Hi Gosh, Em sáb, 22 de jun de 2019 às 09:09, kamal ghosh <kk_ghosh@rediffmail.com> escreveu:

.Dear all, Right now I am working with spin transport. Kwant documentations 2.3 of docu1.0.5 and 2.7 of docu1.3.2 are very much helpful and informative to my study. I have a few questions/ doubts to understand the Hamiltonians meaningfully.

Hamiltonian for spin (docu2.7) :- H= -Σ‹ij›Σα│iα›‹jα│+ JΣiΣαβ mi. σαβ│iα›‹iβ│ (1)

Hamiltonian for spin (docu2.3) :- H= (-ħ2/2m)(∂x2+∂y2) – iα(∂xσy - ∂yσx ) + Ezσz + V(y) (2)

(i) Is there a missing of hopping energy tα (t alpha) in eqn.(1) because the first term takes care of the hopping ? Further, are the kinetic and potential parts for charge transport not considered. I mean, term like the first term in eqn.(2) ? As both the charge and spin transport are there so should we not consider them simultaneously ? Also, does the J in eqn.(1) signify the magnetic field arising out of Rashba interaction which is clearly expressed in eqn,(2)?

The hopping term is the first term in eq. 1. As you can see, that term is responsible for processes in which a particle with spin [image: \alpha] goes from position [image: j] to position [image: i]. Since the equation treats an homogeneous and isotropic material, [image: t] is the same all over the crystal, and generally, it's not spin dependent, so you can drop the index in [image: t_{\alpha}]. Finally, such energy is used as the energy scale, so one can set [image: t_{\alpha} \equiv t =1]. The energy $J$ is actually the Heisenberg coupling. Note that the problem is treated from a mean-field approach, so the goundstate magnetization is included, instead of spin-spin interaction. This is not directly related with Zeeman or SOC, although those effects can influence the mean-field magnetization.

(ii) Am I right to understand that the second and third terms in eqn.(2) signify the Zeeman splitting and Rashba interaction? Please bear with me that I cannot derive these two terms from Zeeman splitting term and Rashba interaction term as found in text books on quantum mechanics. I would be thankful if the origin of these terms be made understood! or else, atleast the reference from where i may get idea.

Yes, those two terms are Zeeman and Rashba. Please be more specific about you starting point to derive those terms (i.e. what are the equations from QM textbooks you are using).

I am earnestly requesting the learned developers of Kwant and / my co-members in the family of Kwant to help solving my problems. All the best and Happy Kwanting. K.K.Ghosh

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-- Antonio Lucas Rigotti Manesco PhD fellow - University of São Paulo, Brazil