---------- Forwarded message --------- De : Adel Belayadi <adelphys@gmail.com> Date: mer. 27 nov. 2019 à 20:27 Subject: Re: [Kwant] Tags and sites To: EUDES THOMAS GOMES DA SILVA <eudes.gomes@ufrpe.br> Dear EUDES, why can tags assume only integers values? In fact, the tight binding approach works like the discretized Schrodinger equation see Ref [1]. In this context each site is defined by an integer lattice coordinates (𝑖, 𝑗) which provide the real-space coordinates (𝑥, 𝑦) as (a1*n, a2*m ). Once you define the primitive vector of the system let’s say *𝑎*1 and *𝑎*2, so the translation to get the whole lattice leads to write *𝑅* = 𝑛*𝑎*1 + m*𝑎*2. Here n and m are integer which refer to the tag in kwant. So building the whole lattice has nothing to with real space position( since we use *translation as 𝑅* = 𝑛*𝑎*1 + m*𝑎*2 ). Now the most important task is to define the hopping between neighboring atoms. A hopping is created between the main cell (for instance (0, 0) ) and a neighboring cell specified by relative index such as (0, 1) and (1, 0). For more explanation, see the enclosed figure ( in case of square lattice ) Additionally, remember that when we use the Bloch theorem. The wave function for a periodic lattice is defined by a phase factor: For instance let as say φ (n∓q, m∓q ). =exp(±iqakx)*exp(±iqaky) φ (n, m). Where q in an integer that way we deal with integer not with space positions. Ps: Ref[1]: Timothy B. Boykin. The discretized Schrodinger equation and simplemodels for semiconductor quantum wells best, Adel Le mar. 26 nov. 2019 à 20:29, EUDES THOMAS GOMES DA SILVA < eudes.gomes@ufrpe.br> a écrit :

Hi Dears,

why can tags assume only integers values?

For example:

lat = kwant.lattice.Polyatomic([(1, 0, 0), (0, 1, 0),(0, 0, 1)], [(1, 0, 0), (0.0, 1, 0.0),(0.0, 0.0, 1)],norbs=1) syst = kwant.Builder()

# it is possible: syst[a(1,0,0)]=4

and syst[a(1.5,0,0)]=4

gives me the same result as before?

Both of them says:

...

...

...

a(1,0,0)

Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0]))

...

...

...

a(1.5,0,0)

Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1, 0, 0]))

The later should be:

Site(kwant.lattice.Monatomic([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [0.0, 0.0, 0.0], '0', 1), array([1.5, 0, 0]))

best regards.

Eudes.