (abs(i2-i1).le.ijmax .and. abs(j2-j1).le.ijmax ) then
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 ) &
= Hij(i2-i1, j2-j1, 1:nband*2, 1:nband*2)
endif
enddo
enddo
enddo
enddo
! return
!>> twist boundary
ratiox= cos(thetax)+ zi* sin(thetax)
ratioy= cos(thetay)+ zi* sin(thetay)
i1= Nx
i2= 1
do j1= 1, Ny
do j2= 1, Ny
if (abs(j2-j1).le.ijmax)then
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 ) &
= Hij(1, j2-j1, 1:nband*2, 1:nband*2)*ratiox+ &
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 )
endif
enddo
enddo
i1= 1
i2= Nx
do j1= 1, Ny
do j2= 1, Ny
if (abs(j2-j1).le.ijmax)then
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 ) &
= Hij(-1, j2-j1, 1:nband*2, 1:nband*2)*conjg(ratiox) + &
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 )
endif
enddo
enddo
j1= Ny
j2= 1
do i1= 1, Nx
do i2= 1, Nx
if (abs(i2-i1).le.ijmax)then
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 ) &
= Hij(i2-i1, 1, 1:nband*2, 1:nband*2)*ratioy+ &
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 )
endif
enddo
enddo
j1= 1
j2= Ny
do i1= 1, Nx
do i2= 1, Nx
if (abs(i2-i1).le.ijmax)then
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 ) &
= Hij(i2-i1, -1, 1:nband*2, 1:nband*2)*conjg(ratioy)+ &
hamk_twist((i1-1)*Nband*2*Ny+(j1-1)*Nband*2+1: &
(i1-1)*Nband*2*Ny+j1*Nband*2, &
(i2-1)*Nband*2*Ny+(j2-1)*Nband*2+1: &
(i2-1)*Nband*2*Ny+j2*Nband*2 )
endif
enddo
enddo
! check hermitcity
do i1=1, Ndim
do i2=1, Ndim
if(abs(hamk_twist(i1,i2)-conjg(hamk_twist(i2,i1))).ge.1e-6)then
write(*,*)'there are something wrong with hamk_twist'
stop
endif
enddo
enddo
return
end