PRB147 said:When the electric field is strong, the Wannier state is localized, see the article
by M Dignam in Phys. Rev. B in 1994.
They are quasi-stable, they are resonant state.
See also the Dignam's article
wdlang said:Thanks a lot!
Why are they quasi-stable?
I take a tight-binding model, and numerically diagonalize the hamiltonian, and find out the eigenstates, i find that the eigenstates are all well-localized and of the same shape. Of course, except for those near the boundary.
PRB147 said:For one dimensional tight binding lattice, without interband tunneling, the Wannier-Stark state
is rigorous localized state. and the eigenenergy is equidistant.
If there exists interband tunneling, the WS state is a resonant state and quasi-stable.
A Wannier-Stark state calculation is a theoretical calculation used in solid state physics to describe the behavior of electrons in a crystal lattice under the influence of a strong electric field. It calculates the energy levels and wave functions of electrons in a crystal subjected to a constant electric field.
A Wannier-Stark state calculation is typically performed using numerical methods, such as density functional theory or tight-binding models. These methods involve solving the Schrödinger equation for the crystal lattice with the addition of a constant electric field. The resulting energy levels and wave functions can then be used to analyze the behavior of the electrons in the crystal under the applied field.
Wannier-Stark states are important because they provide a theoretical framework for understanding the behavior of electrons in a crystal under the influence of a strong electric field. They can help explain phenomena such as electrical conductivity, bandgap engineering, and the formation of charge carriers in semiconductors.
Wannier-Stark states have many applications in materials science and nanotechnology. They are used to study the properties of semiconductors, insulators, and other materials under the influence of an electric field. They are also used in the design and development of electronic devices, such as transistors and solar cells.
Like any theoretical model, Wannier-Stark state calculations have some limitations. They assume a perfect crystal lattice and do not account for defects or impurities in the material. Additionally, the calculations can become computationally intensive for large systems, making them difficult to apply to complex materials. However, these limitations can be addressed by using more advanced theoretical methods and computational techniques.