Basically we know that optical property of nanomaterials may also arise from another quantum size effect. When the size of a nanocrystal is smaller than the de Broglie wavelength, electrons and holes are spatially confined and electric dipoles are formed, and discrete electronic energy level would be formed in all materials. The energy separation between adjacent levels increases with decreasing dimensions. Similar to the above arguments is it possible to establish the size dependence of coherent states of a QD system?
Under the assumption that the excitations don't interact with each other (which is highly questionable in this case, since we're really talking about excitons), you could establish for example in the conduction band what the ground state and first few excited states are by using the effective mass and the particle shape/size. And of course their energies will scale with the particle size according to the usual models which you're already aware of. Then you could construct a conduction-band "coherent state" using the usual exponential-of-a-linear-combination-of-creation-operators formalism (I'm assuming you're familiar with that, since you're asking about coherent states).
However, I seriously doubt that such a state, while in principle constructible, would have any physical significance. It wouldn't be an energy eigenstate, to be sure, and constructing it this way from non-interacting single-particle states surely doesn't do justice to the physics. At the very least you'd want to include the coupling between electrons and holes (i.e. excitonic binding energy).
i realize this answer doesn't amount to much more than, "I don't know, but I do expect that the obvious, simple thing to do won't be very useful," but this question has been sitting for a while with no answer, and hopefully this will prompt someone more knowledgeable to correct me! :)
It was shown by L. Jacak and P.Machnikowski that an action performed on the carrier systems [e.g. excitons] confined in a quantum dot must be accompanied by an appropriate reconstruction of the lattice state [phonons]. Such a dressing process takes place spontaneously if the charge distribution is changed on time scale short compared to timescale of the lattice Dynamics [phonon oscillation periods]. This Spontaneous process destroys the quantum coherence [decoherency] of the system and may preclude coherent nanotechnology applications [QDs information processing].
in the real case, it's not possible: one have to solve the Schrödinger equation with appropriate coordinate system
In principle, the answer is yes. However, to establish such relations one has to use many-body quantum theoretical methods, rather than semi-empirical approaches. My book with Elsevier coming shortly is devoted to answering this question and demonstrates such answers in numerous cases of small quantum dots composed of semiconductor compound elements.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Materials Science
- Materials
- Semiconductor