[Wannier] Tunneling hamiltonian hr_plot

Giovanni Pizzi giovanni.pizzi at epfl.ch
Fri Dec 27 11:58:04 CET 2013

Dear Satrio,
first of all I would like to remember that the posting guidelines invite you to sign your posts with your full affiliation.

Regarding your question:

The Hamiltionian in real space IS Hermitian. Probably, you are comparing H(m,n)[R] with H(n,m)[R]. Instead, the correct relationship for the Hamiltonian to be Hermitian is

H(m,n)[R] = H(n,m)[-R]*

because the complex-conjugate elements must refer to the same pair of Wannier functions. To understand this better, remember that
H(m,n)[R] is the matrix element between a Wannier function in position
and Wannier function in position
r_n + R
therefore if you just fix R, and invert m with n, you are not looking at the same pair anymore; you have instead to also invert the sign of R.


Giovanni Pizzi
Post-doctoral Research Scientist
MXC 340 (Bâtiment MXC)
Station 12
CH-1015 Lausanne (Switzerland)
Phone: +41 21 69 31124

On 27 Dec 2013, at 07:05, satrio wrote:

Dear All

I have generated hr_plot for single layer MoS2. I found something that i cannot understand. It seems the hamiltonian in real space is not hermitian. For the same distance, the Hij is not conjugate of Hji. Im not sure what cause this as i know the Hamiltonian should be hermitian. Is there anyone know about this issue?

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