Correlation and the density-matrix approach to inelastic electron holography in solid state plasmas

Collective excitations in solid state plasmas are a good candidate to measure correlation lengths of conduction electrons. The method of choice seems to be energy filtered electron holography in the transmission electron microscope (TEM) since the interference fringes contain information on the partial coherence of those electrons. Previous experiments showed surprisingly high coherence. We calculate the density-density correlation function in the Al plasma excitation from the dynamic form factor and compare it to results based on similar arguments. For the Al plasma excitation, we find a small extension of 0.1−0.3 nm over which the movement of charges is correlated. Using the density-matrix formalism, the coherence length of plasmon scattered fast electrons in the TEM is calculated and found to agree with experiment. We show that the small correlation length of conduction electrons does not contradict the coherence length of $>10\mathrm{nm}$ found for fast probe electrons having excited a plasmon in Al. The difference of nearly two orders of magnitude can be traced back to the long-range Coulomb interaction between probe and target electrons. Two unexpected predictions ensue from the present approach: Inelastic holography experiments should show strongly increased contrast of interference fringes in vacuo, i.e., outside the specimen, and contrast inversion of fringes in inelastic holograms of very small particles.