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.
As previously stated, a system without translational symmetry *does not have a band structure*, so asking to calculate it is a task that is doomed to fail. It is analogous to someone asking what the color of an electron is: the question is predicated on a false assumption, so there is no correct answer! I would recommend reading a book on quantum transport to get a good grasp of the fundamentals. The book by S. Datta [1] is quite reasonable. Happy Kwanting, Joe [1]: https://doi.org/10.1017/CBO9781139164313