Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang
Dear Qingtian,
kwant.lattice.honeycomb() creates a honeycomb lattice that as you noted lets you also access easily next-nearest neighbors via neighbors(2).
There are two things to note here:
1. kwant.lattice.honeycomb() just creates a lattice - this is not a Hamiltonian yet. For this you need to specify values that you do with kwant.Builder() - this always the same in kwant. (Please check the tutorial examples). That said, you can implement any Hamiltonian that lives on the honeycomb lattice using kwant.lattice.honeycomb().
2. Note that if all next-nearest-neighbor hoppings have the same value, things are easy and you can just write for example
sys[lat.neighbors(2)] = 0.1
However, you can also specify each type of hopping (i.e. all hoppings that go in a certain direction) separately, using kwant.HoppingKind. Note that in fact lat.neighbors() returns a *list* of kwant.HoppingKinds. How to set individual hoppings in kwant is demonstrated on the simpler example of a square lattice and spin-orbit in tutorial 2.3.1.
Pleae note that we cannot give specific advice on how to implement a particular physical model, although you are welcome to ask questions if you have specific problems with code in kwant.
Best,
Michael
Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang
Dear Michael, Thanks a lot. i think i know more about the features of Kwant. i will try some specific cases. Best, Qingtian
2014-02-23 22:31 GMT+08:00 wimmer@lorentz.leidenuniv.nl:
Dear Qingtian,
kwant.lattice.honeycomb() creates a honeycomb lattice that as you noted lets you also access easily next-nearest neighbors via neighbors(2).
There are two things to note here:
- kwant.lattice.honeycomb() just creates a lattice - this is not a
Hamiltonian yet. For this you need to specify values that you do with kwant.Builder() - this always the same in kwant. (Please check the tutorial examples). That said, you can implement any Hamiltonian that lives on the honeycomb lattice using kwant.lattice.honeycomb().
- Note that if all next-nearest-neighbor hoppings have the same value,
things are easy and you can just write for example
sys[lat.neighbors(2)] = 0.1
However, you can also specify each type of hopping (i.e. all hoppings that go in a certain direction) separately, using kwant.HoppingKind. Note that in fact lat.neighbors() returns a *list* of kwant.HoppingKinds. How to set individual hoppings in kwant is demonstrated on the simpler example of a square lattice and spin-orbit in tutorial 2.3.1.
Pleae note that we cannot give specific advice on how to implement a particular physical model, although you are welcome to ask questions if you have specific problems with code in kwant.
Best,
Michael
Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang
Dear Qingtian,
First, I would like to precise that I am not a specialist of Graphene or spin hall effect (neither Kwant) so you need to take the
solution I give you with precaution and you need to do tests knowing the expected results.
The amazing thing with Kwant is that the process of defining the Hamiltonan becomes simpler once you precise the Tight
binding model.
So, when you have the lattice expression of the Hamiltonian forget the x and y directions and work as in a graph (sites
neighbors and links).
The starting point to your problem is may be the simpler case of electrons with spin in honeycomb lattice (without SO interaction).
You should understand that the state | n,m, sigma> =|n,m> [image: \otimes]|sigma> ,where [image: \otimes] is the the tensorial product. Your
hamiltonian becomes H=h [image: \otimes] 1 . h is the spinless hamiltonian in graphene and 1 is the 2x2 identity matrix. So now, with the
definition of the tensorial product (matricial version) you can understand why we need to change in the spinless hamiltonian all
the elements (sites and hopping) by hij*1 (hij---->identity *hij) to obtain the whole Hamiltonian with spins.
With the interaction presented in the model of Kane & Mele, you need to do the same and understand how is the Hamiltonian is
written as a Tensorial product.
you will understand that in the Hamiltonian with the second nearest neighbors you need to change the elements hij by matrices
as follows:
hij ------> 1j*t2*Vij*Sigma_z
you need just to be careful with the hopping Vij which are site-dependent .
For this you need to just define the Vij in the clockwise: Vij=+1 by choosing the directions for the next nearest neighbors as
follows: (1,0) (-1,-1) (0,-1)
we do this for the two sublattices a, b.
The other anticlockwise hoppings Vij are directly insured by hermeticity.
The same procedure is done for the leads.
The results at the end seems to me at least "not bizarre" but you need to check this with specialists.
The program following these remarks is included with this mail.
Regards
Adel Abbout www.abboutadelhomepage.weebly.com
On Sun, Feb 23, 2014 at 1:03 AM, Qingtian Zhang qtzhang@mail.ustc.edu.cnwrote:
Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang
Dear Adel, It is very useful for me to learn Kwant programming, thank you vey much. Qingtian
2014-02-24 9:41 GMT+08:00 Abbout Adel abbout.adel@gmail.com:
Dear Qingtian,
First, I would like to precise that I am not a specialist of Graphene or spin hall effect (neither Kwant) so you need to take the
solution I give you with precaution and you need to do tests knowing the expected results.
The amazing thing with Kwant is that the process of defining the Hamiltonan becomes simpler once you precise the Tight
binding model.
So, when you have the lattice expression of the Hamiltonian forget the x and y directions and work as in a graph (sites
neighbors and links).
The starting point to your problem is may be the simpler case of electrons with spin in honeycomb lattice (without SO interaction).
You should understand that the state | n,m, sigma> =|n,m> [image: \otimes]|sigma> ,where [image: \otimes] is the the tensorial product. Your
hamiltonian becomes H=h [image: \otimes] 1 . h is the spinless hamiltonian in graphene and 1 is the 2x2 identity matrix. So now, with the
definition of the tensorial product (matricial version) you can understand why we need to change in the spinless hamiltonian all
the elements (sites and hopping) by hij*1 (hij---->identity *hij) to obtain the whole Hamiltonian with spins.
With the interaction presented in the model of Kane & Mele, you need to do the same and understand how is the Hamiltonian is
written as a Tensorial product.
you will understand that in the Hamiltonian with the second nearest neighbors you need to change the elements hij by matrices
as follows:
hij ------> 1j*t2*Vij*Sigma_z
you need just to be careful with the hopping Vij which are site-dependent .
For this you need to just define the Vij in the clockwise: Vij=+1 by choosing the directions for the next nearest neighbors as
follows: (1,0) (-1,-1) (0,-1)
we do this for the two sublattices a, b.
The other anticlockwise hoppings Vij are directly insured by hermeticity.
The same procedure is done for the leads.
The results at the end seems to me at least "not bizarre" but you need to check this with specialists.
The program following these remarks is included with this mail.
Regards
Adel Abbout www.abboutadelhomepage.weebly.com
On Sun, Feb 23, 2014 at 1:03 AM, Qingtian Zhang qtzhang@mail.ustc.edu.cnwrote:
Dear all, I note that we can easily consider the next-nearest-neighbor hopping in honeycomb, however, what is the model (Hamiltonian) for this code? In graphene, the intrinsic SOI is included in the reference:PRL 95, 226801 (2005) and we also have that in silicene: PRL 110, 026603 (2013). Is the model for Kwant the same as the two reference papers? Moreover,can we consider the Rashba SOI using the Tinyarray package in honeycomb? the hoppings along x and y direction are more complicated in honeycomb. Regards, Qingtian Zhang
-- Abbout Adel