Query about longitudinal and hall conductance in 4 terminal
Dear Sir, I am using Kwant for 2 months. I've studied the conductance behaviour in a square lattice for two terminal case. But for the 4 terminal case I've some confusion about the hall conductance. I've read your post about the hall resistance. You wrote there, nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1] Why did you put the currents I_0=1, I_1=0 and I_2=-1? Also can you please tell me how do I calculate the longitudinal conductance for the 4 terminal case. With regards, Sudin Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India-781039
Sudin Ganguly wrote:
nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1]
Why did you put the currents I_0=1, I_1=0 and I_2=-1?
The code line you cite is taken from the valve.py example script From the Kwant paper. Did you have a look at the full example that can be downloaded at http://downloads.kwant-project.org/examples/kwant-examples-njp.zip? Non-local conductance measurements in the Landauer-Büttiker formalism are explained in Sec. 2.4 of the book by S. Datta “Electronic transport in mesoscopic systems”. In short it works like this: In the cross geometry, we want to measure the Hall resistance, that is the transverse voltage divided by the longitudinal current when there is no transverse current. Thus, we set the longitudinal current to 1 and the transverse current to 0. The Hall resistance is then given by V[1] - V[3] = V[1]. Christoph
Dear Sudin, Just to add to Christoph's reply, there's an example of Hall and longitudinal conductance calculated over here: http://nbviewer.ipython.org/github/topocm/topocm_content/blob/master/w3_pump... (to see the code, click the button at the top of the notebook). You may find this useful. Best, Anton On Wed, Mar 18, 2015 at 10:36 AM, Christoph Groth <christoph.groth@cea.fr> wrote:
Sudin Ganguly wrote:
nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1]
Why did you put the currents I_0=1, I_1=0 and I_2=-1?
The code line you cite is taken from the valve.py example script From the Kwant paper. Did you have a look at the full example that can be downloaded at http://downloads.kwant-project.org/examples/kwant-examples-njp.zip?
Non-local conductance measurements in the Landauer-Büttiker formalism are explained in Sec. 2.4 of the book by S. Datta “Electronic transport in mesoscopic systems”.
In short it works like this: In the cross geometry, we want to measure the Hall resistance, that is the transverse voltage divided by the longitudinal current when there is no transverse current. Thus, we set the longitudinal current to 1 and the transverse current to 0. The Hall resistance is then given by V[1] - V[3] = V[1].
Christoph
Dear Sir, Thanks to all of you for showing me the right path. With regards, sudin
Dear Sudin,
Just to add to Christoph's reply, there's an example of Hall and longitudinal conductance calculated over here: http://nbviewer.ipython.org/github/topocm/topocm_content/blob/master/w3_pump... (to see the code, click the button at the top of the notebook). You may find this useful.
Best, Anton
On Wed, Mar 18, 2015 at 10:36 AM, Christoph Groth <christoph.groth@cea.fr> wrote:
Sudin Ganguly wrote:
nonlocal_resistance = np.linalg.solve(cm, [1, 0, -1])[1]
Why did you put the currents I_0=1, I_1=0 and I_2=-1?
The code line you cite is taken from the valve.py example script From the Kwant paper. Did you have a look at the full example that can be downloaded at http://downloads.kwant-project.org/examples/kwant-examples-njp.zip?
Non-local conductance measurements in the Landauer-Büttiker formalism are explained in Sec. 2.4 of the book by S. Datta âElectronic transport in mesoscopic systemsâ.
In short it works like this: In the cross geometry, we want to measure the Hall resistance, that is the transverse voltage divided by the longitudinal current when there is no transverse current. Thus, we set the longitudinal current to 1 and the transverse current to 0. The Hall resistance is then given by V[1] - V[3] = V[1].
Christoph
-- ==================== Sudin Ganguly Research Scholar Dept. of Physics IIT Guwahati Assam,India-781039 ===================
participants (3)
-
Anton Akhmerov -
Christoph Groth -
Sudin Ganguly