Re: [Kwant] Question about lead_info[].wave_functions[]
Hi Joe, Thank you. This might be a silly question, but what is the meaning of orbitals here? Is it not only 1? The orbital elements seem to be conjugate of each other. Best, Camilla
Hi,
Thank you. This might be a silly question, but what is the meaning of orbitals here? Is it not only 1?
When I say "orbitals" it's really a shorthand for "degrees of freedom". If you have a lead with 2 sites in the unit cell, and each one has a single degree of freedom associated with it (i.e. the onsites are just numbers) then the wavefunction would be a vector with 2 entries. If you have, say, spin 1/2 particles, then each site would have 2 degrees of freedom associated with it (spin up & spin down). In the same way, if a site really represents an atom, then your "internal degrees of freedom" could be the different atomic orbitals (s, p, d etc.). Of course, Kwant makes no assumptions about what these degrees of freedom actually mean -- it is up to the user to define what they mean by describing the appropriate Hamiltonian.
The orbital elements seem to be conjugate of each other.
I think you are looking at the wrong axis of the `wave_functions` array. The *first* axis runs over the orbitals, and the *second* axis runs over the modes. For a given band, I would expect the left- and right-propagating modes to be conjugates of each other, as they are related by time-reversal symmetry (unless you have some terms in your Hamiltonian that break this, but I think not). Does that clarify? Joe
Hi again, and thanks. I think I am getting there, so for a system with two bands each row has 4 elements which corresponds to 2 left-going and 2 right-going modes. Is that correct? And the orbitals in this case, corresponds to spin? I haven't implemented spin or anything manually to the model, is this done by Kwant by default? The output I get is a 2x4-matrix. Is the output wavefunction a spinor? Best, Camilla -----Original Message----- From: Joseph Weston [mailto:joseph.weston08@gmail.com] Sent: 16. november 2016 15:13 To: Camilla Espedal <camilla.espedal@ntnu.no> Cc: kwant-discuss@kwant-project.org Subject: Re: [Kwant] Question about lead_info[].wave_functions[] Hi,
Thank you. This might be a silly question, but what is the meaning of orbitals here? Is it not only 1?
When I say "orbitals" it's really a shorthand for "degrees of freedom". If you have a lead with 2 sites in the unit cell, and each one has a single degree of freedom associated with it (i.e. the onsites are just numbers) then the wavefunction would be a vector with 2 entries. If you have, say, spin 1/2 particles, then each site would have 2 degrees of freedom associated with it (spin up & spin down). In the same way, if a site really represents an atom, then your "internal degrees of freedom" could be the different atomic orbitals (s, p, d etc.). Of course, Kwant makes no assumptions about what these degrees of freedom actually mean -- it is up to the user to define what they mean by describing the appropriate Hamiltonian.
The orbital elements seem to be conjugate of each other.
I think you are looking at the wrong axis of the `wave_functions` array. The *first* axis runs over the orbitals, and the *second* axis runs over the modes. For a given band, I would expect the left- and right-propagating modes to be conjugates of each other, as they are related by time-reversal symmetry (unless you have some terms in your Hamiltonian that break this, but I think not). Does that clarify? Joe
Hi,
I think I am getting there, so for a system with two bands each row has 4 elements which corresponds to 2 left-going and 2 right-going modes. Is that correct?
If you evaluate the modes at an energy at which both bands are open, then yes. You will need to refer to the documentation to find out what order the modes are stored in.
And the orbitals in this case, corresponds to spin? I haven't implemented spin or anything manually to the model, is this done by Kwant by default? The output I get is a 2x4-matrix. Is the output wavefunction a spinor?
If you haven't implemented spin or anything then there will not be any spin. I would expect the `wave_functions` array to have shape (2, 4) in the case you described above, i.e. there are 4 (2 left-going, 2 right-going) modes and the wavefunctions have 2 elements, corresponding to the 2 sites in your unit cell. Joe
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Camilla Espedal -
Joseph Weston