Kwant.greens_function
Dear all, Since I used NEGF in my previous study, I want to use Green's function in Kwant. I have tried a simple Kwant program to check my understanding of "kwant.greens_function" and "lead.selfenergy(energy)", but it gives wrong results. I used Fisher-Lee relation to calculate the conductance: G = kwant.greens_function(sys, energy) Gr=G.submatrix(1,0) # r indicates retarded Ga=conj((Gr).T) # a indicates advanced Sigma_Lr =flead0.selfenergy(energy) #r indicates retarded Sigma_La =conj((Sigma_Lr).T) #a indicates advanced Sigma_Rr =flead1.selfenergy(energy) Sigma_Ra =conj((Sigma_Rr).T) Gamma_in =1j*(Sigma_Lr-Sigma_La) Gamma_out=1j*(Sigma_Rr-Sigma_Ra) #TM=Gamma_out*Gr*Gamma_in*Ga TM=Np.dot(Np.dot(Np.dot(Gamma_out,Gr),Gamma_in),Ga) #Fisher-Lee relation data.append(real(Np.trace(TM))) #Fisher-Lee relation Do I do I misunderstand anything? Can you please find my mistakes? My Kwant program code is attached at the end of this email. Thanks in advance! Best wishes, Weiyuan Tong
Hi,
Dear all, Since I used NEGF in my previous study, I want to use Green's function in Kwant. I have tried a simple Kwant program to check my understanding of "kwant.greens_function" and "lead.selfenergy(energy)", but it gives wrong results. I used Fisher-Lee relation to calculate the conductance:
G = kwant.greens_function(sys, energy) Gr=G.submatrix(1,0) # r indicates retarded Ga=conj((Gr).T) # a indicates advanced
Sigma_Lr =flead0.selfenergy(energy) #r indicates retarded Sigma_La =conj((Sigma_Lr).T) #a indicates advanced
Sigma_Rr =flead1.selfenergy(energy) Sigma_Ra =conj((Sigma_Rr).T)
Gamma_in =1j*(Sigma_Lr-Sigma_La) Gamma_out=1j*(Sigma_Rr-Sigma_Ra) #TM=Gamma_out*Gr*Gamma_in*Ga TM=Np.dot(Np.dot(Np.dot(Gamma_out,Gr),Gamma_in),Ga) #Fisher-Lee relation data.append(real(Np.trace(TM))) #Fisher-Lee relation
Do I do I misunderstand anything? Can you please find my mistakes? My Kwant program code is attached at the end of this email. Thanks in advance! Best wishes, Weiyuan Tong
You are doing everything correctly, and this *should* give the correct result. The reason it does not is because you have finalized the leads separately from the system to which they are attached, and then used these. If you use the finalized leads which are present as part of your finalized system then you obtain the correct results, i.e instead of: sys = sys.finalized() flead0 = lead0.finalized() flead1 = lead1.finalized() use: sys = sys.finalized() flead0 = sys.leads[0] flead1 = sys.leads[1] The reason for this is due to the arbitrary ordering of sites in finalized systems. The Greens function calculated is defined on the interface sites of the central region, and the self energy is defined on interface sites in the lead. Clearly in order to multiply the two matrices (and for the result to be meaningful) the ordering of the sites needs to be the same in the two cases. If you finalize the leads separately then the lead has no way of knowing which way its sites should be ordered. When you finalize the full system (central region + leads) kwant takes care to ensure the ordering of the sites is compatible. You could also calculate the transmission directly using the `transmission` method of the `GreensFunction` object ("G" in your code"). This clearly isn't very intuitive; a significant percentage of issues that people have posted on this mailing list stem from misunderstanding / lack of documentation for the ordering of sites. Any suggestions as to how this could be made more intuitive are welcome! Hope that clarifies, Joe
Dear Joe, Thank you. Your reply is very clear and my problem is solved. Best, Weiyuan Tong On Mon, May 18, 2015 at 3:41 PM, Joseph Weston <joseph.weston@cea.fr> wrote:
Hi,
Dear all, Since I used NEGF in my previous study, I want to use Green's function in Kwant. I have tried a simple Kwant program to check my understanding of "kwant.greens_function" and "lead.selfenergy(energy)", but it gives wrong results. I used Fisher-Lee relation to calculate the conductance:
G = kwant.greens_function(sys, energy) Gr=G.submatrix(1,0) # r indicates retarded Ga=conj((Gr).T) # a indicates advanced
Sigma_Lr =flead0.selfenergy(energy) #r indicates retarded Sigma_La =conj((Sigma_Lr).T) #a indicates advanced
Sigma_Rr =flead1.selfenergy(energy) Sigma_Ra =conj((Sigma_Rr).T)
Gamma_in =1j*(Sigma_Lr-Sigma_La) Gamma_out=1j*(Sigma_Rr-Sigma_Ra) #TM=Gamma_out*Gr*Gamma_in*Ga TM=Np.dot(Np.dot(Np.dot(Gamma_out,Gr),Gamma_in),Ga) #Fisher-Lee relation data.append(real(Np.trace(TM))) #Fisher-Lee relation
Do I do I misunderstand anything? Can you please find my mistakes? My Kwant program code is attached at the end of this email. Thanks in advance! Best wishes, Weiyuan Tong
You are doing everything correctly, and this *should* give the correct result. The reason it does not is because you have finalized the leads separately from the system to which they are attached, and then used these. If you use the finalized leads which are present as part of your finalized system then you obtain the correct results, i.e instead of:
sys = sys.finalized() flead0 = lead0.finalized() flead1 = lead1.finalized()
use:
sys = sys.finalized() flead0 = sys.leads[0] flead1 = sys.leads[1]
The reason for this is due to the arbitrary ordering of sites in finalized systems. The Greens function calculated is defined on the interface sites of the central region, and the self energy is defined on interface sites in the lead. Clearly in order to multiply the two matrices (and for the result to be meaningful) the ordering of the sites needs to be the same in the two cases. If you finalize the leads separately then the lead has no way of knowing which way its sites should be ordered. When you finalize the full system (central region + leads) kwant takes care to ensure the ordering of the sites is compatible.
