Hall effect (4contacts measurement)
Dear all, I read some advices about the Hall effect (4leads measurement) in previous posts referring to the code on the website: http://nbviewer.ipython.org/github/topocm/topocm_content/blob /master/w3_pump_QHE/Laughlinargument.ipynb However, I'm wondering if the following code is well correct in order to get the potential of each lead when a current I=1 is "imposed" between the contacts 4 and 5. r = np.linalg.inv(G) V = r.dot(np.array([0, 0, 0, 1, 1])) where G is the conductance matrix ( G[i,j] gives the conductance between lead i and j) and hence, r is the resistance matrix. V[0] is the potential of the lead 0 V[1] is the potential of the lead 1 V[2] is the potential of the lead 3 This would mean that, for example, V[0] = r[3,0]  r[4,0] However, is it more correct to write V[0] = r[3,0]  r[0,4] ? Indeed, r[0,4] is not equal to r[4,0] when we apply a magnetic field (the time reversal symmetry is broken). I think it is better to use r[0,4] in order to set a current flowing from lead 4 to lead 5. Am I right? Thank you in advance for your help. Best regards, D. Cabosart
Dear Damien, The conductance and resistance matrices are indeed not symmetric when magnetic field is present. However everything we do can be derived fromt the definition I = G V, where I is the vector of currents and V the vector of voltages. This is why I'm not sure what you mean when you say that using some matrix elements is better. Can you please elaborate? Best, Anton On Mon, Dec 28, 2015 at 3:39 PM, Cabosart Damien <damien.cabosart@uclouvain.be> wrote:
Dear all,
I read some advices about the Hall effect (4leads measurement) in previous posts referring to the code on the website:
http://nbviewer.ipython.org/github/topocm/topocm_content/blob /master/w3_pump_QHE/Laughlinargument.ipynb
However, I'm wondering if the following code is well correct in order to get the potential of each lead when a current I=1 is "imposed" between the contacts 4 and 5.
r = np.linalg.inv(G)
V = r.dot(np.array([0, 0, 0, 1, 1]))
where G is the conductance matrix ( G[i,j] gives the conductance between lead i and j) and hence, r is the resistance matrix.
V[0] is the potential of the lead 0 V[1] is the potential of the lead 1 V[2] is the potential of the lead 3
This would mean that, for example, V[0] = r[3,0]  r[4,0] However, is it more correct to write V[0] = r[3,0]  r[0,4] ?
Indeed, r[0,4] is not equal to r[4,0] when we apply a magnetic field (the time reversal symmetry is broken). I think it is better to use r[0,4] in order to set a current flowing from lead 4 to lead 5. Am I right?
Thank you in advance for your help.
Best regards,
D. Cabosart
participants (2)

Anton Akhmerov

Cabosart Damien