Thank you Joesph. That clarifies my understanding of band structure and
translational symmetry.
My end goal is to see changes in the band structure as the electric field
is varied. For an external magnetic field (wherein I modify the hopping
parameter only) the band structure changes as the field is changed. I want
to be able to see changes with an electric field as well. What should be my
approach for this.
Thank you for the help!
Shivang
On Tue, Jun 26, 2018 at 3:32 AM Joseph Weston
wrote:
> Hi,
>
>
> > I want to plot the band structure for my system, i.e. a quantum dot. I
> > am still confused as to what code I need to write to plot that, or
> > whether sys.leads[0] is actually correct for what I need.
>
> Calculating a band structure for a quantum dot is not mathematically
> well-defined.
> A quantum dot does not have translational symmetry, so momentum is not a
> good quantum number. You cannot label the eigenstates of your
> Hamiltonian with a unique momentum 'k', so plotting the associated
> eigenvalues as a function of 'k' (i.e. the band structure) is not possible.
>
> Even if you attach leads to your quantum dot you'll still have the same
> problem. While the leads *individually* have translational symmetry, the
> combination of leads and quantum dot does not, because the quantum dot
> breaks the translational symmetry.
>
>
> Given this, it is difficult for us to interpret what you mean when you
> say you want to plot "the band structure for your system". If you
> provide more context for what your end goal is, we may be able to help
> more.
>
> Happy Kwanting,
>
> Joe
>
>
>
--
*Shivang Agarwal*
Junior Undergraduate
Discipline of Electrical Engineering
IIT Gandhinagar
Contact: +91-9869321451