You could also calculate the transmission directly using the `transmission` method of the `GreensFunction` object ("G" in your code").
This clearly isn't very intuitive; a significant percentage of issues that people have posted on this mailing list stem from misunderstanding / lack of documentation for the ordering of sites. Any suggestions as to how this could be made more intuitive are welcome!
Hope that clarifies,
Joe
Dear Weiyuan, Just a small remark. If all you need is a basic transport property like transmission, I strongly advice to use the scattering matrix (smatrix.transmission) due to its higher stability and higher numerical efficiency. Best, Anton On Mon, May 18, 2015 at 10:57 AM, Weiyuan Tong <weiyuantongtrans@gmail.com> wrote:
Dear Joe, Thank you. Your reply is very clear and my problem is solved. Best, Weiyuan Tong
On Mon, May 18, 2015 at 3:41 PM, Joseph Weston <joseph.weston@cea.fr> wrote:
Hi,
Dear all, Since I used NEGF in my previous study, I want to use Green's function in Kwant. I have tried a simple Kwant program to check my understanding of "kwant.greens_function" and "lead.selfenergy(energy)", but it gives wrong results. I used Fisher-Lee relation to calculate the conductance:
G = kwant.greens_function(sys, energy) Gr=G.submatrix(1,0) # r indicates retarded Ga=conj((Gr).T) # a indicates advanced
Sigma_Lr =flead0.selfenergy(energy) #r indicates retarded Sigma_La =conj((Sigma_Lr).T) #a indicates advanced
Sigma_Rr =flead1.selfenergy(energy) Sigma_Ra =conj((Sigma_Rr).T)
Gamma_in =1j*(Sigma_Lr-Sigma_La) Gamma_out=1j*(Sigma_Rr-Sigma_Ra) #TM=Gamma_out*Gr*Gamma_in*Ga TM=Np.dot(Np.dot(Np.dot(Gamma_out,Gr),Gamma_in),Ga) #Fisher-Lee relation data.append(real(Np.trace(TM))) #Fisher-Lee relation
Do I do I misunderstand anything? Can you please find my mistakes? My Kwant program code is attached at the end of this email. Thanks in advance! Best wishes, Weiyuan Tong
You are doing everything correctly, and this *should* give the correct result. The reason it does not is because you have finalized the leads separately from the system to which they are attached, and then used these. If you use the finalized leads which are present as part of your finalized system then you obtain the correct results, i.e instead of:
sys = sys.finalized() flead0 = lead0.finalized() flead1 = lead1.finalized()
use:
sys = sys.finalized() flead0 = sys.leads[0] flead1 = sys.leads[1]
The reason for this is due to the arbitrary ordering of sites in finalized systems. The Greens function calculated is defined on the interface sites of the central region, and the self energy is defined on interface sites in the lead. Clearly in order to multiply the two matrices (and for the result to be meaningful) the ordering of the sites needs to be the same in the two cases. If you finalize the leads separately then the lead has no way of knowing which way its sites should be ordered. When you finalize the full system (central region + leads) kwant takes care to ensure the ordering of the sites is compatible.
You could also calculate the transmission directly using the `transmission` method of the `GreensFunction` object ("G" in your code").
This clearly isn't very intuitive; a significant percentage of issues that people have posted on this mailing list stem from misunderstanding / lack of documentation for the ordering of sites. Any suggestions as to how this could be made more intuitive are welcome!
Hope that clarifies,
Joe
participants (3)
-
Anton Akhmerov -
Joseph Weston -
Weiyuan Tong